Introduction
This report will summarize major findings of the University of Illinois at Chicago (UIC) during six years of operating a high school/university collaboration called the College Preparatory Mathematics Program (CPMP). Its success has been demonstrated in three major components.

• Student achievement: CPMP students, under-represented minorities in particular, have performed significantly better on an array of standardized tests, have taken more college preparatory mathematics courses than students of similar backgrounds not in the program, and exhibit positive attitudes toward mathematics.

• Teacher enhancement: CPMP teachers have been supported to change their teaching strategies in the direction of the NCTM Standards, to make significant improvements in their classroom environments, and to use their new-found power to help change their departments and their schools.

• Curriculum change: The Interactive Mathematics Program (IMP), an innovative problem-based curriculum developed with funding from the National Science Foundation, has been implemented in three Chicago high schools, with six more beginning Fall 1996. The curriculum has also been introduced to a large number of area teachers and administrators at the awareness level.

This report includes evaluation results and also describes expansion and dissemination activities that extended the lessons learned in the original CPMP to a wider audience, with results varying from awareness to, in some cases, real systemic change.

Background: The pilot project, 1990-1993
In 1990, nationally, less than 15% of high school graduates and less than 8% of African-Americans and Latinos were successfully completing four or more years of college preparatory high school mathematics. [1] In Chicago high schools, with a dropout rate of over 50%, the majority of students are African-American or Latino. An expressed goal of UIC in starting this program was to increase the pool of under-represented minority students able to succeed in college-level mathematics and science. A specific objective of CPMP was to increase the number of students successfully completing four or more years of college preparatory mathematics in high school, targeting students that were beginning with algebra in ninth grade.

CPMP, initially funded by the State of Illinois' Scientific Literacy Program as a pilot "high-school Treisman [2] project," began in Spring 1990 as a cooperative arrangement between UIC and the Chicago Board of Education. The CPMP cluster model involved UIC (3 staff members) and 7 schools (15 teachers), linked in a collaborative relationship. CPMP's approach called for an active, challenging curriculum, the use of cooperative learning as a primary strategy, more time on mathematics, and high expectations for teachers and students.

UIC staff designed an innovative, multi-purpose Summer Institute: an enriched summer mathematics course for students and a laboratory for teachers learning how to use manipulatives, student-centered methods, and technology. To experience and assimilate the teaching methods, teachers in teams of two prepared and taught the summer course at their own schools. Students learned to work together, got a head start on high school and began to have a changed view of mathematics.

During the following academic year, each school offered at least one double-period enriched algebra course for the students, taught by one or both CPMP teachers, attempting to continue the approaches learned during the summer. More detailed descriptions of the features and activities are given in Section II.

In 1990, 144 entering ninth graders attended CPMP's first summer program. The classes were augmented in the fall, and around 200 students took a double-period enriched algebra course in academic year 1990-91. Due to CPMP's enthusiastic reception, UIC secured funds for an expanded summer session in 1991. The assistance of the Chicago Community Trust (CCT) [3] was crucial, not only in providing financial support for a two-year period, but in advising and encouraging CPMP staff. CCT's representative suggested that UIC make a commitment to support its first cohort of students at some level through their four years of high school, rather than emphasize recruiting new students each year. An additional Scientific Literacy grant enabled CPMP to attempt both. Additional teachers were recruited, and in 1991 CPMP met a new cohort of entering freshmen and offered summer enrichment classes for rising sophomores.

Here is an excerpt from a report written by CPMP staff in July 1991, after one full cycle (summer session, then academic year) plus the second summer session:

Teachers' perceptions of success and the contagion of their enthusiasm precipitated an expansion of the program. The teachers recruited 15 additional teachers and new classes of freshmen in their schools... appropriate courses were offered for returning students. Around 310 students completed the 1991 four-week summer enrichment program at their schools... [During the academic year] attendance has been much better than usual, with several teachers citing a 95% record for their CPMP classes. Teachers' reports on what most CPMP students are able (and willing) to do range from satisfactory to glowing, as compared to other classes of similar students. CPMP students were more involved, seemed to do more homework, and together would work longer at harder problems than otherwise. Many of the students reported, in their journals and on student evaluation forms, that they liked their mathematics class (using words like "fun," "exciting," and "interesting") and that they liked working in groups.
Teachers have been invigorated by participation in the group; plans are being made to strengthen the base of support at their schools. Requests for information and assistance are being received from other teachers and from other schools; several of the teachers have already given presentations or conducted workshops on cooperative learning in their own schools or professional organizations. The UIC staff's interim assessment would be that CPMP's progress is not only satisfactory, but better than expected.

In this enthusiastic climate, while carrying on the ongoing program, the UIC Co-directors took the leadership in forming a consortium that worked together over a two-year period to seek funds for expansion--with planning meetings, work sessions, and joint preparation of a major proposal. The proposal submitted, along with subsequent negotiations, resulted in the current grant from the National Science Foundation, which began in Spring 1993. This evaluation report addresses the activities and impact of that grant.

Purposes of NSF grant
In cooperative agreements between three divisions, NSF supported UIC to:
* conduct a thorough evaluation of CPMP from its inception in 1990, with funding from the Research and Evaluation Division.
* continue CPMP in the original cluster of seven schools and act as consortium leader and trainer to expand the model to two more clusters, supported by the Teacher Enhancement Division.
* implement and study the feasibility of the Interactive Mathematics Program, sponsored by the Curriculum Materials Development Division, in area high schools.

Other components of the program, such as the actual teaching of high school students in the Summer Institute classes, were funded by various other agencies. (See Appendix 1: CPMP Financial Support for a list of principal funding sources since the program's inception).

Overview of CPMP and this report
By 1992 CPMP had developed into a complex program that included student support and year-round intensive teacher-enhancement through the Summer Institute, monthly meetings and classroom visits by UIC staff.

Features that contributed to CPMP's success with teachers included the school-university collaboration, in which UIC math faculty arranged with the schools to work directly with teachers; the use of cooperative learning as a primary strategy of teaching and learning; curriculum change, through exposure to significant innovative mathematics materials; leadership development, through sharing of responsibilities with teachers; team-teaching, for support and depth of understanding; and the conviction that students and teachers could achieve at high levels.

From the beginning in 1990, CPMP had tried to describe, measure and document the program's progress in a variety of ways. [4] This grant provided the resources for scoring and analyses of tests and evaluation of other data that had been accumulating, and included student assistants and faculty release time to assist with evaluation activities. Not having a specific evaluator regularly assigned to the program turned out to be a weakness of the project design, however, since the CPMP staff members were fully concerned with the operational details of an expanding, evolving program.

However, a benefit of the NSF funding was the project's ability to hire consultants who were expert in various aspects of education. While they were not involved in operational details, they helped staff to look at the larger picture. Betsy Becker, of Michigan State University, suggested statistical analyses appropriate for the ongoing evaluation. (She also recommended the hiring of a compulsive research associate to manage the data, and such a person was not available.)

In a meeting of the five-person expert panel, [5] October 25-26, 1993, Lizanne DeStefano helped organize the staff's thinking about the ongoing comprehensive project. The resulting graphics list the main features and activities of CPMP (Figure 2), along with expected outcomes for students, teachers, their schools and the school system (Figure 3). These graphics, often used by the Co-Directors in explaining the program at professional meetings, provide an organization for this report. (See Appendix 2: Annotated Program Summary for a more detailed version of Figures 2 and 3.)

Section II

This section describes the features of CPMP in the UIC cluster (1990-1994), followed by the features, activities and outcomes in:

* The student program, the emphasis of the initial project.
* The teacher enhancement component, as it evolved into the primary focus of CPMP.
* Curriculum change, specifically the implementation and evaluation of the Interactive Mathematics Program.

This chapter lists important features of the overall program during the first four years. Some are elaborated here; others are discussed in other, more appropriate, places in the report.

1. School-university collaboration

University math faculty wanted to help schools produce students who were well prepared for success in mathematics, science and engineering at the university. For students to achieve at the desired level, CPMP staff recommended excellent teaching, more time on mathematics and new curriculum materials that contained significant mathematics and incorporated manipulatives, calculators and computers. UIC staff knew that teachers needed help to break from tradition and try new classroom strategies, spending more time on problem-solving and enrichment. The project aimed to provide in-service and other resources to assist teachers in making these changes.

In turn, the individual schools needed to support both students and teachers during the summer and the academic year. To build a base for such support, UIC held conferences on the theme, "Success for Everyone," for teachers, principals and district staff. At the February 1990 conference, UIC staff explained the newly funded pilot project and invited schools to apply for participation.

The particular collaborative structure of this project would not have been possible a few years earlier. But under the Illinois School Reform Law, Chicago Public Schools were ordered by the state legislature to change to site-based-management in 1988. Schools were to assume considerable autonomy over their own operation, through their principals, guided by elected Local School Councils (LSC's). In 1990, no effective structure had yet been generally implemented to transfer power from the district to the over sixty public high schools in Chicago. Even the most progressive principals were confused about what they were allowed or could afford to do. Therefore the decision to apply for participation in CPMP was a significant educational choice a school could make for its students.

The competition for a school's selection for CPMP was a lengthy one, including teacher questionnaires and a written essay, in which schools described their reasons for applying and identified their goals and the characteristics of the students to be targeted. Around 25 schools applied; after UIC's examination process, including site visits, 7 were chosen. The commitment of each selected school was formally recorded by the signatures of major school players, from the participating mathematics teachers to the principal and chairman of the LSC.

The university/grantor contribution: Through a variety of grants, UIC furnished stipends for the teacher participants, meeting space and parking, resources such as exemplary curriculum materials, and support and encouragement through in-service sessions, meetings, classroom visits and consultation (described more fully in the Teacher Enhancement chapter).

The school contribution: Schools were encouraged to provide tables and chairs, or easily moveable desks, to make student group work easier. CPMP lobbied for permanent rooms for teachers, an overhead projector for each room, and occasional use of video-monitoring equipment. In addition, CPMP requested that each classroom be provided:

* books or supplementary materials that emphasized problem-solving and that encouraged students to work together;
* a classroom set of calculators;
* measuring tools, such as meter sticks, protractors, tape measures, rulers, stop watches; and manipulatives, such as construction tools, pattern blocks, area tiles;
* various media for students to work with and to show their work, such as paper for folding, graph paper and colored pencils, chart paper and markers, transparencies and markers;
* computers readily available (optimally) or access to a computer lab for at least an hour once or twice a week;
* software, including non-drill tools for students, such as word processors, spread sheets and LOGO.

Most importantly, schools were asked to underwrite a second period of algebra instruction, so that classes would have 80 minutes in which to accomplish the enriched CPMP curriculum.

For teachers, the school administrators were expected to provide needed moral support for this pioneering effort and to assist in scheduling students and clearing bureaucratic difficulties. The teacher team needed time to talk together about mathematics and their teaching, preferably with planning periods at the same time.

2. More time on mathematics
Students needed to spend time studying mathematics. Attendance problems and external distractions decreased the total engaged time from already short periods (40 minutes). The actual time CPMP students spent on mathematics was increased by the 4-week summer program, followed by a strong, double-period algebra course in ninth grade, for a start. [6] Improved attendance and extra course-taking yielded even more time on mathematics.

3. Cooperative learning
In order to improve students' concept development and problem-solving skills, as well as to create a student peer group that would support each other in learning mathematics, teachers were asked to use cooperative learning as a strategy in their classrooms. Teachers learned about such interactive approaches through assigned readings and their own experiences in the in-service sessions.

4. Curriculum change
In the in-service sessions, teachers discussed NCTM's suggestions for changes in mathematics teaching; they experienced as learners innovative student materials located or developed and provided by UIC, and were challenged to try some of them with their students. Materials from funded projects such as TIMS and MWM were included. In the search for appropriate curricula, staff examined the Interactive Mathematics Program. Some teachers were very excited about IMP, and later, through NSF support, they were able to use it. See Chapter 5 for a thorough discussion of the IMP implementation in Chicago.

5. Leadership development
Throughout the program, CPMP teachers were asked to share their work with the whole group, take responsibility for parts of the in-service sessions, and learn the channels through which to present their and their students' needs to their own school administration. Teachers were also encouraged to attend conferences and actively participate in professional organizations, such as the National Council of Teachers of Mathematics.

6. Team teaching
A powerful feature of the program was the team-teaching requirement during the summer, resulting in a pair of teachers committed to the same goals, working together in learning, planning, reflecting, and adapting. Many teachers said they were able to discuss mathematics and mathematics teaching with a colleague as never before. Teachers were also teamed for tasks that were hard to do alone (make a presentation for the first time, initiate a meeting with the principal to discuss CPMP, write a proposal for school Eisenhower funds, for example).

7. Conviction--High expectations and commitment to change
Chicago high school teachers cared for their students and worked hard to help them to learn mathematics. But UIC staff were convinced that Chicago students could succeed in mathematics at much higher levels, and that CPMP approaches would help. Teachers who participated in CPMP accepted this assumption and worked to pass on this conviction to their students.

To encourage students to raise their expectations and think of college as an option for themselves, teachers and counselors were asked to consider implementing or adapting some of the approaches that had shown success in other cities: motivation, a la Escalante; [7] active counseling for college, demonstrated by Hart, [8] and racial/cultural consciousness-raising, through presenters such as Kunjufu. [9]

Teachers needed to believe that their students could and would work hard and learn challenging mathematics. Classes began with exciting, relevant activities designed for early success, and teachers would build on this foundation.

8. Continual input/feedback: formative evaluation
At every stage, UIC staff asked for and received input and feedback from teachers. This program would not have continued for six years without the commitment of a core group of teachers reinforcing and encouraging the staff.

The teachers had all the information--about the schools and what their lives were like in the schools. Staff needed this information to make appropriate decisions about the overall direction of the program and about minutiae such as whether to meet at 12:30 or 1:00 PM (such decisions sometimes having considerable impact). Staff visited the classrooms, consulted with teachers and kept voluminous field notes, and asked for teacher input in a variety of written and oral formats.

In turn, CPMP teachers depended upon frequent student feedback in many forms. Positive reactions about how the new methods and activities were being received and how the group work was going, inspired the teachers to work harder and more creatively, to get even better results. Further reinforcement comes when a student exclaims ("out of turn," in a traditional class), "Hey, I can do this math stuff!" What students were thinking and learning (or not learning) was often factored into the lessons of the very next day.

The 1990 CPMP project was aimed at students--to enable them to succeed in college preparatory mathematics and science. During 1991, an especially reflective teacher spoke for several when she said, "We started out trying to fix the students. Then we found out that what we needed to fix was ourselves." In 1992 she stated that what still needed to be fixed was the curriculum. The next three chapters will discuss the UIC's program in that order: student program, teacher enhancement, and curriculum change.

Who were the students?
Chicago's student population consists primarily of African-American and Latinos, largely under-represented in upper level mathematics and science courses. More details can be found in Appendix 3: Demographics of CPMP.

Students who entered CPMP as freshmen at the seven UIC schools had base scores slightly above the national mean on the mathematics section of the eighth grade Iowa Test of Basic Skills (ITBS). The mean ITBS math percentile of incoming CPMP students was 59.1 in 1990-91, 54.2 in 1992-93. [10] Thus it seemed that they should have been able to achieve near the national average in college preparatory mathematics.

In 1990, two math credits were required for graduation from Chicago Public Schools (CPS). Just under 3/5 of graduating seniors citywide [11] took more than the two courses. But, less than 50% of incoming freshman were actually graduating; so at most 30% of entering freshman took more than two years of college preparatory mathematics. This situation had led UIC to believe in the necessity of CPMP's intensive intervention.

The Setting (CPS)
Most CPS elementary schools accommodated Kindergarten through eighth grade students; schools usually had few teachers well-prepared in mathematics. Some schools offered special programs such as Early Involvement (algebra in eighth grade); to participate, students often had to be transported, meeting before or after the regular school day. The majority of students entered high school without having passed an algebra course.

Some options provided by Chicago Public Schools (CPS) for students and parents seeking quality high school education include magnet schools. The two magnet schools in the CPMP cluster, Lane Tech and Whitney Young, have entrance examinations and draw students from across the city.

There were also various "tracks" within the schools. Incoming students with higher test scores assessed as potential college material were identified and tracked into Honors classes (or even High Honors), sometimes by subject and sometimes block-scheduled for all subjects. Other students were classified as Regular. Schools had still another track for students with weaknesses in basic skills. In mathematics, for example, students seen to be weak in basic arithmetic skills would be registered for Pre-Algebra. Students who had not already completed algebra when they entered high school might never have the opportunity to catch up, change tracks, or accelerate. Thus many students were at risk of not receiving a strong foundation in college preparatory mathematics.

Target students
CPMP undertook to recruit "the best students who would not otherwise take four years of college preparatory mathematics in high school." The project targeted incoming ninth graders who had not yet had algebra. The individual schools devised additional selection criteria in keeping with their own stated goals. Here are two examples.

Englewood High School: a neighborhood school of around 1,000 all-Black students in a high-crime area; its attendance rates were among the lowest in Chicago. Many of the more able students in the area, with the help of proactive parents, attended other schools (magnet schools or parochial schools), so that the college-intending population remaining at Englewood was small--less than 50 students per freshman class.

Englewood was already making efforts to encourage those students academically--grouped in the ASTRA program, they were given Honors algebra as freshmen; but historically, the percentage of these students graduating was low. Teachers targeted these students for CPMP.

Lane Technical High School: the largest in the city at around 4,000, a magnet school with an excellent reputation. Since incoming students had passed the entrance examination and since Lane Tech was a very desirable placement for teachers, many questioned the school's participation in CPMP. But math teachers were disturbed that while the freshman class was about 35% Latino and 25% African-American, there were very few minority students in the upper level mathematics classes. In fact, the head of the math department had observed that in the 20 years she had been teaching at Lane Tech, only 5 African-American students had taken Calculus. With a goal of making the advanced math classes look more like the incoming class, Lane Tech targeted Regular (i.e., not Honors algebra) students with average and above average scores (50th to 80th percentile on the ITBS) for CPMP.

Features of the program for students
CPMP students and teachers were highly interdependent, as illustrated in this passage, written by Yolanda, a student from the West Side of Chicago, during her first semester at UIC in 1994. It is a summary of her four CPMP years, 1990-94.

My experience with the CPMP program at Lake View High School is a very memorable one. This program helps involve both the teachers and students in solving problems and working together, which is an important factor of this program. It is also a wonderful way to become active in learning, achieving good grades and making friends. Because my high school was of so many different cultures, the CPMP students learned a lot from each other, both personally and academically. The teachers were very helpful and showed consideration toward our learning and understanding. During my four years at Lake View there were summer CPMP programs that consisted of learning, picnicking, parties, sports and activities that caused the students to not only have fun but think mathematically.

The second sentence above was expressed another way by a CPMP teacher. In describing the classroom at Lake View where students and teachers gathered at lunch and after school to do mathematics, she said, "We became a community of scholars."

Here are some of the features of CPMP that were especially affected the students, as they participated in the summer enrichment program and special academic year classes:

More time on math: Students received a firm foundation for college preparatory mathematics, beginning with the 4-week summer program, followed by a strong, double-period algebra course in ninth grade.

Cooperative learning: Students had time in class to get to know each other and learn to work together, resulting in a peer support group centered around mathematics. In the resulting mathematical discussions and arguments, students developed increased confidence, problem-solving skills and understanding of concepts.

Curriculum change/innovative materials: Mathematics lessons were fun. Materials were interesting, challenging and different from what they had seen for eight years.

Team teaching in the Summer Institute: The two teachers provided a real-time model of cooperation in a learning environment. Students observed how persons could have legitimate differences of opinion and yet resolve their differences for the sake of a common goal.

Conviction; high expectations: Students felt special, because teachers told them they were special and showed that they believed it. In addition to providing calculators, refreshments, and many other resources beyond paper-and-pencil, teachers listened to students and valued their opinions. Students were expected to work hard, help each other, and learn.

On questionnaires, students were asked early and often whether they planned to go to college. Teachers suggested (sometimes very strongly, depending on the teacher's personality and beliefs) that students should go to college and should start preparing immediately by attending school regularly, doing homework and taking tests such as the Preliminary Scholastic Aptitude Test. Often the CPMP counselor took a proactive role. University staff visited CPMP classrooms, sometimes giving presentations or pep talks, but more commonly interacting with individual students or small groups. With peer pressure applied as well, the vast majority of CPMP students (including those who had not been selected from college preparatory tracks) replied, "Yes, I am planning to go to college."

Continual input/feedback, formative evaluation: The many-faceted, ongoing program evaluation was actually part of the instructional program. Students' learning to express themselves was an integral part of the CPMP experience. they in turn received feedback from classmates as well as teachers. And teachers were able to hear students' thinking as never before--orally and in writing, formally and informally. In the Summer Institute, especially, many teachers read student journals immediately after class; what students were thinking and learning (or not learning) was often factored into the lessons of the very next day.

Activities in the student program
Selection and Recruitment
In the ideal case, the schools were responsible for selection and recruitment of students in their target groups. Two CPMP teachers recruited students for their own pre-ninth grade summer class. In Chicago, free summer school had previously been provided only for those who failed classes, so recruitment procedures included visiting eighth grade teachers and counselors to explain that this was not a remedial program, but a first step toward college. Letters were sent to students who qualified (good attendance in elementary school was a primary selection criterion in most schools). Some schools invited students and parents to an evening of math activities and further explanations. Entering ninth grade students who, with the permission of their parents, made the commitment to attend summer school and to take a double-period enriched freshman algebra course in the fall, became CPMP students.

Summer Institute
Here is a description of a summer CPMP pre-freshman class at one school: a composite of the more than 30 enrichment mathematics classes delivered during the first four Summer Institutes. (More information and sample activities can be found in Appendix 4, Summer Institute Student Curriculum.)

On a CPMP summer day, it is hot. Students attend math class 3 hours a day, 5 days a week, for 4 weeks. There is no air conditioning, so the two teachers have provided a water cooler and fruit drinks in the classroom.

Students are now comfortable working in small groups on mathematics. Sometimes an activity takes half the morning and they do not give up. Students are encouraged to ask questions or seek help from group members before asking the teachers. Many students have made friends they will keep throughout high school.

There is no text book. The class uses mathematics and science materials from a variety of sources, some written or adapted just the day before by their teacher team; others, innovative materials under development as near as UIC and as far away as England and Australia. Students experience an active curriculum that emphasizes estimation and measurement and problem-solving, that is enriched with equipment such as overhead projector, manipulatives such as meter sticks, colored tiles and balls. Calculators are used routinely; computer programs when available and appropriate.

Today they have just completed "View Tube," a TIMS experiment. [12] In this activity, students estimated the length of the portion of a meter stick that they are able to see while looking through cardboard tissue cores. Each student group handed in only one report, signed by all the group members.

During the morning, there were visitors -- not unusual, except that, in addition to a familiar face from UIC, there were two faculty members from the University of Newfoundland. The students are quite comfortable having visitors, so most of them did not even look up from their work.

The class is planning for a field trip, to be taken with the CPMP class from a neighboring school. The students have previously taken mini-trips inside and outside the building, beginning with a tour of their school building and including a mathematical scavenger hunt and a trip to the gym to play basketball. Student committees are planning for food, getting-to-know-you games for the other class, and details such as bus fees.

The last 15 minutes of today's class will be reserved for feedback. The students write in their journals several times a week: sometimes they respond to questions about "how my group is working" or "what I learned in math today." Teachers have prepared questions for students to answer in writing, such as:

1. How did each member of your group contribute to the end product?

2. Can you think of a practical use for the measuring technique you learned in this activity? Please explain. [13]

Academic year courses: The above vignette described a typical CPMP class. Following them into the fall would show that students were usually added to bring the total up to 28, enrolled in a double-period algebra course. Teachers tried to incorporate the best practices from the summer program into teaching algebra. The additional students were assimilated into the CPMP group [14] earned the techniques of working together on mathematics, primarily from their classmates. Mathematics classes were 40 minutes per day; the double-period provided the extra time needed for for small-group work, field trips and challenging problem-solving.

After the 1990 Summer Institute, teachers from 6 of the 7 schools discarded their traditional algebra books for a new, more challenging, problem-oriented text (Benson et al., 1991) that integrated matrix algebra, geometry and other mathematical topics in the algebra applications. There were "word problems" on almost every page, and students were expected to read the book. One teacher summarized the results of these challenges by saying, "CPMP students work longer on harder problems."

Definitions: CPMP student and CPMP teacher
For purposes of reporting to funding agencies, the District Office, principals and school administrators, parents, and the teachers themselves, it was necessary to define "CPMP student" and "CPMP teacher."

In the 1990 model, a CPMP student was a student who had been selected and recruited and in turn had made some commitments, with the permission of parents, to * work hard in mathematics and prepare for college
* ask for help when needed and give help when asked
* spend more time on math--(4-week summer class, double-period algebra class during freshman year)
The freshman algebra course was taught by a CPMP teacher, that is, a teacher who had been a full-time participant in at least one Summer Institute.

However, some students did not attend Summer Institute, but were added to the CPMP classes in the fall. In addition, some counselors not familiar with the program added incoming students or overflows from other classes. [15]

After much deliberation, staff decided that a CPMP student was a student who had been taught by a CPMP teacher for at least one full academic year. This definition raised further questions, but in the early years it served to identify the students to be counted, tested, and otherwise examined. [16]

Over time, the "CPMP teachers" definition was strengthened to include "and identify themselves as CPMP teachers and/or say that they are trying to implement CPMP approaches." [17]

Succeeding years: Each spring, students in CPMP classes were recruited for the next summer school, or at least for the next college preparatory mathematics class in the fall.

CPMP teachers and staff continued to organize appropriate summer classes. In Summer 1991 a four-week pre-geometry course, emphasizing topics such as measurement and data analysis, was offered for rising sophomores.

Teachers at one of the magnet schools, however, decided that on the basis of their strong foundations in algebra, their CPMP students were ready to take a full 8-week geometry course, equivalent to the academic year course.

Various opportunities for acceleration have been offered to students by the schools. In one school in 1990-91, students took both algebra and geometry during their freshman year. With the credit courses in the second summer, around 200 students had completed two years of math in one academic year. This enabled students to take five years of college preparatory mathematics in four years. For the past few summers, one school has offered an eight-week pre-calculus course to enable seniors to take calculus.

For rising juniors and seniors, UIC offered an un-tracked summer mathematics course on campus. Students in UICMath were integrated, not only across schools (magnet and neighborhood), but also grade levels; some students had just completed second year geometry and some, pre-calculus. Teacher teams, also integrated across schools, were challenged to provide discovery-type activities that students could explore together. In the afternoons, math faculty members planned with teacher teams and developed original problem sets that incorporated material not in their current textbooks, such as geometric probability.

In the four summers,1990 through 93, around 900 students completed CPMP summer enrichment courses . Table 1 shows the distribution. Although no such summer courses had been offered previously, some schools gave credit for these toward graduation.

Table 2 gives the number of college preparatory mathematics courses completed by UIC's CPMP students during 1990-94. There were 918 students completing college preparatory courses beyond geometry. Comparisons with courses taken by non-CPMP students are given below in Student Outcomes.

Table 1. Number of Enrichment Mathematics Courses Completed by CPMP Students in the First Four Summers (1990 - 1993)

Table 2. Number of College Preparatory Mathematics Courses Completed by CPMP Students in the First Four Years (Summer 1990 - May, 1994)

Student outcomes
Here is an overview of student outcomes and evaluation of the outcomes.

CPMP's goal for students can be operationally stated as increasing enrollment in, and completion of, advanced college preparatory mathematics classes in high school. UIC felt that Chicago high school students were able to achieve in mathematics at much higher levels, that students performing at least roughly "on level" as they enter high school could in significant numbers complete 4 years of mathematics. And staff believed that CPMP's approach would help more students to be successful and persistent. This was found to be true.

CPMP recruited capable students who would not historically be expected to take 4 years of college preparatory mathematics, and involved them in the comprehensive program described previously. At the end of the first four years, it was found that:
* Among the first CPMP senior class (1994), there were about twice as many students who took 4 or more years of mathematics than in comparison classes in each school the previous year. [18]
* Moreover, minority enrollment in advanced classes at the integrated schools increased even more dramatically.

In working backward from the goal, CPMP made these (over-simplified) assumptions:
Increasing the pool of Chicago-area students ready for college-level mathematics and science depended upon students' persistence in
* taking more advanced math courses and passing them, and
* attending school and graduating in greater numbers.

Necessary intermediate outcomes were the achievement of demonstrable short-term performance goals:
* satisfactory course grades for advancing to the next course, and
* satisfactory scores on appropriate standardized test(s).
Long-term performance, of course, would be the cumulative record of students' accomplishments, semester by semester and year by year.

Inter-related sub-goals for helping students persist on a day-to-day basis to achieve that success were:
* active involvement in school in general and in math class in particular, and
* a changing attitude toward school and toward mathematics, as something do-able and worth doing.

Immediate and ongoing student feedback was necessary to inform teachers and staff in planning. In fact, the getting and using of student input was an integral part of the instructional program, and in turn, students themselves received frequent feedback from teachers and their classmates. Here are some of the ways CPMP included extensive formative evaluation at every stage of the program to monitor student outcomes, beginning with active involvement and changing attitudes.

Active student involvement and changing attitudes
Here are some specific aspects of evaluating student involvement and changing attitudes.

Student writing: Students' opinions and feelings were sought regularly, especially in the Summer Institute. At the end of the first day, students were typically asked to write about how the day went for them, and whether it was what they expected. Typical replies were:
I expected to be bored, but I wasn't!
I think working together is a great idea because we learn while having fun.
I felt like I was in a science class.

The friendly, informal classroom atmosphere produced a level of trust in which students were able to express themselves. Student writing routinely included journal entries, answers to open-ended questions and explanations of problem solutions. The results provided information for teachers' assessment of student progress and understanding. See Appendix 5, Student Journals, for further discussion.

Student talk: Student talk, an essential element of working together to solve problems and learn mathematics, is an activity. But when students have the opportunity to express themselves, they get better at it. When students as a result become effective speakers, able to express themselves in small or large groups about mathematics or other topics, that is an outcome.

Here is an example. At "Success for Everyone" conferences, aimed at recruiting new CPMP schools, CPMP students from different schools were asked to act as a panel in one of the sessions; to briefly "tell about CPMP," then accept questions from the audience. These student presentations were uniformly well done and well received. In an instance in February 1993, at Lane Tech High School:

The students recruited were assisting as "runners" during the conference, and so had not prepared remarks in advance. In the panel presentation, observers noted that
* the students quickly organized themselves to make sure each would get a chance to speak;
* students were not awed by the audience of teachers and administrators; and
* as they made positive statements about their CPMP teachers and classes, students were articulate (prompting one observer, a professor from a Michigan university, to say that she wished her graduate students could express themselves as well).

Some members of the audience asked how well the multi-cultural students and teachers got along. Each of the students acknowledged that there was racism in their school, but not in their CPMP classes. ("We don't see color.")

A year later a Wisconsin CPMP teacher would write, about the corresponding conference at UWP:

I was most impressed with what the teachers had to share and especially with the enthusiasm of those very articulate students. It occurred to me that if those kids in Chicago could be successful with this program, we should think about trying it at our school. [19 ]

Other qualitative data from observations: The gathering of data concerning students' active involvement turned out to be exciting duty. Staff took detailed field notes during visits to classrooms and used them as a basis for conferences with the teacher and with each other. In addition, CPMP teachers opened their busy noisy classrooms to a variety of other observers. [20]

Over the years and across schools, CPMP teachers and staff were delighted to have visitors observe ordinary students engaged in on-task mathematical behavior:
* asking questions and volunteering solutions
* making presentations, using chalkboard, overhead or other aids
* working together comfortably
* arguing about mathematics

CPMP encouraged involvement of the entire educational community. For example, Dees urged that her UIC students in mathematics education choose CPMP schools for their required observation hours. A student working on a Master of Science in Teaching (MST) degree visited both CPMP and non-CPMP classrooms in March, 1992, and recorded these observations in CPMP freshman algebra classes:

Class A

The students start solving the new problems. One student feels defeated and the other group members encourage him. Teacher tries to let students work problems out themselves and rely on each other. Teacher comments that it is hard not to help them.

Class B

This class uses cooperative learning also. The students work at finding errors in worked out problems. Every group is working on it. Teacher is milling around helping students. I get to help also and it is good experience. Some groups work well together; others don't. In some of the groups only one student does the work and the others copy the answer. Are there other ways to use cooperative learning?

Class A (second visit)

The teacher rolls dice for a team to solve one of the problems and explain it to the class. There is good interaction among the groups. I help out. One of the students sits me down and explains the cooperative learning. I asked him if test taking was hard because that is done without the group. He told me no because the cooperative learning gives him confidence to do well on the test.

Class B (second visit)

Class is in the computer lab. Students put absolute value and parabolic functions into the computer for graphing. They then answer questions pertaining to the graphs. The students are in pairs and each student takes turns typing in the equations. The students are interested in the material and are working well together. I help out, but students do most of the work on their own. This computer graphing is a great application.

Two years later this graduate student became a CPMP mathematics teacher.

A math education professor from a nearby university spent his sabbatical semester at UIC, Spring 1994. He visited UIC's funded curriculum projects, but concentrated on CPMP. Dees encouraged him to keep field notes and to turn them in to staff as progress reports. Here is an except from the appendix to his paper. [21]

A Sample of Progress Reports and Observations

The focus of the progress reports changed as I became more knowledgeable about CPMP and the teaching strategies employed by CPMP teachers. There are at least three reports from each of the three neighborhood schools which I visited. Reports range in time from January to April.
These reports were not evaluations, but merely my perceptions and impressions as I observed the students and how teachers worked with the students. All were enjoyable.

Excerpt from CPMP algebra class:

Reports in class; Practice for Interdisciplinary Panel with English Teacher
Setting: Classroom was large with lots of chalkboard or bulletin board area. Two walls were covered with graphs and charts which the students had prepared.
This morning the students were giving group reports on their research, data gathering and statistical analysis. The presentations were being videotaped by one, or a team, of class members. The topics was Economics and its impact on Education.
These reports were given in the classroom during the first half of the class period. Students were attentive and encouraging to one another. There were no calls to "Speak up" or "Whadja say?" The teacher did give encouragement: "Take your time:, "You're doing fine," etc.
About 9:00 the class moved to the Social Room, a large room with straight chairs. Students practice the Talk Show presentation related to their research. Students on the panel played the roles of suburban parent, project housing parent, discouraged principal, and parent-volunteer. Students in the audience worked on questions to ask and rejoinders.
Another class was to come in after Division (Homeroom) to be part of the spectator audience.
Summary: What a contrast between the student work done in this mathematics class and the "normal" class. The students had gathered the information, made the graphs, prepared their written and oral reports. They learned the "textbook" mathematics, but used problems from their lives and their world. It was impressive.

Quantitative data about student attitudes: In 1990, CPMP staff, wanting a standard, quantifiable record of students' evaluations of their summer program, designed a student questionnaire that has been used for several years. The survey instrument (Appendix 6, Student Evaluation Form) included Likert-type scales on statements such as,
My math classes in grade school before this were fun.

along with open-ended questions such as,
Is the work that you have done this summer different from the work you have done in math classes before? If yes, how was it different?

CPMP staff collected the completed forms from teachers, collated the results and returned them to the teachers. A complete collation of a class from 1990 is included as Appendix 7, Student Evaluation Lake View 1990.

Figure 4. Excerpts from Student Evaluation, Lake View, Summer 1990
From 26 students entering a low-income, mostly Latino neighborhood school, responses to: "Please circle the number which tells how much you agree (1 is the most) or disagree (5 is the most)."

Figure 5. Excerpts from Student Evaluation, Whitney Young, Summer 1990
From 24 students entering the city's top-rated magnet school, responses to: "Please circle the number which tells how much you agree (1 is the most) or disagree (5 is the most)."

In general, few students responded that they had "worked a lot in groups" in math classes before CPMP (in these two examples 4 of 26 and 4 of 24 "agreed most" that they had, respectively), but most responded that they had worked a lot in groups in the CPMP summer program (22 of 26 and 23 of 24).

The weighted average (AVE) gives a statistic that can be reviewed comparatively with varying numbers of students. As this example is stated, a lower average, indicating greater agreement, is desired. AVE of 3.73 and 3.54 for "worked a lot in groups" indicated that students disagreed: No, we didn't work a lot in groups. AVE for the summer class on this statement decreased to 1.12 and 1.04, indicating high student agreement with the statement that they had worked a lot in groups.

Freshman CPMP students were generally consistent across schools, teachers and summers. Students as a whole usually reported, as in these Figures, that they found math more fun when in CPMP classes and that they became more interested in mathematics because of CPMP.

The CPMP Summer Institute did improve students' attitudes toward school and toward mathematics. Attendance reports were excellent during the summer classes; this usually continued into the academic year CPMP classes. Teachers and staff were encouraged by student attitudes, as stated in their formal and informal feedback, and student learning, demonstrated in their performance in mathematics content, as observed in their daily work, teacher-made quizzes and tests. The positive experiences that students had in the summer program increased their ability to work together productively, as measured by their self-reports and later, during the academic year, by their observed engagement with appropriate classwork.

Student achievement in mathematics
Students were enjoying themselves, but were they learning mathematics? The expressed intent of CPMP was to provide a strong foundation in algebra (over the whole year) as a basis for the rest of the college preparatory mathematics courses, but the summer curriculum itself was not designed to teach algebra skills. UIC staff wrote that:

...the active experiential curriculum, with cooperative learning as a primary strategy, is expected to increase students' ability to use given information effectively, to perform multi-step processes and to employ a variety of problem-solving strategies. [22]

Summer Institute and Academic year courses
When the pilot project began, the major component was to be the CPMP double-period freshman algebra (building on the foundation laid in the summer enrichment course for those able to attend). Students were to receive the comprehensive CPMP program, with features described previously, and decreased time in traditional lecture and seatwork. Staff wanted to determine whether these students were performing at least as well as similar students taught in traditional classes on standardized achievement tests, while exhibiting other gains expected from the CPMP approach: better cooperation, more positive attitudes toward math and greater problem-solving skills.

Since CPMP was not designed as a research program, there were no "control" groups assigned in advance. (There were no other students at all in the summer program.) Therefore, in Fall 1990, teachers were asked to try to find colleagues who were teaching students as similar as possible to CPMP students and who would be willing to help by administering tests to their students.

In 1990-91, analyses involving these comparison groups included consideration of how similar they actually were by examination of their scores on pretests or the math score on the eighth grade Iowa Test of Basic Skills (ITBS) at the beginning of the academic year. In one school, the entire college preparatory population was in CPMP, so their teacher went to a nearby school for a comparison group.

The Pre-algebra Problem-Solving Test (PSTest)
Staff wanted to see whether the emphasis on problem-solving in the summer program, before algebra instruction, was having an effect. Unable to locate an appropriate instrument, CPMP devised and validated a test of problem-solving ability in three forms, adapted from the Romberg-Wearne Problem-Solving Test (Collis, Romberg & Jurdak, 1986).

The UIC adaptation, the Pre-algebra Problem-Solving Test (PSTest) was intended to measure power, not speed; to be brief and easily administered; and to be interesting, so that students would be willing to give their best effort. The test was multiple-choice or short-answer, but students worked on and wrote their responses on the test paper. This feature not only reduced transfer errors, but was helpful to teachers and CPMP staff in examining students' thinking. [23] Students easily completed the test in 40 minutes, and many commented that it was fun.

The PSTest has 7 "superitems;" each contains three related questions increasing in difficulty, for a total of 21 questions. The test has three versions; superitems 3, 4, 5 and 6, called "core" items, are essentially the same in all the versions. Thus the Core score is the number of items correct out of 12. (See Appendix 8, PSTest Information and Sample Copy,] for further discussion and a copy of the test.)

Results from the 1990-91 PSTest The test was administered at the beginning of Summer Institute 1990, a second form in early fall and the third in Spring 1991.

Freshman students in the 7 CPMP schools were classified in three groups:

* Group A: CPMP students attending Summer 90 through Spring 91.
* Group B: CPMP students in academic year only, Fall 90 through Spring 91.
* Group C: Comparison students (defined above), Fall 90 through Spring 91.

Students in Group A took the PSTest at the beginning of Summer Insitute 1990. All students took the PSTest in Fall 90 and in Spring 91. There was no statistically significant difference between the initial scores (Summer Score for group A, Fall Score for groups B and C) of CPMP students and the comparison group.

Table 3 shows the performance of CPMP students in Group A, using a t-test for significant differences.

Table 3. PSTest Raw Score, Core Score, and Gains Means for CPMP students over whole program, 1990-91

Next the performance of CPMP students who were in the academic year only, Group B, and Group C are compared. As previously stated, the comparison group was obtained by asking the teachers working in the program to have the test administered in classes that they felt were comparable to their CPMP class in their own schools. One magnet school, Whitney Young, was especially energetic in this endeavor, providing 271 comparison students.

Table 4 shows the mean improvement, adjusted for prescores and school effect both with and without Young. It shows an overall significant positive effect of CPMP, p<.05 and without Young, p<.005.

Table 4. Adjusted Mean Gain Score on PSTest, Academic year 1990-91 (adjusted for prescore and schools), for CPMP and Comparison Students

Interpretation: This is an example of a phenomenon that increased throughout the analyses. Overall, students entering magnet schools are, by definition, stronger than those remaining in neighborhood schools, since they pass admission exams. Furthermore, parents may be more supportive, socioeconomic status may be higher, the school's program may be better. Yet CPMP shows improvement over current programs in the magnet schools, with stronger results in the non-magnet schools.

During the second year of CPMP (1991-92), testing emphasis shifted to geometry as the first cohort of students moved into their sophomore year. But the PSTest was again given to 392 freshman students in 1992-93.

Results from the 1992-93 PSTest
The groups were:
* Group A: CPMP students attending Summer 92 through Spring 93.
* Group B: CPMP students in academic year only, Fall 92 through Spring 93.
* Group C: comparison students in academic year, Fall 92 through Spring 93.

In addition to the total score (out of 21), a "core" score was computed. The core score is the total over the superitems 3, 4, 5 and 6 (max core score=12), which were virtually the same in all three forms of the test.

Table 5 contains a summary of the data.

Table 5: Total Score and Core Score Means for CPMP students and Comparison Students, 1992-93

Table 6 shows the analysis with means adjusted for prescore (the Summer Score for group A and Fall Score for groups B and C). There were significant differences, favoring those having the program, between the three groups, but the group that took the full program, including the Summer Institute, performed the best of the three groups. Students who had not been exposed to this material before, but were ready to learn, sometimes made a large gain during the summer, and then a moderate gain during the year. On the other hand, some students made small gains in the summer, but with improved attitudes made a larger gain during the academic year.

Table 6: Total Score and Core Score Means, Adjusted for Pre-score, for CPMP students and Comparison Students, 1992-93

Student testing program
In addition to teacher-made tests and the PSTest, CPMP staff procured several instruments for use in evaluating CPMP students' mathematics learning. Six different tests were given at 20 different times in 18 schools to over 8,000 students. As the program continued through additional funding, the first cohort and students joining CPMP along the way were tested extensively by the time they graduated in Spring 1994. The testing program, carried out in the 9th, 10th, and 11th grades, gave a profile of the first cohort of CPMP students and their successors.

The standardized test data support a general conclusion that students in the CPMP classes performed better than similar students not in the program, on a variety of tests on traditional college preparatory mathematics courses (algebra, geometry, advanced algebra, AP calculus). These results reflect the impact on the students of the combined, essential features of CPMP: increased time on mathematics, cooperative learning, innovative curriculum materials and high expectations.

Here is a list of the instruments used across the program in the first few years:

PSTest: The Pre-algebra Problem-Solving Test discussed above.

Three tests from the Comprehensive Assessment Program (CAP) battery.(American Testronics, 1990):
* CAP Algebra
* CAP Geometry
* CAP Advanced Algebra
All three were standardized 40-question multiple-choice tests, with national norms provided.

Three tests from the Cognitive Development and Achievement in Secondary School Geometry Project (CDASSG, 1981): The Entering Geometry, Van Hiele and Geometry Proof tests were used by permission from the University of Chicago's National Institute of Education geometry project.
*Entering Geometry test consisted of 20 multiple-choice questions on basic vocabulary of geometry.
*Van Hiele test was a 25-question multiple-choice test intended to identify students' level of ability to understand geometry. The Van Hiele test was originally chosen in an effort to determine whether the increased student interaction in CPMP classes might help students move from one Van Hiele level to the next higher. The test was administered to CPMP geometry classes in 6 schools, pre and post, during 1991 to 1993, but the data were not used in the manner for which the test was designed. UIC staff were not agreed on the validity of the test for CPMP's purposes, and the scoring for determining levels was complex. However, teachers felt the test covered geometry concepts well, so the results were analyzed using the total raw score (out of 25) as the variable. The results, given in Appendix 9, Van Hiele Test Results, are somewhat similar to those on the CAP Geometry test, discussed below.
*Geometry Proof test was open-ended; students were to answer questions and complete proofs on the test paper itself. The Proof test was administered only to those classes that were taught proofs in their geometry course, according to their teachers. UIC did not have the resources to analyze these, but the teachers scored the tests and said that students' performance seemed better than on similar teacher-made tests in other years.

No appropriate trigonometry, pre-calculus or calculus tests were located.

Preliminary Scholastic Aptitude Test (PSAT). This test was used in three ways.
* Non-analysis use. One of the features of the program was high expectations for the students. Staff found that in non-magnet schools, and some groups in magnet schools, a low proportion of students were taking PSAT, SAT, or ACT. This was because they did not expect to attend college or could not afford the fees, or other factors. Not taking these tests at the appropriate stage in high school limited students' information and options if they decided to pursue higher education. Therefore CPMP teachers actively encouraged their students to take these tests, from "requiring" participation to getting donations to pay for students' fees. Program wide, the proportion of students taking these tests increased.
* Comparisons. In 1993-94, publicly available versions of the PSAT were used as pre and posttests to compare performances of IMP and non-IMP CPMP students on an external measure. (See Chapter 5 for a complete discussion of the results.) Some schools also began to give the PSAT to all sophomores as a general indication of their students' progress.

Student test results
In each comparison, after controlling for students' score on a pretest and adjusting for school effect, the CPMP students' scores were significantly better than those of the comparison group. Significance level used throughout the report is .05 unless otherwise noted.

Conclusion 1: Students who attended the summer school and double-period freshman algebra classes taught by CPMP teachers performed significantly better than comparison groups of students in other algebra classes.

Table 7. Eighth Grade ITBS Math Scores and Mean scores on CAP Algebra, CPMP and comparison classes, 1990-91

Near the end of the 1990-91 academic year, 467 students, 183 from CPMP and 284 from a comparison group, were tested on CAP algebra. The Math ITBS Normal Curve Equivalent (NCE) from the previous year was used a prescore. The mean ITBS score for CPMP students was 59.1%, while that for the comparison group was 65.2, as shown in Table 7. At the end of the year, the order of the CAP algebra means was reversed: the mean CAP percentile score for CPMP students was 56.7 and that for the comparison group was 50.7, showing a superior performance by the CPMP students.

Further, when the ITBS score, gender, race, school lunch eligibility (as a family income measure) were used as covariates, the difference between the CPMP students and the comparison group was statistically significant. The adjusted mean percentile on the CAP algebra was 66.85 for CPMP students and 56.40 for the comparison group.

As the first cohort of students advanced to sophomore level, testing emphasis shifted to geometry (to be discussed ahead) in 1991-92, but the algebra testing program was administered again in 1992-93 to 222 students.

The adjusted mean CAP score in 1992-93 (adjusted for school effect and ITBS score) was 19.72 for CPMP students and 16.88 for the comparison group. The results summarized in the following Tables 8 through 10 show that the difference between performances of the CPMP and Comparison students is statistically significant after eliminating prescore and school effects.

Table 8: Eighth Grade ITBS Math Scores and Mean scores on CAP Algebra, CPMP and comparison classes, 1992-93, All Schools

Table 9: Eighth Grade ITBS Math Scores and Mean scores on CAP Algebra, CPMP and comparison classes, 1992-93, Magnet Schools only

Table 10: Eighth Grade ITBS Math Scores and Mean scores on CAP Algebra, CPMP and Comparison Classes, 1992-93, Non-Magnet Schools only

School effects often were found to be caused by one or both of the magnet schools, given the difference in incoming students' preparation and the school's program, expectations, and other factors. Table 9 shows that CPMP students in the magnet schools performed better than the comparison group students, but Table10 shows a highly significant positive difference for CPMP students in non-magnet schools.

Program Growth, 1990-1992
The list of classes shows how the program for students grew through the first two years. "5x" indicates that the class meets five times per week. The double-period classes show as "10x." Some schools experimented with 8 classes per week, usually paired with a science class to provide extended time for laboratories twice a week.

The chart above shows variation in how the program was implemented at the different schools. The ordinary sophomore course was geometry, which was the next course to be tested.

Geometry results
Both in UIC's region and nationwide, there has been concern about students' progress in geometry (CDASSG, 1981). CPMP tried to learn as much as possible about how well CPMP students were learning geometry.

Here are definitions for this discussion:
In general, a CPMP student is one who took at least one CPMP class (algebra and/or geometry).

* The non-CPMP group consists of students who are not CPMP students, neither for algebra nor geometry.
* The CPMP geometry group consists of those students who took a CPMP geometry class during the academic year (and may or may not have also had CPMP algebra).
* The CPMP OtherGeom group were CPMP students in freshman algebra but took a geometry course from a non-CPMP teacher; ergo they were CPMP students in a non-CPMP geometry class.

The CPMP OtherGeom group was constituted in the following ways:
A school may have consciously decided to split up the CPMP students for geometry to "seed" the sophomore classes.

The school may have decided against continuing the block programming, or some CPMP students had schedule conflicts.

The school may have actually skimmed off the highest achieving CPMP freshmen and put them into Honors classes beginning sophomore year.

The following discussion of the geometry results refers to the groups defined above.

Conclusion 2: Students who attended CPMP algebra were significantly better prepared for geometry than students who took normal algebra.

Entering Geometry test consists of twenty multiple-choice questions. There were 1,104 students from the six schools who took the Entering Geometry test in fall of 1991. Results are given in Tables 11 through 13.

Table 11: Mean scores on the Entering Geometry Test of CPMP and Comparison Students, Fall 1990

In each table, "Adj Means" are the means adjusted for school effect. Means with the asterisk, *, on the same column are not significantly different. Otherwise, there is a statistical significant difference among the groups.

The mean scores on the Entering Geometry test, administered to 1104 students in Fall 1991, when adjusted for school effect, were 8.27 for non-CPMP students and 10.25 for students who had had CPMP algebra.

At Young and Lane, the department heads were CPMP teachers; they were anxious to include as many students as possible in the testing, not only to cooperate with CPMP but also to gain information for their schools. Thus again there are large numbers of their students, and they do affect the outcomes disproportionately. Excluding the magnet school Young, there are 833 students with the statistics given in Table 12.

Table 12. Mean scores on the Entering Geometry Test of CPMP and Comparison Students, Excluding Young, Fall 1990

Results for 573 students, excluding both magnet schools, Young and Lane, are in Table 13.

Table 13. Mean scores on the Entering Geometry Test of CPMP and Comparison Students, Excluding Young and Lane, Fall 1990

Several factors contributed to CPMP students' being somewhat better prepared for their geometry course. In addition to the extra time in CPMP algebra, and in the summer program for some students, students had geometry in their curriculum. Teachers chose textbooks that included geometric figures to provide context for algebra problems, and they provided supplementary materials such as computer LOGO and activities in estimating and measuring distances, perimeter and area of plane figures and volumes of solids. Thus CPMP students' actual gains in geometry were acquired over the two years.

Conclusion 3. Students who attended first year CPMP algebra and second year geometry taught by CPMP teachers performed significantly better on a standardized geometry test than comparison groups of students who took the normal algebra and geometry. (This is not apparent from Table 14 below, but becomes clear when the magnet schools are separated from the rest in Tables 15 and 16.)

CAP Geometry test results 1991-92
There were 822 students from the six schools who took the CAP geometry test in Spring 92. "Adj Means" are the mean raw scores (out of 40) adjusted for school effect. For the following tables, the difference among the groups is statistically significant.

Table 14. Mean Scores on CAP Geometry Test for CPMP and comparison Students, 1991-92.

At Young and Lane, many CPMP students took geometry during the Summer Institute rather than during the academic year. Excluding Young, there are 546 students with the following statistics:

Table 15. Mean Scores on CAP Geometry Test for CPMP and Comparison Students, Excluding Young, 1991-92.

Excluding both Lane and Young, there are 397 students with the following statistics:

Table 16. Mean Scores on CAP Geometry Test for CPMP and Comparison Students, Excluding Young and Lane, 1991-92.

There is also a significant difference among the groups if CPMP OtherGeometry students are excluded (effectively including only those students who took geometry during the academic year).

CAP Geometry, with Entering Geometry as Covariate, 1991-92
The Entering Geometry test was taken in Fall 1991 and CAP Geometry in Spring 1992 by 702 students. The analysis used was General Linear Models, with Entering Geometry as covariate. "Adj Means" are the means adjusted for the school effect; means with the asterisk, *, in the same column are not significantly different. There are significant statistical differences among the groups as shown in Tables 17 through 19.

Table 17. Means on CAP Geometry Test Adjusted for Entering Geometry Test, for CPMP and Comparison Students, 1991-1992.

Excluding Young gives 443 students with the following statistics (Table 18):

Table 18. Means on CAP Geometry Test Adjusted for Entering Geometry Test, for CPMP and Comparison Students, Excluding Young, 1991-1992.

Excluding both Young and Lane leaves 307 students, with results in Table 19.

Table 19. Means on CAP Geometry Test Adjusted for Entering Geometry Test, for CPMP and Comparison Students, Excluding Young and Lane, 1991-1992.

By 1992-93, CPMP methods had been disseminated among the math departments so that it was not possible to secure an "uncontaminated" comparison group. Teachers continued to test their own CPMP classes and results seemed fairly stable.

Interpretation
Even though the CPMP students perform better on geometry standardized tests than comparison students, scores of CPMP (not in magnet schools) are still discouraging, considering that these mean scores are out of a possible 40 on the CAP Geometry test. UIC staff members present the following facts as possible factors in the relatively poor performance of CPMP students.

Schooling: Examination of elementary school textbooks and teaching practices used in Chicago in the years leading up to 1990 shows that public elementary school children in Chicago generally received weak preparation in geometry.

* Rather than being integrated throughout the text, Geometry was one chapter, often at the end of the book. Since most teachers had not been prepared in the teaching of geometry, the chapter was often omitted.
* Elementary school students seldom used manipulatives in mathematics class, nor did any type of measuring.
* Computers were either not generally available or used for reading and/or writing. Mathematics software available was typically designed to teach arithmetic skills.

Outside experience: Urban children were not as likely as those in suburban cities or rural areas to build things such as birdhouses, to have part-time jobs such as mowing lawns or to have extracurricular activities such as orienteering. Television, a common babysitter, was a wasteland as far as geometry was concerned.

NCTM'S emphasis in the Standards on active geometry and measurement lessons at all levels are having some effect. In 1996 elementary textbooks are much more likely to integrate geometry throughout the text. And while teacher pre-service training and in-service in teaching elementary geometry have lagged behind, the outlook is improving.

Comparison with national norms
CPMP students overall generally retained their standing at the national mean on a standardized test in algebra, while a comparison group did not.

Conclusion 4: Students who attended the double-period algebra classes taught by CPMP teachers performed approximately at the national average on standardized algebra tests.

Table 20shows that the mean CAP percentile score for 183 CPMP students taking the CAP algebra test in Spring 1991 was 56.7; the mean CAP raw score for 156 CPMP students in Spring 1993 was 19.08, compared to the national average of 19.5.

Table 20. CPMP Scores and National Averages on CAP Algebra Test, Spring 1991 and Spring 1993

Conclusion 5: Students in the seven UIC CPMP schools performed approximately at the national average on standardized algebra and advanced algebra tests but below national norms in geometry.

Data
The national mean on the CAP algebra, geometry, and advanced algebra tests used (1990 version) were 19.5, 17.9, and 18.3. Examination of Tables 10 through 12 give several results.

Table 21. CPMP mean raw scores (out of 40) on CAP Algebra, Spring 1993

In 1992-93, 156 CPMP students took the CAP algebra test and had an average score of 19.08 (28.87 at magnet schools and 15.82 at non-magnet schools), as shown in Table 21.

Table 22: CPMP mean raw scores (out of 40) on CAP Geometry, Spring 1992

Table 22 shows the average CAP geometry score for 253 CPMP students was 16.54 (25.14 at magnet schools and 11.46 at non-magnet schools).

Table 23: CPMP mean raw scores (out of 40) on CAP Advanced Algebra at 4 CPMP schools, Spring 1993

The average CAP advanced algebra score for 107 CPMP students in 1992-93 was 18.72 (19.04 at magnet schools and 18.2 at non-magnet schools) as shown in Table 23.

Note: In the two required courses, Algebra and Geometry, Tables 10 and 11 show that in these data, CPMP students in magnet schools performed twice as well as in non-magnet schools. But Advanced Algebra, the third year course, is not required in non-magnet schools. In this group of CPMP students who persisted to Advanced Algebra (1993), the difference between the two groups (magnet and non-magnet) is almost erased (Table 23).

Four schools had CPMP Advanced Algebra classes (so identified by their CPMP teachers) that included the first cohort of CPMP students. In some schools, CPMP students had been dispersed by their junior year. In other schools there might not be a suitable comparison class, since CPMP teachers were teaching all sections of the course.

Data on the Spring 1993 CAP Advanced Algebra test is available on 129 students in those four schools, 104 CPMP students and 25 comparison students. The students were mostly from grade 10 (55 students) and grade 11 (66 students); 72 were females, 57 males. Table 24 gives a brief summary of the data.

Table 24. Mean raw scores (out of 40) on CAP Advanced Algebra, CPMP and Comparison Students, Spring 1993

In order to compare the performances of CPMP and comparison students, the effects of school, grade and gender were eliminated by Analysis of Variance (ANOVA). The effects of grade and gender were not statistically significant, but the effects of school and CPMP together were significant at the 5% level. When means were adjusted for differences in schools (Table 25), CPMP students scored signifcantly higher than comparison students (p < .01)

Table 25. Adjusted means on CAP Advanced Algebra Raw scores, Spring 1993

Since results were similar at freshman and sophomore levels (CPMP students performing better than comparison students, often significantly better), staff and teachers were less inclined to continue the time and labor-intensive testing program. However, most teachers continued to administer standardized tests in their own classes for their own and their students' information.

The third and fourth year courses varied at the schools (college algebra, pre-calculus, calculus, AP calculus). No program-wide tests were attempted, but faculty provided old UIC placement tests and sample calculus exams to CPMP teachers.

Student persistence conclusions The persistence data evaluates the effect of the program as a whole on both the students and the school. Both "true persistence" data showing the persistence of CPMP students in taking mathematics and comparisons of the number of students taking target classes in advanced mathematics show major positive effects. Because of the tremendous variance in course taking at the various high schools, a target class was chosen at each high school and the percentage of CPMP freshman taking this course was compared with the percentage of a comparison group of students the previous year who reached the same level.

The persistence of CPMP students in taking mathematics (year to year and over 4 years) and the total number of students taking advanced mathematics courses were recorded for each school, with particular attention paid to the enrollment in the target classes for each school. [26]

The increase was partially due to the CPMP students persisting in math into the third year, but also, there was a definite ripple effect, and the persistence into the third year by non-CPMP students also occurred. At least two causes have been identified.

* CPMP teachers expected more and encouraged more from more students, not only their CPMP students;
* Students infected their non-CPMP friends with their positive attitudes towards mathematics and towards planning for college. It began to be, if not "cool" at least not "un-cool" to take math.

The ability to track the original cohort for four years varied from school to school, depending on the size of the school and the commitment of the teachers. While it turned out that careful work with individual teachers was more accurate than the citywide database, the results were expensive and also unreliable, because of dependence upon which teachers were interested. Particularly troublesome was the fourth year of the program (1993-1994), when some students were "lost."

Conclusion 6: Enrollment over three years, in target third year courses, increased by at least 20% in each UIC - CPMP school, as enumerated in Table 26.

Englewood's target class, advanced algebra-trigonometry, increased from 33 in 1991-92, the comparison year, to 47 in 1992-93, when the CPMP class reached their third year (an increase of 42%).

Furthermore, Englewood did not have the resources to offer a calculus course. Some small schools in this situation bus their students to neighboring schools that do have the desired courses. But Englewood's CPMP students were fortunate in connecting with the University of Iowa and The Amoco Foundation. The Foundation offered support throughout high school, including summer sessions at the U. of Iowa, tutoring in their school, and calculus in Saturday and after-school classes, provided the students kept their side of the bargain. Students were further promised full 5-year scholarships at Iowa if they passed the AP calculus exam. Four students out of the first CPMP cohort, the class of 1994, were the first to participate in this program. Based on students in previous years, the department head, Mary Willmore, feels that these students would not have been able to take advantage of this opportunity without CPMP. The program's active approach, with cooperative learning, improved their skills, self-esteem and aspirations, she says. The scholarship holders also tutored and inspired younger students, and every succeeding year three or four students have followed in their footsteps.

Table 26. Number of students completing third-year target classes, compared to the previous year when there were no CPMP students.

As shown in Table 26, Lane Tech's target class was pre-calculus, which increased by 168 to 260, an increase of 55%.

Furthermore, Slaughter, a Lane Tech teacher who became a CPMP coordinator, did a study of the effect of the program on the math achievement of minority students after two years at Lane for a course in her Master's program in Research and Educational Administration. [27] In looking for a comparsion group for the first CPMP class, she was shocked to find that of non-CPMP students who were admitted in 1990 year, almost 50% of them were not even in the junior class at Lane. The CPMP class had lost relatively few; not all were in the target class, but most were still in school at Lane.

According to available data (Table 27), the proportion of African-American and Latino students in upper level courses improved as well, making the CPMP classes look more like the hallways, in terms of diversity of the student body.

Table 27. Increase in Proportion of Minority Representation in above target classes

Conclusion 7: Enrollment in Advanced Placement Calculus increased by an average of 10 in the six UIC- CPMP schools that offered calculus. Four of these schools had students taking the Advanced Placement Calculus examination, and there was a slight drop in the success ratio compared to the previous year.

Table 28. Number of CPMP Students Completing A.P. Calculus and Taking A.P. Exam, UIC Cluster, 1992-93 (Comparison Year) and 1993-94

Table 28 shows A. P. calculus enrollment and the results of the A.P. test, in 1993-94 and the comparison year, 1992-93, at the four CPMP high schools that made a concentrated effort to accelerate CPMP students through AP calculus. There are several aspects of the results that deserve further mention.

First, comparing the 1993-94 results with 1992-93 disguises increases attributable to CPMP in the number of students taking the A.P. exams at several of the schools, before the first cohort of CPMP students reached that level. This effect is explained by Horn, writing about school change by Year 3 of the overall program.

Beginning from the first year, all five classes of each of the six (or more) teachers were being touched by their emergent belief in the basic right of all students to succeed in a quality program and their conscious effort to pay particular attention to the needs of underrepresented minority students. So by the third year, upper level math class enrollment had significantly increased. This increase was above that which could only be explained by the presence of the orginal CPMP class. [28]

At Young the calculus class had already doubled by 1992-93, as a result of the work of the CPMP teachers Horn and Bukowski.

Secondly, since increases in enrollment and in taking the exam were partially due to the more inclusive atmosphere fostered by CPMP, distinct improvements in minority representation were seen at Whitney Young and Lane Tech. Concerning the proportion passing the exam, anecdotal evidence from other schools around the country where there has been markedly increased enrollment in AP calculus is that the success rate is low at first. Also, the results here lump together performance on the AB and BC test. There were many low scores on the BC test which may indicate that students took an inappropriate exam. The CPMP calculus teachers from the schools that offer calculus have formed a support group for the mutual improvement of their courses.

Conclusion 8: The rate of CPMP student persistence to a third, fourth and fifth year of mathematics was significantly better than the comparable group of students who entered as freshman the year before CPMP was introduced.

Table 29. Percent of Original CPMP Classes and Comparison Classes Who Completed a Third Year of Math

The comparison groups chosen (Tables 29, 30 and 31) were those who were enrolled in similar classes as freshman. (e.g., not the students programmed into pre-algebra at the neighborhood schools. Also, the comparable algebra class, Honors or Regular, had to be used.)

Table 30. Percent of Original CPMP Classes and Comparison Classes Who Completed a Fourth Year of Math

Table 31. Percent of Original CPMP Classes and Comparison Classes Who Completed a Fifth Year of Math

Students taking the fifth year of math in four years, as mentioned, did this by taking two years of math concurrently or by taking courses in the summer, usually taught by CPMP teachers.

Persistence summary
The evaluation effort of student persistence to date includes unofficial longitudinal studies, such as teacher, school and student reports, and more systematic efforts by the Board and by ACCESS 2000, a federally funded program for students, which supported the summer activities for students over several years. These data indicate that the program is a successful intervention strategy for increasing the pool of students ready to undertake college mathematics and science courses. CPMP students:
* have better than average attendance, usually ranging from 80% to 95%, depending on the school;
* take more mathematics courses (around 80% of entering freshman take at least a third year of mathematics, while the city average is less than 60% of graduates); [29] and
* graduate at a higher level (around 80%) than the Chicago students as a whole (around 50% in 1990).

Also, a higher proportion of minority students in CPMP classes go on to advanced mathematics classes, the difference depending on the school. These results were not achieved by "creaming," or recruiting the best students, as the enrollment in advanced courses at CPMP schools increased by at least 20%.

Bonus outcomes
Other student outcomes, not necessarily expected, were reported incidentally, almost accidentally. For example, teachers report that CPMP students have more school spirit and take more leadership in extra-curricular activities.

A teacher notices that all the National Honor Society officers and most of the members are CPMP students.

Another finds out by chance that a student goes from the afternoon CPMP help session/study group to tutor younger children in a program she started at her church.

Many of the first cohort of CPMP students at Lane Tech, in the Class of 1994, were still in school, still "tight," after four years. They decided to have a banquet in Spring 1994, to celebrate each other and to thank CPMP, especially the teachers, CPMP counselor and school staff who had helped them through the years. A committee of students approached Slaughter and told her that all the assistance they needed was in finding a site. They would take care of everything else - planning, invitations, food, favors. And they did. Entertainment included students' songs, poems and tributes, with presentations of gifts to their invited guests. Slaughter said such an event, wholly originating from and carried out by students, was unprecedented in her 20+ years of teaching.

The successful student program described above was delivered by CPMP teachers in their own high schools. But lasting teacher enhancement will ultimately have positive effects far beyond helping a particular class or group of students. The next chapter describes the teacher change in the first cluster and the role of CPMP in supporting that change.

The previous chapter focused on the student program, first implemented through the 1990 Scientific Literacy grant, which had as its goal to increase the pool of under-represented minority students well qualified to study further mathematics and science. During that first year, UIC recognized that teacher enhancement was an essential element of changing the classroom for all students, minorities in particular. The proposals requesting funds to continue the program in 1991 included an additional goal, to:

... develop a core of teachers trained in the use of innovative, enriched workshop methods; these leaders will help rebuild and/or strengthen the college preparatory mathematics programs in one-third of Chicago high schools, within an effective model for school-university collaboration. [30]

The structure of this school-university collaboration was described in Chapter 1. Here is a discussion of UIC's program for developing the core of teacher leaders, the teacher enhancement program that became the foundation for the current NSF grant, in the following order:

Who were the teachers?
Features of the teacher enhancement program
Activities for Teacher Enhancement
Teacher Outcomes

Who were the teachers?
UIC staff recruited teachers at the 1990 Success for Everyone Conference and afterwards by informal discussions and classroom visits. UIC required that there be a team of two committed teachers, and that the team take leadership in writing the school's essay applying for participation in the CPMP. Teachers selected themselves as candidates for the program, by convincing their schools to enter the competition. These teachers were already looking for new ideas; some had attended UIC's Success for Everyone Conference in 1989. Thus that first group of teachers were already leaders.

Six schools were chosen. Lane Tech High School wanted to participate, but a conflict between the administration and the Local School Council (LSC) prevented their approval of the application. Even though they were not able to have summer classes, three determined Lane Tech teachers attended the CPMP summer in-services voluntarily, without stipends. They also visited and gave assistance to teachers in the other six schools. By fall, Lane Tech was officially the seventh CPMP school.

The department heads of four of the seven schools were among the participants. Table 32 gives gender and ethnicity of new [31] recruits in the seven schools for the first four years.

Table 32. Ethnicity and Gender of New CPMP Teachers, 1990-93

Features of the teacher enhancement program
The following is a discussion of the program features as they relate to teachers.

1. Chicago Public Schools - UIC collaboration
This school-university collaboration was an relationship for CPMP teachers. UIC faculty were relating to high schools and teachers in a new way--not teaching courses, not doing demonstration lessons, not doing a research project using teachers or students as subjects. Instead, staff attempted to collaborate with teachers to improve mathematics teaching. Faculty visited teachers' classrooms to show interest and support, to learn from their strengths, to experience the real world of the classroom, and to identify problem areas in which to offer assistance.

UIC has shared the assumptions about teachers stated in reports of a major 10-year urban project (Pitman, 1994):
* teachers are the agents through whom change in classrooms is to be achieved;
* teachers have both formal and practical knowledge about subject matter and pedagogy;
* any radical reform will involve change in these teachers' practices and consideration of new knowledge (p. 67)

UIC's CPMP staff further believe that:
* teachers are motivated to help their students (majority African-American and/or Latino) to learn more, and more significant, mathematics.
* teachers need to experience the new ways of learning for themselves.
* teachers need massive and ongoing support at the school level to make and internalize these changes.

The last of these assumptions was the foundation for insistence that CPMP be a comprehensive, year-round school program. Therefore the competition for a school's participation was a lengthy process for determining the likelihood of program support, including site visits and a competitive written application. The school's commitment was formally recorded on a signature page for major school players, from the principal to the participating mathematics teachers.

2. More time on mathematics
Students were to receive more time on mathematics. Teachers generally did not enter the program to learn more mathematics; most felt that regular university courses were the way to learn mathematics. However, they were willing to do almost anything that would help their students. UIC staff's plans for in-service called for teachers to work together through math activities suggested for their students. Because the approach was so different, it was necessary for them to experience the activities as learners: working together, experimenting, discovering and writing about their discoveries. In this model, teachers would learn new mathematics content, if necessary, or gain a deeper understanding of the math they knew, in a comfortable environment that they would want to duplicate for their students. Teachers often chose to learn more, or different, mathematics in order to advance through college preparatory mathematics courses with their students.

3. Cooperative learning
An important feature of the program was the use of cooperative learning as a primary teaching/learning strategy. Many different methods, techniques, schools of cooperative learning were presented, but none as the correct way or the only way. However, teachers were asked to choose from among methods that would increase cooperation and decrease competition in their classrooms.

Dees emphasized that cooperative activities should begin with oral and/or written guidelines, clearly spelling out for students how they are to work together and what product is expected, and end with opportunities for reflection, both on how the group did on the problem/task and on how the group worked together.

The change process: Using cooperative learning is not easy for teachers with only traditional training and experience. They need experience, practice, and support. Veteran participants say that one of most important things about CPMP Institutes and workshops and is that the leaders model the desired methods, enabling teachers to experience them as learners.

In considering the factors that might inhibit change, NCTM's A Core Curriculum: Making Mathematics Count for Everyone (1992)emphasizes that teachers need opportunities to share their experiences while in the process of change:

Areas of concern might include the need for stability, a frequent longing to go back, uneasy feelings of doing things for the first time, extra expenditures of time and energy, and the difficulty in changing expectations in students and ourselves. (p. 105)

CPMP teachers experienced all of these; staff scheduled time during meetings for reflective writing, both focused and open-ended, and both small-group and whole-group discussions of the techniques of designing group work and concerns about how the groups were working. CPMP found that the average time for project teachers to become comfortable with using cooperative learning in the classroom was two years.

4. Curriculum change
The program began during an exciting time in mathematics education. CPMP teachers were encouraged to study and discuss the NCTM Standards, published in 1989, and subsequent Addenda. CPMP's emphasis on cooperative learning served to introduce the teachers to the more interactive classroom advocated by the reform movement.

To ensure that teachers re-examined their views of mathematics and mathematics teaching, CPMP in-services included in-depth exposure to a variety of innovative materials -- new curricula, enrichment supplements , manipulatives and technology (graphing calculators and computer software). Teachers worked together to re-examine their own textbooks and make recommendations about changes.

5. Leadership development
Development of teacher leaders meant providing the teachers opportunities for leadership and encouraging them to rise to the challenges. It meant giving them professional respect and asking them to take some responsibility for parts of the overall program. And it meant that while the teachers were asked to stretch themselves, the teachers could also veto something the co-directors wanted them to do.

The description of the teacher enhancement activities will show how teacher leadership was encouraged and how teachers who were ready stepped forward to take on the needed roles.

6. Team teaching
Team teaching is an essential element of the Summer Institute, contributing toward several goals. Teachers in teams of two experience some of the best elements of cooperative learning -- working together toward a common goal, and learning together about mathematics and mathematics teaching.

In sharing not just a classroom, but materials and lesson plans with their partners, as well as mutual responsibility for students, the teachers each made themselves open to another teacher. It was not a difficult next step to open their doors to other professionals. CPMP classrooms became teaching laboratories; the teachers modeled working-together and cooperation for the students and other school personnel.

The two team members continue to provide at-school support for each other during the following academic year, reducing isolation and beginning to build community. Teachers came to value feedback from each other and sought joint planning time during the school year as well.

7. High expectations
From the beginning, CPMP staff told the teachers that they were special, caring enough about their profession and their students to work really hard and to help each other. CPMP expected them to try the new methods in their classes and report back to the group on how they worked. The teachers were invigorated by the responsiveness and abilities of their students, which they were able to observe as they provided opportunities for increased student interaction. Teachers began to expect their students to work hard, to learn more challenging mathematics, and to plan for college. In turn, teachers raised their expectations of themselves. Many began doing things they had never done before -- making presentations, field-testing new textbooks, presenting requests for needed changes to their school administrations.

8. Continual teacher input/feedback, formative evaluation
The input and feedback of teachers (far more substantive than whether today's workshop was helpful) have been essential to the planning, development and modification of CPMP's in-service and support. The importance of teacher input is recognized in the "Ten key principles of staff development" (Clarke, 1994). [32]

Staff developers addressed issues of interest identified by the teachers themselves and provided a degree of choice for participants as recommended (p. 38).

Recognizing that only teachers had the necessary information about needs at the school and classroom level, CPMP staff sought assistance from participants; early on CPMP teachers freely voiced their opinions and were included in the work and governance of the project. Teacher working groups developed summer meeting schedules and planned common activities. Pairs or small groups of teachers were responsible for the content of part of each CPMP meeting.

Addressing one teacher concern, staff provided information on local funding and how to get it, and CPMP teachers began to seek Eisenhower funds for calculators or other student materials and for substitutes and expenses for attending professional meetings. When CPMP was "between funds" (1991), a committee of teacher participants prepared and submitted a proposal to Chicago's high school district office and secured a grant to pay their own stipends for the 1992 Summer Institute. [33]

Activities for Teacher Enhancement
Focus of in-services

From 1990 the program goals were embedded in observable behaviors that teachers could undertake for the sake of their students. CPMP expected that, as teachers experimented with new ideas and methods, they would become a peer support group and thereby multiply the resources available to each.

The desired mathematics program for students was described concretely as containing certain characteristics: behaviors that could be observed in the classroom, listed and briefly annotated here.
a) an active, experiential curriculum
Operationally, this meant getting the students out of their chairs and/or having them do something -- measure, build something, make shapes with their bodies, bounce a ball, take a survey.

b) cooperative learning as a primary teaching/learning strategy
Students were to work together on mathematics content, clarifying their own thinking by explaining, justifying and defending it, and become a peer support group.

c) problem-solving as a principal activity.
A "problem" was defined as something students did not yet know how to do, so much of the time was to be spent struggling with new concepts.

d) supplementary computer use for non-drill, non-practice situations
Recommended software included simulations, such as Lemonade Stand (shareware), the mathematical language LOGO and graphing programs such as Green Glob. Word processing programs and spread sheets were also used. Later Geometer's Sketch Pad, Derive and other programs were recommended as they became available.

e) routine use of calculators
Classroom sets of scientific calculators were to be available and integrated into the lessons (graphing calculators as they became affordable).

f) use of A-V and/or manipulatives
Teachers were encouraged to use the overhead projector and also to let students use it, to make presentations more flexible and interesting. CPMP advocated the viewing of prepared videotapes for math concepts and the use of videocameras to tape students' presentations. Manipulatives demonstrated included geoboards, square tiles, tangrams and always measuring tools.

g) other teaching aids to increase students' interest and involvement
Teachers were to share any such discoveries. One was an individual white board for students.

One advantage of this list format was that it helped structure the in-services, since teachers would need to experience each of these themselves if they were expected to implement them.

Another advantage of this format is that it provided an easy but non-threatening checklist for staff to use in determining which attributes/behaviors were observed in CPMP classrooms, and for teachers to use in self assessment. A teacher team could say, "We don't have computers available, but we use calculators and cooperative learning. " During the academic year, teachers were asked to consider their most "CPMP-like" class and assess the characteristics of their classrooms. (See Program Characteristics Teacher Questionnaire in Appendix 12, Teacher Evaluations)

The Summer Institute
The primary CPMP activity is the Summer Institute, with preparatory "spring training" beginning around March, was participated in by teachers from the seven schools 126 times during the first four years, as shown in Table 33. Teachers usually participated in the Summer Institute at least twice, many taking on leadership roles in the program in subsequent summers.

Table 33. Number of teachers per UIC school attending CPMP Summer Institutes and participating in the program through the following academic year (1990-1994)

The participants in all clusters during all six years are given in Appendix 11, Teacher In-service Sessions: Total Training Provided.

Designing the CPMP student curriculum: During the first few years of CPMP, the opportunity to teach a 4-week summer course, 3 hours per day, without specific curriculum requirements, expanded the range of possibilities for math teachers, who tried out new student materials together in the non-threatening environment of the CPMP meetings. Teachers in their teams of two could then effectively choose activities from among from them for their own students, adapting them as they thought best, as they planned the enrichment course for their own students. CPMP teachers were asked to let their goal for the first day be getting the students to come back the second day (and so on).

UIC staff had worked out suggested themes or strands for emphasis (for pre-freshmen, estimation and measurement of distance, area and perimeter, the rectangular coordinate system, the notion of variable). CPMP introduced teachers to a variety of innovative curriculum materials for students, from materials being written at UIC, such as Maneuvers With Mathematics (Page et al, 1992) and Teaching Integrated Mathematics and Science (Wagreich et al., 1981-91) to the Shell Center Project (Problems With Patterns and Numbers, 1984; The Language of Functions and Graphs, 1985) highlighting good points of each.

TIMS activities were used every year, because they met criteria of CPMP: complex activities that get students up out of their chairs and that take more than one student to accomplish; contentwise, they reinforce the concept of variable. Probably the most popular were View Tube [34] and Bouncing Ball. Not only were these experiments already prepared, each was accompanied by a high quality Teacher Lab Discussion explaining the concepts and where they would lead. [35]

Other activities, especially those provided by the university mathematicians, were focused on particular mathematics concepts. Excellent examples include the suggested lessons on Chicago Geography (See examples in the Mathematics Activities in Appendix 4 for students and in Appendix 10 for teachers). Many teachers used these materials to enrich the mathematics in their classes.

Cooperative learning
Teachers knew in advance that they would be experiencing cooperative learning and trying it in their classes, but many were not sure what it was. CPMP staff introduced the method as potentially very powerful for the learning of mathematics, and suggested that teachers first experiment in a limited way, in student pairs, for example, and perhaps once a week. A distinction was made between sitting next to each other but working independently and true cooperative learning, in which the content of the student interaction was mathematics and students clarified their own understanding by questioning, explaining, defending. [36] Teachers were asked to tell what happened at the next meeting; such sharing has been identified as teachers as one of the best aspects of the program.

The CPMP staff devised a variety of activities, many specifically addressing aspects of cooperative learning, such as forming groups or how to teach social skills. Materials used included Davidson, 1990, Johnson & Johnson, 1983 & 1986, Cohen, 1994, and others, and original material prepared by Dees and the teachers. (A list of resources is included in Appendix 10, Teacher In-service Sessions, along with typical meeting agendas and other sample activities.)

One approach was to give teachers an idea or lesson to work on with their partners. The task was to adapt it for a small-group student activity. Excerpts from the booklets of the NCTM Addenda Series (A Core Curriculum: Making Mathematics Count for Everyone, 1992) were used as the stimuli on several occasions.

Monthly meetings and small group meetings
The second most important activity for teachers is the monthly meeting during the academic year, usually held on Saturday at the university, 10 per year for 6 hours; and after-school meetings, 4 per year for 3 hours. Overall attendance at UIC cluster whole-group meetings averaged 25 teachers. In addition to the teachers, several school counselors attended CPMP meetings often, other school and district personnel occasionally.

Content was similar to that described above, but teachers were concerned with their individual classes, not a common curriculum. As the Curriculum and Evaluation Standards (NCTM, 1989) became more familiar to mathematics teachers, it became simpler to summarize CPMP curriculum goals as "implementation of the NCTM Standards," whether or not there was an exact correspondence of principles/ideas. The following material documents the reciprocal way in which the program evolved, through teacher input and active involvement.

During each semester of the academic year, CPMP staff developed a schedule of teachers' classes for visitation purposes. In addition to conferences at the school, staff were available for phone conferences in the evenings. In return the teachers accepted early on the responsibility and privilege of helping to support and govern, and thus became an important part of a program that they expected to continue.

CPMP subgroups (school teams, ad hoc committees, subject-matter groupings, etc.) held meetings after school or on the weekends, sometimes at a restaurant or teacher's home, sometimes organized and attended by staff. Examples are the groups collecting and organizing cooperative mathematics activities and writing proposals. Other teacher-initiated small groups met for various reasons; a notable example beginning around the third year was the loose association of calculus teachers across the schools. They met occasionally to discuss calculus and to share ideas, such as how to integrate the graphing calculator into the curriculum, and in the spring joined together in AP study sessions for students.

Leadership development
Teachers were encouraged to take on in teams of two (or more) various tasks that would be scary to do alone. During the first summer, teachers reported to the whole group on their small groups' problem solutions and their discussions. A little more formally, each teaching team was asked to show-and-tell other teachers what went well in their classes. The presenters received positive reinforcement, since the group was eager to find out about the experiences of the others: it multiplied their own learning and resources. Presenting looked easy, fun. Even the shyest teachers became unafraid to speak before the group. It was a natural next step to share the good news with other teachers not in the program -- in their own schools, in affiliated groups.

Chicago's new site management model of school governance was an excellent framework for leadership to emerge at the school. The Local School Councils (LSC's), in conjunction with the principal, were learning to take responsibility for school policies and budget. A few CPMP teachers became members of their LSC's; many teachers made presentations before the LSC about the changes and support needed for improving their math programs. Teachers lobbied for the program in various settings; by chance staff heard of a plea for funds one teacher made before a group of businessmen.

As the program grew, additional CPMP staff were recruited from among the teachers for various duties, beginning with co-planning and leading meetings and visiting other teachers' classrooms. The contributions of the teacher leaders will be seen throughout this report. By the end of the project, five teachers were regular CPMP staff members and at least 20 more had taken on paid consulting and training duties at various times.

The comprehensive program in action
Here are some examples of how it worked. Teachers met in July 1990 to de-brief the Summer Institute and to plan for Academic Year 1990-91. This is a summary of notes from their meeting. It lists CPMP staff's questions for consideration, along with a collation of the teachers' answers.

Group tests; take-home tests; problems should be more complicated and layered; how do you avoid the A-student doing all the work; statistics problems; group projects; C cutoff, B cutoff; does homework count; allowing all to contribute; various grading schemes.

[Q] Who (at your school) should be involved in CPMP activities?
[A] Teachers identified key players at their schools, including necessary staff (Who makes the schedule?) and personnel (counselors and teachers) they wanted to recruit to work with CPMP.

[Q] How do you see CPMP working at your school next year (1991-92)?
[A] Teachers asked/recommended:

• the freshman classes (double period) expected for AY 1990-91. What happens to this group? Would like a summer school in geometry Summer 91. Keep students together for second year if possible. Keep these teachers for two years; add two new teachers one algebra-trig, one geometry. LSC (at one school) will fund 2 classes for summer 1991 if University doesn't.
• another group (of students) in Summer 1991. Try to involve other teachers and other departments (like Banning model).
• keep this group together, have geometry teacher in mind. Ideally recruit a new group of students, one double-period algebra each year. Try to get Principal's scholars involved next year.
• design a program involving both math and science teachers?

[Q] What do you want from the university?
[A] Teachers asked for:

• encouragement for other teachers;
• Problem Solving Tests for fall (The teachers make arrangement to pick them up, for administration week of 9/11/90.)
• meetings: Most like meetings entire group. Perhaps bi-monthly; buddy schools not enough; sharing esssential; newsletter is a good idea. But not only sharing - brainstorming - fix topic in advance. Write out sharing report in advance? End each month with objectives for next month.
• presentations to this group and other teachers (not just this group!)

As illustrated in the above notes, teachers from the 1990 Summer Institute had made it clear that they wished the program to continue. CPMP staff agreed to seek more funds and the teachers were responsible for recruiting new teacher teams from their schools. By the end of the year, interested fellow teachers had discussed and observed the freshman algebra class and had some knowlege of the hard work and extra time involved, and so were able to decide whether to apply. CPMP planned that the second year teachers would each pair with a new participant, to more easily share the program's principles and activities.

Thus 1991 teachers were chosen based on the following criteria:

• their expressed interest and commitment,
• whether the original team felt the new participants would be a good fit with themselves in the intense teamwork, and
• the teaching needs for the summer laboratory classes for their own students, as determined by the original CPMP team and school administration.

In the schedule below, returning teachers are in bold. The two Lake View teachers, who became and still are leaders in the reform effort, successfully argued for staying together to consolidate what they had learned over the algebra year.

Summer Institute 1991 seemed like a three-ring circus, with (at least) four different curricula. The second-year teachers took seriously their responsibility to disseminate their knowledge and materials. (CPMP did not use the "coaching" model, but sharing between equals.)

During the summer, two open-ended questions were asked of the CPMP teachers.
1. What are the good things about the summer program?

a) for the kids
b) for teachers

2. How can we get them to continue during the academic year?

a) for the kids
b) for teachers

Briefly, here is the gist of teachers' answers. (Full collation in Appendix 12, Teacher Evaluations.)

About a third of the good things for the kids concerned the low-stress, comfortable atmosphere, another third, a head start on school, and the rest, opportunities for students to interact with others.

For teachers the low pressure atmosphere was important, with time for preparing, experimenting and reflecting, as well as the opportunities for them to interact with others.

To get the good things for kids to continue, teachers took responsibility for maintaining the program within their own classroom and suggested extending in-services to other teachers and other departments within their schools. Suggestions included student mentors, counselor involvement, credits to be given, and scheduling changes.

Teachers wanted interaction to continue and increase, at the school level by having prep periods scheduled with their partners, and sharing across the program in meetings and through mail runs.

Thus, by the end of the second summer, teachers were recommending not only things to do in their own classrooms and in CPMP activities, but had also turned their attention to making changes in their schools.

Notes taken at the September 14, 1991 meeting (in Appendix 12, Teacher Evaluations) show that teachers were very enthusiastic about their fall classes and therefore the program, were eager to share successes with the CPMP group, and wanted the principles to spread at their schools. Teachers wanted to have input toward change in their schools.

The notes illustrate how, in the meetings,

* discussion of the philosophy and principles of the program,

* cooperative learning techniques,

* feedback/evaluation, and

* leadership development through planning and taking responsibility

were integrated at the meetings and therefore difficult to separate.

For teachers not ready to participate fully in the program, and for additional support at the request of CPMP teachers, staff developed introductory short courses in cooperative learning techniques. Short courses in cooperative learning (in mathematics and/or science) have been offered for CPS lane-advancement credit seven times at various schools throughout the city (Appendix 11, Teacher In-Service Sessions). These short courses became a major component of the "spring training," but other teachers were actively recruited, to increase awareness or and support for other teachers not able to participate in the full program. The formal in-service components are summarized:

Summer Institute, CPMP immersion [38] consisting of

Pre-summer Spring Training 60 hours

Summer afternoons, following morning laboratory classes 30 hours

Total 90 hours

Courses

UIC Continuing Education courese, not for degree credit, not on grant time, tuition paid by teachers (not emphasized)

Short courses (15 contract hours) developed and led by CPMP staff and approved by CPS staff for lane advancement

The teacher network: a peer support group

Going to an afternoon meeting after an exhausting day at school was a little bit easier for teachers who knew that refreshments and parking stickers would be waiting, along with friends, old and new. It was at a CPMP family potluck dinner that a teacher said, "I feel like this is my faculty, and not the teachers at my school."

When the teachers themselves began giving workshops and teaching short courses, they usually followed the CPMP meeting model, bringing refreshments to the first in-service meeting or class they led and encouraging the participants in teams to provide them for succeeding meetings. Meetings usually began with some variant of the mixers CPMP used, usually a math "opener" and/or pair-interview-and-introduce activity.

The overall program described above was constantly evolving through the formative evaluation that was an integral part of the program. Teachers gave immediate feedback, oral and written, about the meetings. Open-ended questions both provided information for staff and stimulated the teachers' reflection and discussion. This question given in July 6, l992, pushed teachers to visit each other:

Describe your visit to another team's class.

(If you have not visited yet, when do you plan to do so?)

Reflection informs practice for CPMP teachers and staff

Individual and group reflection contributed to the evolution of the program as CPMP staff responded to feedback. Here is an example:

In May 1994, as the first cohort of CPMP students were preparing for graduation, teachers were involved in spring training for the fifth Summer Institute. The monthly meeting provided time and place for assimilating new teachers into the ongoing CPMP network. The method included group discussions like the one held May 17, 1994, structured as follows:

Guidelines: Discuss in your group, and come to consensus on:

If you had to describe or explain our program to another professional, what would you say?

In brief, what is a CPMP teacher?

An overall list was collated from the resultant whole-group discussion and appears in Appendix 12, Teacher Evaluation. One favorite was,

A CPMP teacher is a warm, caring, cooperative, industrious, and tired person.

Teachers were also asked to evaluate the meeting individually in writing, also included in the Appendix 12. Here are the three questions, along with the most brief of the teacher responses and two a little more eloquent.

1. What were your expectations of today's meeting?

2. Were your expectations met?

3. How do you feel about the meeting?

I expected to sleep.

I woke up.

It was a good meeting and I learned a lot, also nice group.

To meet with all (most) of my CPMP Lane teachers and decide on the summer program. This was not quite met.

I didn't expect every activity to go on according to the agenda and it did. Very good.

I did not expect to work on a very nice mixture problem and was pleasantly surprised.

This has been a very good beginning for our summer institute.

I wasn't sure what to expect. I thought we would spend some time actually planning for the class we'll be teaching this summer.

I think it was a well organized and well run meeting. I am glad I got the chance to meet other teachers. I enjoyed the wine/water problem. The calculator presentation was helpful since I have limited experience using them. Thank you for the hand-outs and for lunch. Again, I thought it was very organized and worthwhile. Talking to other teachers about the summer program was a good idea.

The teachers' comments illustrate the atmosphere of mutual respect and trust between and among CPMP staff and teachers.

Teacher Outcomes

CPMP met its goal of developing a core of teacher leaders able to work with and within their schools and school systems to rebuild and/or strengthen their college preparatory mathematics programs. Some of the teacher outcomes were expected and planned for; others were bonuses, arising from the synergy of the group: the whole is sometimes greater than the sum of its parts.

Changing attitudes toward mathematics and mathematics teaching

Teachers began in varying degrees to view the nature of mathematics as an organized but still growing body of knowledge, as opposed to a collection of algorithms and formulae to be memorized. They began to feel competent to make decisions about content that needed to be included, such as probability and statistics, data analysis, use of computers for spread sheets and graphing utilities. This necessitated the harder questions, about what should be omitted. Here they were helped by the NCTM Standards' list of suggestions--what should be increased and what should be decreased.

Teachers made a major leap in abandoning the outdated idea that students should not be allowed to take regular high school courses such as algebra until they mastered the basic skills of elementary school. In the Summer Institutes, teachers saw for themselves that students could expand their understanding of fractions when the need for them arose in an interesting probability context. Such experiences built support for more heterogeneous classrooms and for a decrease in tracking.

Change in instruction: use of cooperative learning

During the Summer Institute 1992, a third curriculum was added. The rising juniors were given a class at UIC. Both students and teacher teams were integrated across schools. At half-way through the summer, a "midterm evaluation" was administered to all teachers, including these two questions:

1. Is this summer experience what you expected? How the same? How different?

2. There are several aspects of the desired program. For example:

team teaching

cooperative learning

implementation of the NCTM Standards

innovative curriculum

less teacher-directed

more student oriented

more manipulatives

use of appropriate technology (calculators, computers)

For each of the above:

a) How satisfied are you with your team's efforts

b) what could we have done/ can we do to help you in this area?

Question 2 was complicated and space-consuming, included here to illustrate the detailed reflection requested from teachers.

Replies to Question 1 are given in full in Appendix 12, Teacher Evaluations. The responses and others over the life of the project indicate that new teachers are sometimes preoccupied with techniques.

Same: I expected the classroom to be active and that the kids would enjoy doing math; I expected to learn how to design cooperative lessons; I am getting a sense of the ability level of the entering freshman; Exposure to curriculum materials. Different: I expected a more structured curriculum and a more explicit set of goals for the summer; I expected more training in designing and executing the lessons; too much time in meetings that are not productive.

... same as I expected in that it is an opportunity to try out and learn how to carry out new activities. It is also an opportunity to try out and learn cooperative learning methods. I didn't expect it to be so hard. I didn't expect to feel like a new teacher again, in the sense that I'm not sure what will work and what won't until we try it.

Some time during the second year, the teachers begin to be comfortable with cooperative learning, begin to have more confidence in themselves.

Same: Yes, I'm teaching the same class, so I know what materials need to be covered in the eight-week period. Different: I am using different techniques, more manipulatives; lecturing less; enjoying myself and the class more because I know what is expected of me; helping to train a new teacher; being more responsible because of past experiences; and attending more training sessions than last summer.

Yes indeed! We planned, we delivered, and are in command! We've done more group activities than last year. It seems like we have more resources.

The third year teacher group really seemed to be having fun.

No. It is better in many ways: my partner turned out to be an "advanced" person in so many ways. I knew he was good, but . . . The training is more organized and on target. Good for pi's and pi²'s especially.

This summer's session was good. In addition, I enjoyed working with my partner who was a pi². We have worked together in our school for nine years and have never been as close as we are now. I could say she was/(still will be) my mentor. In addition, our kids have been introduced to several things in Pre-Geometry that will help them in the school year to come.

Interpretation: On average, it took about two years for a novice teacher to become comfortable with CPMP approaches.

Reflection on practices

As illustrated, teachers were asked to reflect on how their lessons went and what they could have done to make them better--more interactive, more clear, more exciting.

This process was internalized by many teachers, and they offer unsolicited reflections as well.

One teacher, on being visited during one of her noisier classes, explained the problems the groups were having, and said, "I'm not there yet!" (At the next meeting, copies of an article from Cooperative Learning magazine called, "You never get there!" were distributed.)

Empowerment to take leadership roles

As the project has grown in size, the form of governance has changed to make use of the talent and skills among the empowered teachers, five of whom work as coordinators. Baldwin, Biddulph, Dees, and Horn met as the Steering Committee at least bi-weekly through academic year 1994-95 to reflect, work and plan. The Year 2 report, submitted in December 1994, was a group task: various sections were written by subsets of the committee and reviewed by others. The Co-Directors and teacher-coordinators formalized this in the notion of a larger steering committee across clusters.

Several Chicago CPMP teachers now write proposals and negotiate directly with universities, CPS and the CSI, having established their credibility both as teachers and teacher educators. Horn, Small and Slaughter have described their current work in Chapters 5, 8 and 12 of this report.

Continued professional development

In June 26, 1991, after the first Spring Training and at the beginning of Summer Institute, teachers were asked to respond in writing to questions including, "What do you want for yourself professionally out of CPMP this year? One teacher said, "That's funny; I never thought of professional goals for myself." She was typical of CPMP teachers in being motivated primarily by her dedication to teaching and by her students' needs. Later, she said,

* This summer with CPMP, my classroom has been visited more than in the 20 years I've been teaching.

* You (UIC staff) treat us like professionals.

A year later:

* We've been professionalized.

Another year later:

* We've been empowered.

The majority of CPMP teachers now belong to professional organizations, state and/or local, and attend conferences en masse. Many teachers can now qualify for group discounts for NCTM registration without leaving their schools.

Teachers also undertake and/or continue formal education at local universities. Some are working toward Type 75 (administrative) certificates. Four of seven students who entered UIC's new PhD program in mathematics education in 1995 were CPMP teachers.

Moving toward the Interactive Mathematics Program (IMP)

The joint preparation of curriculum materials as described above was a rich learning experience, but extremely difficult and labor-intensive. Seeing the possibilities made the teachers even more dissatisfied with the traditional and/or outdated textbooks provided in their schools. After the first Summer Institute, CPMP teachers in 6 of the 7 schools changed to the McDougal-Littell Algebra, at that the time the text most oriented toward problem-solving, cooperative learning and the integration of geometry with algebra.

As teachers attended professional meetings, they continued to actively seek new materials oriented toward problem-solving and inducing student interaction. CPMP became aware of the Interactive Mathematics Program (IMP) curriculum, and invited Diane Resek, an IMP author and director, to meet with CPMP teachers at an NCTM meeting. Margaret Small and Carol Caref, teachers at Lake View High School, actively pursued involvement in IMP.

Also, as students matured and needed higher level mathematics, it became impossible for teacher teams to design their own materials. And as the number of teachers grew, it was more difficult to monitor and support teacher teams all teaching their own curricula.

CPMP needed some prepared materials that were Standards-based, so that teachers and staff could concentrate on the staff development needed for implementation and/or simply bringing new participants to an awareness level. The Interactive Mathematics Program (IMP) was a natural choice. This curriculum contains approximately 20 units, each organized around a major problem. Student group work is assumed. IMP features a discovery approach to learning, challenging (smaller) problems, called Problems of the Week (POW's), a significant amount of writing, and the use of assessment rubrics. [39]

IMP curriculum units introduced in Summer Institute

In 1993, with UIC's NSF funding and in cooperation with IMP National, UIC staff and IMP teacher-leaders continued to visit IMP sites and attend training, both in California and in Chicago. In Summer 1993, with permission of the Directors at IMP National, CPMP used The Game of Pig, an IMP unit, as the core mathematics in the Summer Institute. This unit is based on a central problem and pushes teachers to change their teaching style, mode of assessment, and view of mathematics. About half the time in the laboratory classes was spent on IMP material. For the other half, the teachers developed activities which complemented and expanded on that material.

For teachers, this involvement with the curriculum provided:

* ready-to-go student materials that made it possible to concentrate on the mathematics and the pedagogy;

* a curriculum that was already designed for students working together in groups;

* awareness of the mathematics recommended by the NCTM Standards, such as probability;

* an in-depth trial for those teachers who were seriously thinking about implementing IMP; and

* a common experience for the participants.

UIC faculty supported teachers in understanding the concepts of probability, new to many of the teachers. They worked with the teachers in the in-service sessions, visited classes and conferred with teachers. This faculty support continued during the academic year at a reduced rate, depending on release time.

In Summer Institute 1994, the combined UIC and DePaul CPMP clusters used as core student materials a unit of IMP. The additional teachers at Lake View who would be teaching IMP for the first time in Fall 1994 thus had the opportunity to not only attend the regular IMP training, but also, with a partner and in the non-threatening Summer Institute, try out the material with students. Other teachers would be able to study new mathematics, become familiar with the Standards-recommended approaches, and sample the IMP curriculum for possible use at their schools. The pre-Algebra classes used the first unit in the series, Patterns, and the pre-Geometry classes used Shadows, the last unit of Year 1.

In Summer 1995, coordinators of the two clusters returned to The Game of Pig, because this unit worked better as a stand-alone unit. Also, though probability was recommended by NCTM and the mathematics education community in general as a topic that should be included in modern curricula, the material on probability was new to many teachers.

But IMP in Chicago agreed with IMP National that teachers should have a choice.

A second group of teachers, teaching pre-algebra, pre-geometry and integrated math-sccience, elected to use a potpourri of innovative activities mostly organized around area, perimeter, and data analysis. A third group was composed of the teachers who taught the CPMP upperclassmen at the universities a curriculum based on applications in advanced level high school mathematics. The meeting agenda for May 20, 1995, in Appendix 10, shows a typical procedure for whole-group meetings.

A majority of the teachers were pleased with the IMP units. Even though the teachers thought much of the material was quite challenging, they found that the majority of their students became engaged by it and stayed on task. Several teachers became interested in implementing IMP in their schools.

Thus the two components were intertwined and mutually supportive. All CPMP teachers were influenced by the IMP materials, and some CPMP teachers became determined to implement the IMP curriculum at their schools.

The next chapter is an evaluation of IMP in Chicago.

About the authors: This chapter was written by Anne Horn and Margaret Small. They were members of the first group of CPMP teachers in summer 1990 and were early implementers of program principles. Horn was head of the mathematics department at Whitney Young High School, and, with the support of the principal, had been looking for ways to improve mathematics instruction. The day after the Summer Institute ended, Horn was leading a workshop she designed for Whitney Young math and biology teachers; since then she has continued making presentations at all levels of the profession.

The NSF grant enabled UIC to hire Horn full time January 1993 as Program Coordinator. In this capacity she has been responsible for planning and leading in-service sessions, organizing various activities of CPMP and visiting and consulting with teachers.

Small, a teacher at Lake View High School, was a member of the Local School Council and participated actively in the mathematics department. She took a leading role in the development of Lake View's largest and most effective CPMP team among the seven schools. With the support of the principal, Small and her partner, Rich Kaplan, led the department in changing expectations, instruction and curriculum.

Small and Horn became convinced that they had gone as far as they could go with the ideas of CPMP while using traditional curricula and textbooks. They became leaders of the IMP implementation, visiting IMP schools nationwide, participating in all appropriate IMP training sessions, and attending Directors' meetings. Both entered the doctoral program at UIC in 1995 and so assumed responsibility for coordinating the evaluation of the IMP implementation. This is their report.

The effective implementation of the IMP curriculum in three diverse Chicago public high schools, Lake View, Whitney Young, and Foreman, gives some indication of the potential for success of NSF curricula in the urban environment.

* Initial measures of student achievement in two of these schools indicate that IMP raised the test scores of lesser prepared students, and maintained the level of achievement by higher achieving students.

* IMP students are more likely than their peers in the traditional curriculum to view mathematics as an integral part of their lives.

* Staff development based on implementation of the IMP curriculum produced more rapid and sustained change in teacher classroom practice than had the previous CPMP teacher enhancement efforts.

* Teachers, with the support of IMP program staff and school administration, made critical changes necessary to use the curriculum effectively with their students.

1) Three Chicago schools are teaching IMP

IMP was introduced in CPMP for the Summer Institute of 1993, with the goal of beginning IMP 1 at two or three CPMP high schools that fall. A severe budget crisis in the Chicago Public Schools led to a delay in school opening and caused serious staff cutbacks. In the face of budget uncertainty, only Lake View High School, under the leadership of principal Donna Macey, was willing to commit to the new curriculum. Macey saw IMP as way to provide a challenging, problem-based math experience for all students.

In spring 1994, three new schools had expressed interest in implementing the IMP curriculum for 1994-5. Two of them did not have the full support of the administration even though parents and teachers were eager to move ahead. On the advice of CPMP staff, both schools decided to work for more institutional support and consider implementing IMP at a later date. The third school, Whitney Young Magnet High School, did decide to implement IMP 1 for freshmen in Fall, 1994.

Beginning in September, 1994, Lake View IMP teacher, Margaret Small, worked half time to support existing IMP sites and develop new sites for the following year. This support included visiting schools to work with the teachers interested in beginning to teach IMP in 1995. No clear program was articulated for the high schools by the Chicago Systemic Initiative (CSI), so CPMP staff and teachers made several efforts to share their experience with the CSI high schools, some of which were also CPMP schools. Small made several presentations and provided material concerning Standards-based curricula, the IMP curriculum and, in particular, the success that was occurring at Lake View and Whitney Young.

By the middle of the 1994-95 academic year, several other schools had evidenced interest in beginning to use IMP. In all cases this was driven by teacher interest in moving away from the traditional, algorithm-based curricula to a problem-centered, hands-on, inquiry-based approach. Of the interested schools, only one was able to get active support and cooperation from the principal, math department chairperson, local school council and programmer. With enthusiastic support by a core of five teachers and the principal, Foreman High School began IMP in Fall 1995. Two teachers at Foreman taught three IMP 1 classes during the academic year 1995-96.

There were 480 students enrolled in IMP at the freshman, sophomore, or junior levels during the academic year 1995-96. Five additional schools will begin using IMP in 1996. [40] This will result in about 2000 students in IMP for the 1996-7 school year.]

Chicago IMP sites        year begun   levels        # of          # of          
                                      1996-97       teachers      students      
Lake View                 1993-94     1 - 3         9             500           
Whitney Young             1994-95     1 - 3         6             380           
Foreman                   1995-96     1 - 2         6             380           
Clemente                  1996-97     1             3             90            
CVS                       1996-97     1             2             50            
DuSable                   1996-97     1             8             500           
Harlan                    1996-97     1             1             100           
Richards                  1996-97     1             1             50            

2. Development of Standards-based core curriculum in the Chicago Public Schools

The Curriculum and Evaluation Standards for School Mathematics, (NCTM, 1989), calls for three years of high school mathematics for all students based on a core curriculum. The core curriculum assumes that the curriculum topics will apply to all students and that no students will be limited to rudimentary drill classes. It is to provide a common body of mathematical ideas accessible to all students, so that doors to college programs and vocational training are kept open. This core curriculum includes the study of algebraic concepts, functions, the geometry of two and three dimensions including algebraic geometry, trigonometry, data analysis and statistics, probability, discrete mathematics, informal calculus and mathematical structures. The environment necessary for developing such a curriculum, with increased emphasis on problem-solving and decreased emphasis on computation, is discussed in NCTM's Professional Standards for Teaching Mathematics, (NCTM, 1991). The classroom environment encourages students to "make conjectures, experiment with alternative approaches to solving problems and construct and respond to others' mathematical arguments." (P. 56) Students learn to "use calculators, computers, and other technological devices as tools for mathematical discourse." (P. 52) Instructional decisions are based on the teacher's assessment of the "students' understanding of, and disposition to do, mathematics." (P. 110)

During the last decade, the Bureau of Mathematics of the Chicago Public Schools has made efforts to bring mathematics education closer to the vision of the Standards. First, to insure that technology be made available to all students without regard to income level, calculators were provided and their use was encouraged in all math classrooms. Next, the Algebra Framework was developed to provide a structure for inserting innovations based on the NCTM Standards into traditional algebra curricula. In spite of these administrative efforts, the achievement of Chicago high school students on standardized tests has not significantly improved. Recently the CSI recommended that every student complete the equivalent of a year of algebra by the end of eighth grade. In addition, the Chicago Board of Education raised the mathematics graduation requirement to three years of high school mathematics beginning with students entering as freshmen in Fall 1996. These changes present a clear challenge. A curriculum is needed that will support a significant increase in the number of students successful in completing three or four years of high school mathematics. This must be accomplished without sacrificing the Standards-recommended core of secondary mathematics.

Currently, various stakeholders are examining the mathematics programs at schools where more than 50 of students continue to fail to meet state goals on the IGAP [41]. The central administration is encouraging every school to determine whether the current curriculum is providing opportunities for increased mathematical understanding and success for all. This creates new possibilities for schools to consider the use of new curricula.

The effective implementation of the IMP curriculum in two diverse Chicago public high schools, Lake View and Whitney Young, gives some indication of the potential for success of NSF curricula in the urban environment. Initial measures of student achievement in these schools indicate that while IMP enriched the mathematical experience of all students, it raised the test scores of lesser prepared students, and maintained the level of achievement by higher achieving students. (See Test results p. 6)

One of the strengths of the IMP curriculum is that it is designed for heterogeneous classes. Chicago IMP teachers report that students are able to approach problems on a variety of levels, allowing very advanced students and those with limited mathematical experience to work together to solve problems. The teachers have observed that all students gain from this process and achieve significant growth in mathematical understanding and the ability to use mathematics. Staff development and the IMP curriculum could change the way mathematics is taught, learned and assessed, making it possible to reverse the historical failure rate in high school mathematics.

3. ]Necessary elements for implementing IMP in an urban system

The successful implementation of IMP at over 100 high schools nationwide has been based on several essential elements outlined in the IMP Dissemination Guidelines (Appendix 13). The elements found to be most critical in the Chicago use of IMP are summarized here. We believe these conditions are necessary to begin using any of the Standards-based curricula, because the process requires participation and support by all those in the education process - students, teachers, parents, administrators, and community members.

a) The single most important element in successfully implementing a Standards-based curriculum is adequate and ongoing support for teachers who are working to change their traditional method of teaching. Specifically this includes two major aspects:

Support in changing classroom pedagogy.

Standards-based teaching requires significant changes in the ways that classrooms are organized and arranged. First is the change in the role of the teacher, from information giver to guide, supporting students' investigations. Second is the change in the role of student, from isolated learner to participant in a group investigation. Students learn to cooperate with others and communicate mathematical ideas. Implementation of both these changes requires time and support.

Expanded view of mathematics

Teachers must relearn and expand their understanding of mathematics in the context of the curriculum they are implementing. They need the opportunity to investigate for themselves the mathematical concepts that arise in the context of the investigative activities and to discuss with their peers the variety of methods and approaches to these investigations that might arise in their classrooms. Only when the teachers themselves are comfortable with the mathematics can they recognize and value significant mathematics in the varied student solutions and foster the development of the mathematics based on this student work.

Because the effective use of the Standards-based curricula does require such major changes by teachers, it is important that they receive the support they need during the change process. At a minimum this should include additional professional development time during the school day each year they are teaching a new level of the curriculum.

b) Working together in the CPMP Summer Institute has been an extremely important aspect of the teacher change process towards teaching Standards-based mathematics. The summer experience allows teachers to experiment with new teaching strategies and different approaches to mathematics in a focused and supportive setting. Afternoon inservice sessions provide the context for debriefing and processing the changes teachers are attempting. The Summer Institute also allows teachers who are just beginning to question the effectiveness of the traditional curriculum to become aware of the potential benefits from moving their teaching to a more Standards-based approach.

c) Support for the mathematics reform movement and the philosophy of IMP by the school administration is necessary to sustain a climate of growth and development required for teaching Standards-based curricula in general and IMP in particular. Since IMP is a departure from the traditional curriculum it is necessary for IMP teachers to engage in discussions with other teachers, department heads, counselors, LSC members and other administrators to create an understanding of and support for the IMP curriculum. Teachers can show how IMP is aligned with the State Goals for Learning and the Student Learning Outcomes.

d) Eighth-grade parents and students must make an informed choice about participation in IMP. An integrated problem-based approach to learning mathematics is a different experience from the traditional Algebra-Geometry-Trigonometry sequence. These strands appear throughout the curriculum and do not appear in separate form as in the traditional courses. After obtaining all relevant information about the curriculum, parents should participate with students in the choice of curriculum that will best serve the students' plans and goals.

e) A student-centered high school mathematics environment encompasses several elements. Classes should contain students of all ability levels. Work is done in groups that have ready access to graphing calculators at all times. Assessment is integrated with instruction. Students are encouraged to work together on long-term, open-ended problems. These elements are all part of making challenging mathematics accessible to the diverse students in our schools.

The following measures of student mathematics achievement, student and teacher attitude toward mathematics, and a case study of one teacher's process of change over two years of teaching IMP document some of the effects of initial use of IMP curriculum at Lake View and Whitney Young High Schools.

4. Analysis of student outcomes

a) Test data

Students at Whitney Young, Lake View and Lane Tech were tested as part of the overall evaluation of the IMP implementation in Chicago. The purpose of this testing was to determine how the performance of IMP students on traditional standardized tests and on problem-solving performance assessments compared to that of similar students taking the traditional curriculum. In 1994-95, at both Whitney Young and Lake View, gain scores were calculated based on fall and spring administrations of a version of the PSAT. In 1995-96, a commercial mathematics performance assessment was administered to IMP and comparison groups at both Whitney Young and Lake View. PSAT scores from all Whitney Young sophomores taking IMP 2 and Geometry were analyzed using eighth-grade ITBS math scores as covariate. Details are given in Appendix 14, IMP Student Performance: Summary of Tests and Testing Conditions.

1) Whitney Young results

Three test measures have provided the results summarized below.

(a) Freshman PSAT Results, 1994-95

The IMP 1 classes gained significantly between fall and spring administrations on two forms of a math section of the PSAT. Comparison Algebra I classes at Whitney Young made no significant gain. Table 5-1 [42] shows that the IMP 1 group had a higher average gain score than the Lane Tech CPMP Algebra group but this difference was not significant. The IMP 1 gain score was significantly higher than the gain score of the Whitney Young Algebra I group.

Table 5-1. 1994-95 PSAT Gain Scores: Whitney Young IMP 1 and Comparison Groups

School and Class            Number of    Average Gain Score  T-test Result          
                            Students                                                
Whitney Young/IMP 1            108       1.14                                       
Lane Tech/CPMP Alg. I          55        0.85                p = .29                
                                                                                    
Whitney Young/IMP 1            108       1.14                                       
Whitney Young/Algebra I        48        .04                 p = .03*               

(b) Sophomore PSAT results, 1995-96

The PSAT was administered to all Whitney Young sophomores in October, 1995. The scores of the sophomores using the IMP 2 curriculum were compared with the scores of sophomores taking regular and honors geometry (Table 5-2). An analysis of covariance of the PSAT scores was done using with eighth-grade ITBS math scores as the covariate. The analysis was also run without controlling for previous test scores. Both types of analyses showed no significant difference (at the .05 level) between the IMP 2 classes and all Geometry classes on the Math or Verbal sections of the PSAT.

Table 5-2. 1995-96 Sophomore PSAT: Whitney Young IMP 2 and Geometry

     Group        N      ITBS      Math      Range of   Math         Verbal   
                         Mean      PSAT      Math PSAT  Standard     PSAT     
                                   Mean                 Deviation    Mean     
IMP 2             110      77.1    45.5      30 - 63    6.0          51.3     
All geometry      250      80.1    46.7      23 - 71    7.8          50.3     

(c) Sophomore performance assessment, 1995-96

Whitney Young IMP 2 students scored higher than Lane Tech CPMP geometry students on a holistically scored mathematics performance assessment given in November, 1995, but this difference was not statistically significant (Table 5-3).

Table 5-3. 1995-96 Sophomore Performance Assessment: Whitney Young IMP 2 and Lane Tech CPMP Geometry

      Class         School            Number of         Average Score on        T-test         
                                      Students          Performance Assessment  Results*       
IMP 2               Whitney Young            25         12.2                                   
CPMP Geometry       Lane Tech                33         11.2                    p=.09          

2) Lake View Test results

Two test measures have provided the results summarized below.

(a) PSAT Scores, 1994-95

The IMP 2 classes gained significantly between fall and spring administrations of two forms of the math PSAT (at the .05 level). Comparison Geometry classes from Lake View made no significant gain. Table 5-4 shows that although the IMP 2 group had a higher average gain score than the CPMP Geometry group, this difference was not significant.

Table 5-4. 1994-95 PSAT Gain Scores: Lake View IMP 2 and CPMP Geometry

       Class         Number of      Average Gain Score  T-test Result          
                     Students                                                  
IMP 2                     35        1.02                                       
CPMP Geometry             43        0.34                p = .34                

(b) Sophomore and Junior performance assessment, 1995-96

Table 5-5 shows that the IMP students at both the sophomore and junior levels scored significantly higher than the students in the traditional curriculum on a holistically scored mathematics performance assessment given in November, 1995.

Table 5-5. 1995-96 Sophomore and Junior Performance Assessment: Lake View IMP 2 and CPMP Geometry, Lake View IMP 3 and CPMP Advanced Algebra with Trigonometry

          Class            Number of     Average Score on        T-test         
                           Students      Performance Assessment  Results*       
IMP 2                           22       8.3                                    
CPMP Geometry                   19       5.4                     p=0.015        
                                                                                
IMP 3                           23       7.3                                    
CPMP Adv. Alg./Trig             28       4.7                     p=0.006        

b) Attitude survey

A questionnaire probing student attitudes about mathematics and their mathematics classroom was given in December, 1995, to the six classes involved in the November performance assessment. Results are reported if there was a difference of more than 15 between the responses of an IMP class and its CPMP comparison. Complete results are in Appendix 15, IMP Student Attitude Survey Results; some results of special interest are discussed below.

One goal for a problem-based, contextually situated mathematics curriculum is to enable students to make more connections between school mathematics and mathematics for living. Among the students surveyed, IMP students were more likely than the non-IMP comparison students to feel that mathematics is something they do every day as a natural part of living, that they do math mostly in their heads, and less likely to feel that mathematics is done mostly at school and with a pencil and paper. (Result A)

The idea of mathematics as a finite, unchanging body of knowledge existing outside the control or inventions of mankind is held by many students and teachers. The valuing of different mathematical ideas developed by students in the IMP curriculum is intended to help students develop a more dynamic view of mathematics. IMP students were less likely than non-IMP students to feel that the ideas of mathematics have always been and will always be true. (Result B)

In the IMP curriculum, students develop the mathematics by themselves to solve the large problems encountered in the classroom. An intended outcome of this process is for the students to feel that mathematics is developed and owned by the people who use it. IMP students were less likely than comparison students to agree that the ideas of mathematics were invented by mathematicians, that mathematics was discovered by mathematicians, and more likely to feel that mathematics was developed by people as they needed it in daily life. (Result B)

IMP students are encouraged to develop a broader view of appropriate ways to express mathematics. IMP students were less likely to think that the ideas of mathematics are most clearly explained using numbers or that mathematics can only be explained using mathematical language and special terms. (Result C)

The IMP curriculum emphasizes writing as a primary expression of mathematics. Among CPMP classes with comparable students, the traditional, axiomatic geometry class at Lane Tech, based primarily on deductive proof, involves much more writing than any of the other traditional mathematics classes. Nevertheless, the Whitney Young IMP 2 students were more likely than the Lane Tech geometry students to agree that writing is an important way for them to sort out their ideas in mathematics. (Result D)

The IMP and non-IMP CPMP groups responded quite differently about their classroom processes, even though students in both programs sit in groups of four and spend much of their time working on problems together. IMP students were more likely to report that they often spend time in mathematics class writing words, working with a group, and listening to other students, and less likely to report that they often spend time in class writing numbers, copying from the board, or working from a textbook. (Result E)

An emphasis of the IMP curriculum is on shifting the perceived source of mathematical knowledge from the teacher to the student. Fewer IMP students than non-IMP students rated "the help my teacher gives me" as the first or second most important part of their mathematics course. (Result F)

5. Analysis of teacher outcomes

Inclusion of the IMP curriculum in the CPMP program has increased the effectiveness of the CPMP teacher enhancement program. IMP requires substantial changes in teaching practices for its successful implementation. Conversely, using the curriculum facilitates significant change in the teachers who are using it. The major areas of change required for and facilitated by the curriculum are: teacher view of what mathematics should be taught, integrating the use of graphing calculators on a daily basis, expanding the view of the tools and uses of assessment, expanding the repertoire of instructional strategies, shift from teaching in a tracked to a heterogeneous classroom, and shift from a teacher-centered to a student-centered environment.

Documentation of this change has centered around the eleven teachers who are using the IMP curriculum as their regular academic-year curriculum and 35 teachers who have used an IMP unit in the Summer Institute portion of the CPMP teacher enhancement program. The sources of data are teacher questionnaires and journals, staff observations with written reports, and interviews of teachers by staff.

a) Case study

Appendix 16, Context for Learning: an IMP Teacher Case Study, contains a case study of a teacher who has now finished his second year of teaching IMP. The study examines three areas of the process of change as experienced by this teacher: his views of curriculum, of mathematics, and of the role of the teacher in the classroom. The teacher profiled has much in common with the other teachers in the program. He made gradual positive changes in the two decades prior to his introduction to IMP. The changes toward creating a student-centered classroom since implementing the curriculum have been dramatic and accelerated.

The study was done by CPMP program coordinator, Anne Horn. She and this teacher co-led the 1995 IMP Summer Institute staff development and co-taught an IMP 2 class during the academic year 1995-96. The material is derived from observations, and interviews with the teacher, his students, and other teachers on the Lake View staff.

b) Teacher survey

The eleven teachers teaching IMP at Lake View, Whitney Young and Foreman responded to questions from the IMP Demographic Survey: Teacher's Questionnaire (Wisconsin Center for Educational Research, 1993.

The survey summarizes the views of the teachers regarding using the IMP curriculum. It elicits responses on important conditions for teaching IMP, pre-IMP classroom environment, use of technology, assessment, mathematical content, benefits to students and teachers of using IMP, and teaching strategies important to IMP. Two of the teachers were in their third year of using the IMP curriculum, three in their second, and six in their first year. Survey results are given in Appendix 17, IMP Teacher Survey Results; several of special inerest are discussed here.

When the teachers were asked to rate factors for effectively teaching IMP, the factors receiving the highest ratings were availability of graphing calculators, sharing and discussing work with other teachers, having students do investigations, students' regular attendance to classes, and knowledge of new teaching methods. (Result A)

The teachers were asked to describe a typical class before they started to use IMP. They described a range of attempts to incorporate aspects of the NCTM Standards into a traditional curriculum. Some were asking students to work in groups to solve homework problems in the last part of the class period. Others were trying to change the actual lesson in traditional mathematics by transforming it into a discovery lesson or by bringing in supplementary materials and activities. (Result C)

The survey indicates that calculator technology was used appropriately in all the IMP classes. Computers were used extensively at Lake View, as often as suggested by the curriculum at Whitney Young, and not at all at Foreman. This had to do with the availability of computers and not with the desire or ability of the teachers. (Result D)

Although the IMP curriculum presents multiple opportunities for alternative assessment, teachers do not immediately change their ways of assessing. When asked how they assigned grades to their students, teacher responses showed that they were in transition from traditional ways of assessing to incorporating alternative assessments, and that they were in very different places on the continuum. On one end of the scale, a teacher lists homework, tests, classroom participation and presentations as the basis for her students' grades. Others who list these also add special projects, "problems of the week," portfolios. The teachers have varying levels of understanding of holistic scoring. Some do not mention holistic scoring, while others articulate carefully thought-out holistic principles that they apply to assessments and to assigning student grades. (Result E)

When asked to tell what important content is missing from the traditional curriculum at their schools, all the teachers listed probability and statistics as being inadequate or missing from traditional curricula. Some also mentioned discrete mathematics, mathematics connected to technology, and logic. The teachers listed important curricular format that was missing from the traditional curriculum at their schools: connections between various mathematical areas, mathematics presented inductively, genuine problem-solving, and connections to real-life areas such as politics and nature. (Result F)

When asked how they expected their students to benefit from IMP, no teacher listed specific mathematics skills or content. They expected students to benefit by beginning to see themselves as persons who can do mathematics, by being able to attack difficult problems in ways that are transferable to other areas of life, by being able to effectively use technology and interpret important statistics, by cooperating and communicating effectively and by participating in an intellectual community. (Result H)

Teachers expect to benefit from IMP because it is a fully-developed curriculum, leaving them free to concentrate on teaching and learning issues. "Before IMP, I was just passing along knowledge I already had. Now, I am constantly learning mathematics and seeing connections, making me more aware of the process my students are going through." (Result I)

The teachers' views on what teaching strategies are most important to effectively implement the IMP curriculum include appropriate pacing, asking the right questions, keeping students engaged in problem-solving and constructing knowledge, and allowing students to experience success in a framework of high expectations. (Result J)

6. Comparisons to other IMP implementations

The Chicago IMP directors attended the yearly meetings of National IMP Site Directors in 1994, 1995 and 1996, and have visited urban implementations in Philadelphia, Boston, and Phoenix, as well as schools using IMP in Tracy, San Jose and Berkeley, California.

Characteristics common to the Chicago IMP experience were observed in these site visits. Students were actively involved in examining the relationships and patterns related to their activities. They responded openly to the questions of visitors participating in their small groups. They appeared comfortable talking about the mathematics and were able to explain in their own words what they were doing. The classrooms had a "work in progress" atmosphere which functioned more like an office than a traditional classroom.

Major differences exist in the scope of implementation and systemic support for IMP in different cities. All the schools visited had more teachers using IMP than any one school in Chicago. A larger percentage of the schools in each system was involved in trying new Standards-based curricula than in Chicago. In Philadelphia and Phoenix, a close working relationship between the local Urban Systemic Initiative and IMP was evident. Questions related to expansion and resolving problems with implementation were addressed on a system-wide level. In Boston, expansion has included large suburban districts looking for Standards-based curricula. In contrast, the limited expansion in Chicago reflects the lack of systemic support for curricular change.

A primary strength of the Chicago implementation is the process that allows teachers to move towards Standards-based teaching at varied paces. The Summer Institute gives teachers four weeks to practice the new methodologies and discuss the new mathematics involved, outside of the extreme pressures of the regular school year. The Institute also allows for the formation of professional bonds between teachers at several schools. This provides additional support when problems emerge during the academic year. The Chicago implementation has benefited from the support it gives teachers during the critical months before and during the first year of teaching the new curriculum. In each of these other sites, there is greater unevenness in classroom implementation, when judged by the NCTM Standards, compared to our three-year experience in Chicago.

7. Conclusions and recommendations

The Interactive Mathematics Program curriculum is appropriate and desirable for the range of students and teachers found within the Chicago public school system. Teachers and their students using the IMP curriculum are experiencing success in mathematical growth in heterogeneous groupings in three very dissimilar schools.

Teachers are able to learn the new mathematics and to make the changes in their classrooms required to teach within a Standards-based curriculum. The support teachers need to accomplish these changes varies, but the minimum support includes time to work through the problems in the curriculum and time to discuss the mathematical and pedagogical issues with their peers and those more experienced in Standards-based teaching practices. The changes in classroom practice of teachers using the IMP curriculum has been more rapid and sustained than of those in the CPMP program without a particular curriculum.

The need to nurture students to promote learning is strong in the urban environment. The demonstration sites at Lake View, Whitney Young, and Foreman evidence success in creating this nurturing, student-centered environment in the mathematics classroom. As we enter the 1996-97 academic year supporting new IMP teachers in five more schools representing the complete racial and economic range of schools in Chicago, we are confident that more students will engage and understand more relevant mathematics than has ever been possible in these schools.

The above report was written by Horn and Small, IMP Co-Directors, in Summer 1996. The IMP implementation began as a subset of CPMP and is now becoming an independent site. Further discussion will appear in subsequent chapters, and an IMP update will appear in Chapter 12, Epilogue.

Section II has summarized the features, activities and outcomes of the first CPMP cluster, consisting of The University of Illinois at Chicago and 7 Chicago high schools. In this section, efforts to share the good news and sort out and disseminate the successful practices, up to and including the current NSF grant, are discussed.

Dissemination

To help increase awareness of the need for reform in mathematics teaching, CPMP staff and teachers participated in a variety of activities: workshops for teachers at their own or other schools--for math departments or entire faculties, within elementary schools as well. CPMP staff encouraged teacher teams to give workshops for teachers and presentations to various professional groups, and it became commonplace for CPMP teachers to lead several sessions at area meetings such as Illinois Council of Teachers of Mathematics, Wisconsin Mathematics Council, and Purdue University's annual Conference on the Improvement of Mathematics Teaching. Highlights have included national meetings of National Council of Teachers of Mathematics and the Association for Supervision and Curriculum Development. And eight teachers participated in the International Conference on Cooperative Learning in Toronto, sponsored by the International Association for the Study of Cooperation in Education (IASCE), in May, 1993. The Co-Directors of all clusters have participated in appropriate mathematics, mathematics education and scientific literacy meetings. Over the life of the project, over 150 such presentations were given by teachers and over 50 by faculty.

Such activities developed considerable interest and inquiries about participation in CPMP. But since CPMP is a school program, and because of the intense year-round level of support, a limited number of schools can be accommodated in the cluster model.

Evaluation

Staff had not been able to evaluate the success of the student program as intended; test answer sheets were accumulating beyond resources to analyze the results. And the project would need hard data to convince principals and District administration to support this or similar reforms in other schools, or even to maintain current CPMP support.

The teacher enhancement program also needed documentation. Formative evaluation was an essential feature of CPMP. A common format was an oral or written stimulus along with guidelines for some combination of

small-group discussion,

whole-group discussion,

individual writing,

group writing,

sharing/reporting/presenting,

with the product handed in to staff.

Questions for reflection on practice were embedded in the in-service; the content came from a subset of the following, stated very simply here:

what are the positive, negative aspects of the (ongoing) program?

for the positive, what made it work?

for the negative, how can it be improved?

what aspects of the program do you personally want to continue in your classroom, at your school?

how will you accomplish this if CPMP is not funded any more?

what steps have you taken/will you take toward this goal?

who at your school can help you?

Such reflection on practice often gives the stimulus and/or motivation to make changes and take steps. A teacher observed during her second year, "You were always asking us (in questionnaires) whether we used overhead projectors, manipulatives, calculators--we finally figured out we were supposed to be doing that." The processes modeled in the in-service sessions were often seen again at the school, at team or department meetings, at workshops that CPMP teachers delivered, and in teachers' classrooms.

The many written materials described above needed to be collated, organized, analyzed and reported. The effectiveness of the principles and techniques employed needed to be shared with school personnel in decision-making positions.

Some of the results of NSF's support for these evaluation efforts have been given in previous chapters.

Expansion

Decision to expand

From the "word-of-mouth" advertising of individual teachers, students, and parents, others contacted CPMP staff, wanting to get involved. This was a desirable outcome, but the staff was reluctant to add more schools for two reasons:

* One unique feature of CPMP was the strength of the teacher network, with the intimate "family" feel. By the second year, some of the first cohort of teachers felt that the group of about 35 was already too large for teachers to get to know each other well.

* There was not sufficient staff to include more teachers and still deliver the quality and quantity of teacher support (frequency of classroom visitations, number of hours on phone calls).

On the other hand, reform in UIC's seven schools, only a tenth of Chicago high schools, would not make the necessary impact for moving toward systemic change, so there was high motivation to expand. The cluster model seemed to be a valid one, so CPMP sought partners that had similar goals (improving mathematics instruction, especially for under-represented minority students) and that would act as centers for clusters of schools.

Plan for additional clusters

In Fall 1991, CPMP cast a wide net in seeking other universities to participate in an expansion of the program. UIC first contacted colleagues known already, such those directing Treisman-type calculus workshops. Initial interest was high, with six universities persisting to the proposal-writing process. Three of these were located in Chicago, two in down-state Illinois, and one in Wisconsin. Through a series of meetings and discussions, UIC submitted on behalf of the group a Teacher Enhancement proposal with the following objective:

We propose to help organize several clusters of high schools, each connected with a university mathematician and a mathematics educator. As the lead institution, we would like to share our experience in setting up teacher groups and establishing and using connections among the personnel of the various concerned institutions (high schools, educational service centers, school boards and councils, and colleges and universities). [43]

In April 1992, NSF gave UIC preliminary approval but requested a revised proposal with a budget about 1/3 of the original request. This caused UIC to reduce the number of new clusters to two.

In the choice of universities to be the centers of these new sites, the first criterion was manageability; nearness to UIC was a key component of that. The second major criterion was personnel. The Co-Directors of CPMP at UIC were a mathematician and a mathematics educator with extensive experience working with schools and teachers. Potential sites were evaluated as to the presence of at least two committed co-directors with similar qualifications.

Based on these criteria, the two universities selected to begin CPMP clusters were DePaul University in Chicago and the University of Wisconsin-Parkside in Kenosha, Wisconsin. Between them the two new clusters brought an additional eleven high schools into CPMP. Appendix 3, Demographics of CPMP, summarizes some basic information about the clusters.

Organization of the project

CPMP Organizational Chart

Figure 6

At that time the three university partners were not clear on exactly how much responsibility for in-service came with "helping organize" and "sharing experience." Figure 6 shows a view of the consortium with the UIC core providing central administration and staff for in-service and support for all three clusters.

UWP at first seemed to look at UIC as an equal partner, not feeling a strong need for advice. DePaul staff did not seem to feel as confident about their ability to "duplicate" the UIC cluster. As Lynn Narasimhan expressed it, "If you say it takes an average of two years to 'train' teachers, then how long do you think it takes to 'train' the trainers?"

The in-service for the new clusters included participating in current CPMP sessions and visiting classrooms along with UIC staff. Some took a UIC course in cooperative learning in mathematics. UIC staff met with them in planning for their clusters, and experienced teachers from the UIC cluster were matched with each cluster to assist the university staff as advisors/coordinators.

Questions arose about how far each cluster might/should stray from the original model. Was a new cluster a replication or an expansion? Faced with conflicting schedules and different union requirements, and traditions involving summer school in the districts, the UIC staff was forced to consider which elements of the program were essential.

IMP evaluation

In Fall 1992, during the final negotiations for this grant, the Co-Directors were asked, if possible, to provide an independent evaluation of the IMP curriculum; this was agreed. Over time, as NSF Program Directors changed, CPMP's view of this evaluation changed, because of certain questions.

* How do you evaluate a program when you are in it?

* How can we allow the program to fail? Surely if something doesn't work, we will fix it.

* Since Chicago did not apply to be an independentIMP site, what is the relationship between IMP and CPMP?

In growing more familiar with the IMP curriculum, UIC staff realized the near impossibility of making comparisons of student learning of specific mathematical content between IMP and non-IMP students, because of the sequencing of topics and difference in emphases.

Faced with the double bind of the paradox in self-evaluation and the need to expend increased effort on implementation, CPMP developed an understanding of the IMP implementation as a teaching experiment. Thus the evaluation tasks were to examine the feasibililty of implementing the curriculum in Chicago schools and to evaluate student performance on broad-based achievement tests rather than on specific mathematics. Much of this work was discussed in Chapter 5.

Chapters 7 and 8 are views from the UWP and DePaul clusters, and Chapter 9 will present some views across the project.

About the authors: Skoglund was Mathematics Coordinator, K-12, for the Racine Unified School System. He came in contact with Dees through cooperative learning workshops he arranged for his District. Donna Carr was a logician in the mathematics department of University of Wisconsin-Parkside (UWP), recruited by Baldwin to work with CPMP. The following essay was prepared by Skoglund and Carr in 1995 as their portion of the project came to an (official) end.

Beginnings

Discussions concerning the participation of Racine Unified School District and the University of Wisconsin-Parkside (UWP) in CPMP were started with Phil Skoglund in the spring of 1991. John Baldwin, of UIC, then recruited Donna Carr as the Principal Investigator from UWP and she and Skoglund worked with UIC to complete the Wisconsin cluster application through the summer and fall of 1991.

The first "Success for Everyone" conference was held in February 1993 at UWP to solicit schools to participate in the cluster. Over 100 people attended but only four schools showed an immediate interest in joining the program.

Unlike the two Chicago clusters, where the number of schools applying for participation was much greater than the number requested and, therefore, the application process was competitive, Wisconsin found that they needed to actively recruit schools to the CPMP. Skoglund made contacts with other school districts and made a presentation about the CPMP to a meeting of Milwaukee high school department chairs. As a result, four Milwaukee schools showed an interest in joining the program.

From this process, six schools and twelve teachers were recruited to begin the CPMP in Summer 1993 (two from Racine and four from Milwaukee): Racine Park and Horlick, and Milwaukee Madison, Washington, South Division, and North Division. The two Racine schools had similar demographics, with about 33 African-American and Latino populations total. Horlick had a more significant Latino population. The Milwaukee schools were predominantly minority, with South Division heavily Latino and the other three mostly African-American.

Summer 1993

Preparation began with a kickoff dinner meeting at UWP in April, 1993. Through subsequent informational meetings for students and parents at each of the six schools, along with follow-up phone calls and mailings, summer rosters were developed.

Thirty hours of in-service took place at UWP and DePaul prior to the Summer Institute. During the Institute, sixty hours of afternoon in-service took place at UWP or Milwaukee South Division High School. Workshops were facilitated by Carr and Skoglund with the assistance of Roberta Dees, Rich Kaplan, and Margaret Small of the UIC Cluster. Neither Carr nor Skoglund had much formal experience with cooperative learning, but Skoglund attended a four credit graduate course at UIC in Spring, 1993 to enhance his knowledge and preparation.

The Milwaukee program was funded by Harley-Davidson, who specified six weeks of two hours a day. With the help of Vince O'Connor, math coordinator for Milwaukee Public Schools, schedules were arranged that allowed CPMP students to stay an extra hour and finish at the end of the first four weeks.

Despite this organizational juggling, the overall impression was of an excellent summer session. All of the teachers involved were very capable and motivated. It did seem, though, that a small number of teachers became involved in the hopes that CPMP would be that "magic cure" for the pervasive difficulties of urban education. Three of the teachers may have become disillusioned when this didn't happen and are no longer with the program. However, all of the teachers were in agreement with the basic structure of the program, including double periods, the Summer Institute, and the training sessions.

By the end of the summer session, great camaraderie had been built among the teachers. Throughout the planning and in-services, the teachers had a strong sense of purpose and mutual commitment and at the end of the Summer Institute an all-cluster student activity was held on the UWP campus.

Academic Year 1993-94

In-services were again held prior to the beginning of the 93-94 school year. Twenty-two hours of cluster meetings and eight hours of building planning meetings were held in anticipation of the beginning of fall classes. Throughout the year, monthly meetings and classroom visitations were held.

Teacher Development

CPMP has enhanced the professional effectiveness of participating teachers both inside and outside the classroom. Inside the classroom it has done this by giving them the skills and confidence needed to create classrooms in which students have more productive social skills and hence exercise more responsibility for their own learning.

Although all of our teachers had had some experience with team teaching prior to participating in CPMP, the use of cooperative learning techniques was new to all but one. CPMP has given them opportunities to learn about and practice many different cooperative learning strategies, and all are now deeply committed to it. In fact, most are using it in all of their courses.

Because there was no prescribed textbook for the Summer Institutes, and because most of the traditional curriculum materials are unsatisfactory for our purposes, CPMP teachers devised new materials and methods for teaching traditional topics. These materials were subsequently used in both their CPMP and non-CPMP classes. All of the teachers have also made writing a central part of their pedagogy.

CPMP teachers have generally become frequent users of such manipulatives as pattern blocks, integer chips, build-it blocks, pentaminoes, and tangrams. They have also become enthusiastic users of scientific and graphing calculators, computer software (such as spreadsheets, LOGO and Geometer's Sketch Pad), and other appropriate technology.

Prior to participating in CPMP, most of our teachers had teacher-centered teaching styles and exercised complete control over their classrooms. All acknowledged that the creation and running of a cooperative classroom requires a great deal of planning and hard work, and all expressed appreciation for the continuous sharing, brainstorming and follow-up that CPMP provided.

However, some have remarked that CPMP organizers could have facilitated their work by:

(1) devoting a greater portion of in-service time to planning with their partners,

(2) devoting a greater portion of in-service time to watching videos of actual cooperative classes rather than merely working on practice activities,

(3) providing a bibliography of activities by subject area with basic guidelines for doing them cooperatively.

Professional Development

Perhaps the most exciting aspect of CPMP is the network of outstanding teachers it has brought together; talented like-minded individuals who care about kids, mathematics, and good pedagogy. Prior to participating in CPMP, few of our teachers had many with whom they could share ideas, materials, and concerns at the level afforded by CPMP. CPMP has given them the confidence needed to make presentations at professional meetings, and to assume leadership responsibilities in their schools, boards, and professional organizations. Some examples include:

* Four teachers attended NCTM annual meetings, seven made presentations at meetings of the Wisconsin Mathematics Council, and two presided over sessions at meeting of the Wisconsin Mathematics Council.

* Two teachers are now chairs of their respective Departments. Both are committed to facilitating the use of pedagogies and materials they came across in CPMP in all suitable courses in their departments.

* Three have been invited to run in-service sessions on cooperative learning and alternative assessment for other teachers in their schools.

* Four were granted money for action research on algebra experimental activities to enhance the algebra curriculum.

* One has worked with the Wisconsin State Assessment System in the composition of their mathematics exams.

Closing Comments

All of our participating teachers have declared that they wish to continue to grow in the ways CPMP has nurtured them. Some wish to do graduate work in mathematics education. All wish to continue to share their teaching experiences and curriculum materials with each other, others in their schools, and others in the profession by presenting at WMC and NCTM conferences.

There is a great demand on time for motivated math teachers in the Milwaukee school district, and Milwaukee's participation in CPMP has become more difficult with its successful participation in Equity 2000.

The two CPMP schools in Racine have become involved in an Eisenhower grant project with Ripon College, which will provide a summer academic program on campus for CPMP students as they prepare for Algebra 2 next year.

Participating in CPMP has renewed the professional commitment of all participating teachers. One of them summed it up well in the last few sentences of the evaluation she wrote after the 1993 Summer Institute:

I must admit that I am anxious for family and friends to ask me about teaching. Because I am proud of what I do and proud of the fact that it is most challenging and worthwhile work. I am also proud of the fact that we are trying to meet the challenge by trying innovative methods - everything that CPMP means! Let's face it - we've had quite a rap - I'm so tired of hearing about our deficiencies and failures in teaching mathematics. So I intend to `spread the word' about CPMP!

The above essay was written by UWP Coordinators Carr and Skoglund to give their overall feelings about the program, which remain positive in the effect that CPMP had on the teachers, individually and as a group. Further details and an update follow.

Some details

Below are the 1993-94 CPMP teachers, classes and students at six schools in two different school districts. (Only five schools were required by the project.)

 School               1993 Summer Institute    AY Yr 1993-94  Fall           
                     Teachers n of Students    semester Teachers Classes,    
                                               n of Students                 
Milwaukee           Lypek &  Paape         12   Lypek, 2 classes   23, 17    
Washington                                      Paape, 2 classes   23, 24    
South Division      Bounket &  Wielebski         Bounket               12    
                    20                           Wielebski              9    
North Division      Bernard &  Kern              Bernard               30    
                    16                          Kern                    31   
Madison             Beine & 
McLennan   13          Beine &  McLennan        
                                                            26               
Racine Horlick      Prueher &  Hernet44          Prueher               25    
                    20                                                       
Washington Park     Conner & 
Kirkwood     21    Conner                18    
                                                 Kirkwood             21     
      Total          6 classes 102 students    12 classes 259 students       

Significant characteristics, special challenges of the cluster

Racine Unified District was small; two of its three high schools joined CPMP, but the third school was very traditional and did not participate. In the four Milwaukee Public Schools, many inner-city characteristics were present; in fact, many students had transferred in from Chicago. The two cities were 35 miles apart, but differences in demographics, culture and needs had more impact.

UIC staff members and several experienced CPMP teachers, beginning with Small and Kaplan, participated by visiting classes, helping to plan meetings and leading activities as planned. Co-directors and teachers from UWP also visited Chicago, but the distance, along with traffic, weather and overloaded schedules, kept UWP from taking maximum advantage of the resources of the ongoing UIC cluster.

The summer schools that did exist in Wisconsin were scheduled for 2 hours for 6 weeks, but UIC CPMP found it necessary to adhere to its model of 3-hour, 4-week program for students.

Wisconsin teachers did not expect teaching in the summer to be a normal part of their jobs. Since many had children, the extra pay was not, in general, sufficient motivation. The fact that so many UWP teachers did participate shows their dedication to the goals of the program.

In Milwaukee, the teachers' union invoked the seniority principle for staffing summer school. A compromise allowed the CPMP-trained team to teach, but to some classrooms a third teacher was added from the list of eligible teachers. Although the third teacher had not had any CPMP in-service, the teachers tried hard to make the threesomes work smoothly. But it was confusing to the 13 students in one class, for example, to have three teachers.

Another downside of the Harley Davidson grant in 1993, in addition to the scheduling problems mentioned above, was their insistence on remediation. Harley's vision of preparing for high school was different from CPMP's, and Harley had monitors visiting to make certain that their materials were included.

During the period of the grant, Wisconsin schools have also been in a state of upheaval/rapid change--turnover in Boards and many principals, the abrupt move to algebra-for-all, state-mandated change in student assessment.

Skoglund, the half-time CPMP teacher-coordinator, was supervisor for math instruction in all Racine schools. Thus he was able to share CPMP methods and suggestions as he organized associated high school teacher in-services. But due to a total School Board and District Office re-structuring, CPMP's funded half-time position of Coordinator, to relieve him of his elementary school duties, was not filled for many months. Thus Skoglund had 150% job requirements for a over a year.

Later, all the Racine District curriculum supervisors, including Skoglund, were asked to resign so that the Board could choose whether or whom to re-hire from among the group. The Board apparently did not feel bound by the agreement made with UWP by their predecessors.

1993: In spite of the difficulties, the Summer Institute was successful. Afternoon in-service sessions were especially spirited, and teachers developed a great esprit de corps. UWP teachers have responded positively in writing, in length and depth to questions about their experiences in CPMP. Some excerpts are given in Appendix 18, CPMP at University of Wisconsin Parkside.

Many teachers enthusiastically planned for two CPMP classes each for Fall 1993. In most schools, these went well, as reported by Skoglund and Carr above.

By Spring 1994, CPMP was in competition with other programs for teachers and students. Few new teachers were able to participate. Madison dropped out as the two CPMP teachers left the school, one leaving the system, with no new recruits available to replace them. And logistically it was next to impossible to coordinate the program across the two different school systems.

Reduced program for Summer 1994: Afternoon whole-cluster meetings were held less frequently. In Racine, a new teacher at Horlick completed a teacher team for the Summer Institute. They joined the established Park team to run coordinated classes, with both teachers and students visiting across schools, illustrating an ideal CPMP program.

With the growth and maturing of the Equity 2000 project in the Milwaukee schools, CPMP teachers from Milwaukee found it more and more difficult to be thoroughly involved in both programs. Since the CPMP coordinators felt that the Equity activities were worthwhile, and because institutionalization was a goal of the program, the Co-directors did not insist on maintaining CPMP involvement at previous levels. Two South Division teachers used CPMP methods in a local summer program called FLAG, which involved mathematics along with other subject areas.

AY 1994-95

Four of the six schools participated in CPMP monthly meetings. Staff maintained the school visitation schedule and distributed materials. One teacher made a presentation at the March 1995 all-cluster meeting in Chicago. In Racine, teachers continued to meet regularly and visit each others' classrooms. They also received a $500 mini-grant to get materials and release time to do "action research" on using experiments for mathematical modeling in Algebra 1.

Summer 1995

Since none of the schools anticipated a formal CPMP presence for the 1995-96 school year, due to the end of NSF support, and since the teachers from the four schools in Milwaukee had been included in MPS's EQUITY 2000 effort, no formal Summer Institute was planned.

Classes at Horlick: However, Prueher and Skoglund were able to team-teach 43 students in two Racine classes of remedial algebra. These were conducted as CPMP classes, in a cooperative, activity-based format. (The students, who were in the class because they had failed their math, in no way met the original selection criteria for CPMP students. However, the CPMP experience in Chicago indicated that students who were not recruited/selected and were sometimes negative about the prospect could still profit from CPMP and improve their attitudes toward math and learning in general.)

As a CPMP laboratory, the classes were open; the team expressly invited administrators and teachers to visit, observing and/or trying their hand at the cooperative approaches. The teaching team were pleased that around 10 teachers visited these laboratory classes.

Other activities: During July, UWP hosted a "Success for Everyone" day for about 80 students enrolled in the Summer Enrichment Program at Milwaukee's South Division High School, along with their teachers and some parents. Activities were similar to those of the previous two years, including a campus scavenger hunt in which the students, working in groups, searched the campus for mathematical puzzles the organizers had planted for them.

During the summer, Carr made a considerable effort to get evaluation data, including student test results over the two years, from the two districts. This was all to no avail, since the Wisconsin state assessment program was in transition, and the overextended district staff did not provide promised test results. (Limited information about UWP's participation in UIC's PSTest is given in Chapter 9.)

Carr's data collection from the teachers was more successful. Her teacher interviews and in-depth exit questionnaires revealed the overall positive attitudes reported in this chapter. Carr reported that prior to participating in CPMP some were close to "burn out". Participating in CPMP renewed their professional commitment.

Although all the teachers had had some experience with team teaching prior to participating in CPMP, all remarked that the team teaching experience in CPMP was the most productive and highest quality to date. Further, they viewed it as an opportunity to model the kind of behavior expected of the students.

Carr stated that CPMP has enhanced the professional effectiveness of participating teachers by expanding their network of like-minded professionals with whom to share ideas, hence giving them the confidence needed to make presentations at professional meetings and to assume leadership responsibilities in their schools, boards, and professional organizations.

Spot checks, Fall 1996

At Racine Unified School District: Skoglund is enjoying teaching two algebra classes at a Racine School. He is proud of the transition to a Standards-based curriculum in Racine elementary schools. His coordinating duties this year are centering around re-creating a district math framework to address a number of persistent problems.

At UWP: Carr, partially because of her involvement in this outreach, has been named Chair of the Mathematics Department. This has increased the department's openness to innovation and concern for students.

Carr feels that UWP will experience the fruit of CPMP for semesters and years to come, since several hundred students have been exposed to the campus and challenged with the importance of carrying through on their education. UWP expects to see many of these students as university freshmen.

A CPMP teacher: In Fall 1995, in relating the changes in administration both in central office and in her school, Ronnie Wielebski wrote of "depressing days" at South Division. [45] She said her CPMP class of the previous year had been broken up, but "most of them are doing well this year and they are leaders in the classrooms."

In a followup phone call, early Fall 1996, Wielebski said that her freshman CPMP students, now in advanced math and chemistry, still looked for each other in classes. But there is no team teaching, no double period for freshman algebra, no person to run the computer lab, and she has stepped down as department head.

She continues to love her classes and her students. She and her CPMP partner, Soumali Bounket, collaborate in after-school tutoring sessions, where they model working problems together for the students, and the sign is still on the wall: No One Of Us Is As Smart As All Of Us. Her statement for the record:

I am eternally grateful for what I learned in CPMP. Cooperative learning makes a big difference, once you buy into it and understand that it is an ongoing process. . I made a mistake at the beginning; I thought that once you learned how to do it, you would just know it. But in reality you are constantly evolving. I learn something new every day. [46]

Conclusion

Experiences in the UWP cluster serve to illustrate important points. Difficulties:

* The problems in crossing district lines within the cluster were more than anticipated by UWP Co-directors.

* Crossing a state line as well, UIC was not familiar enough with Wisconsin's and the districts' systems to be totally effective; a year's planning/training before the implementation would have been appropriate.

* Lack of support/keeping of agreements by local systems leads to frustration of all concerned. The worst effect of this is that some participants may feel that they have in some way failed if the program does not grow in the same way as the "model" cluster.

Positives:

* The teachers were the same as those in Chicago in their dedication to students, hard work, enthusiasm for the new methods and appreciation for the support and assistance from the universities and the program.

* The majority of teachers continue to use the CPMP methods in their own classrooms.

* Many work for change within their districts, and their participation in professional activities is strong.

* Some schools made positive changes.

Conclusion: In spite of the constraints described, the UWP cluster was successful in using the CPMP model to help teachers form a peer support group and collaborate to revitalize their mathematics classrooms and work for reform in their schools.

About the authors: This chapter was written by Regeta Slaughter, in close consultation with DePaul Co-Director Lynn Narasimhan. Slaughter was head of the mathematics department at Lane Tech High school in 1990 when she became a participant in the UIC cluster. Early on, she displayed leadership ability that was readily called upon by UIC staff. She helped plan and lead in-service sessions, presented workshops on cooperative learning and gave teacher support through classroom observations and consultations. She was thus well qualified in 1993 to assist the new DePaul cluster as Teacher-Coordinator and thus to become a member of the Steering Committee, the overall CPMP leadership.

As part of her coursework toward a Type 75 certificate, Slaughter conducted a study of CPMP students at Lane Tech. [47] During 1995-96, she assisted Dees in overall evaluation activities that included developing questionnaires and conducting interviews with individual teachers and groups. From her vantage point over a six-year period, Slaughter was able to compare and contrast the developments of the UIC and DePaul clusters.

Narasimhan was Associate Dean of DePaul's College of Liberal Arts and Sciences and former head of the Mathematics Department . She had already tried various innovations in teaching her undergraduate mathematics courses. As Associate Dean she worked with other faculty pioneering inter-disciplinary mathematics and science courses for pre-service teachers. She was active in supporting mathematics education in Chicago Public Schools, participating in committees and task forces of the CSI, for example. After becoming involved with CPMP, she took UIC's course on Cooperative Learning in Mathematics, along with Skoglund of UWP and potential CPMP teachers. Narasimhan has been a leader in the in-service sessions, and a strong partner for UIC in the consortium. She participated in negotiations with NSF, and was author of companion funding proposals and reports (such as the State of Illinois Eisenhower grant she received to help support the summer teaching). She is also DePaul director of the Alliance for Minority Progress and is organizing a program at DePaul for middle-school mathematics teachers.

By the start of the second summer, CPMP had grown to nearly 30 teachers. In some schools, the additional teachers were close duplicates of the original two teachers in their awareness level of the NCTM Standards and the need to change their methods of teaching, and a commitment to increasing the mathematics achievement of their students. Duplicating the hoopla and energy of UIC's first year became more difficult as the cluster grew. Now the larger question was broached: Could the CPMP model be duplicated at other sites? The question was addressed by the formation of the DePaul and University of Wisconsin-Parkside clusters.

DePaul University is currently in its third year of CPMP. This part of the report focuses on some of these questions:

* How did DePaul model the UIC cluster?

* What affect did the new mathematical awareness have on the development of the new DePaul cluster?

* How did the DePaul teachers become empowered to assume the mantle of leadership in their schools?

* What kind of support is needed to institutionalize CPMP in DePaul schools?

Throughout this chapter comparisons of DePaul and UIC clusters will be noted. Special attention will be given to empowerment of teachers and what DePaul has learned.

Following a Master Plan

In February 1993, the third "Success for Everyone" conference was held to recruit schools for the new DePaul cluster. DePaul, in consultation with UIC CPMP staff, chose five schools. The five schools selected included four Chicago High Schools, with demographics similar to those in the UIC cluster, except that there were no magnet schools. The fifth was Evanston Township High School (located in Evanston, a nearby suburb of Chicago), which participated in CPMP for only one year; later another Chicago school was added.

By 1993 many educators were familiar with the NCTM Standards and the implications of its recommendations. The majority of the ten DePaul teachers were already involved in various degrees in professional mathematics organizations and attended conferences on the local, state and national level. Several knew about cooperative learning through conference workshops or short term in-services. However, these new teaching strategies were not being implemented in their classrooms.

Some teachers believed that cooperative learning would become another tool that they could occasionally use in their teaching, but would not be a complete paradigm shift from traditional pedagogy. One teacher commented early in the implementation that she did not need to change her teaching style, she just wanted to "enhance" it.

In their first Summer Institute (1993), DePaul teachers had their initial experience in trying these new ideas and different ways of teaching without the constraints of a prescribed curriculum. But because of the compressed time frame and inexperience of teachers and staff, teachers frequently felt forced to rely on "canned" materials. The demanding summer schedule, increase in expectations to change and the desire to see their students succeed caused some of the teachers to experience stress during the first summer. The stress, one aspect of change (NCTM, 1992), that resulted is not uncommon, and also occurred with some of the UIC teachers during their first summer.

Stress occurs even in desired change because roles and expectations are uncertain until a new pattern is established and accepted. Efficiency and effectiveness often suffer until this occurs. (p. 114)

In addition there were mixed feelings toward UIC. DePaul teachers assumed they would be given a set of materials that UIC had used. But when presented at in-service sessions, many teachers chose not to use the suggested lessons and decided to use activities that they had selected.

After the first summer, the DePaul teachers were more comfortable with using cooperative learning groups. They started to shift the emphasis in their classrooms from being primarily teacher-centered to one that was now student-centered. One teacher commented at the end of the summer that she had been handed a tool that could be refined. Another commented that the best aspect of the summer program was the chance to experiment and get feedback from students.

As planned, during the first year, DePaul tried to mirror the UIC model in its academic year activities. However, to better use the resources at both campuses, CPMP staff combined the Summer Institute training for both clusters in 1994 and 1995. DePaul teachers now had the opportunity to share afternoon sessions with additional CPMP teachers who were also transforming their mathematical thinking and teaching.

Teachers Empowered to Lead

Traditionally most teachers view leadership as a characteristic of those persons that resides at the top of a school organization: the administration or the central office. Because of this narrow view of leadership, most classroom teachers never realize the power that they possess that ultimately can affect their classrooms and those persons around them. Developing leadership was a goal of the CPMP model in 1990 at UIC and at DePaul in 1993. This occurred in both clusters; however, there were some different outcomes for DePaul.

The original group of UIC teachers were either department chairs or others who felt empowered to make real changes in their schools. They were able to make or influence decisions about issues such as programming, curriculum, supplies, allocation of funds, etc. Initially the majority of DePaul's teachers were not in similar positions. But by the third year, the empowerment of the teachers were evidenced by several things, such as:

* In the fall of 1993, all ten teachers attended the Illinois Council of Teachers' of Mathematics Annual Conference in Peoria.

* The same year, three of the five schools chose to pilot an innovative algebra text instead of their math department's traditional books.

* Drastic changes in curriculum have been made. At Orr High School, pre-algebra classes were eliminated upon the recommendation of the new department chair, a CPMP veteran.

* One team developed an enriched curriculum unit containing common CPMP-developed activities that was used school wide.

* Teachers were forming networks with their elementary feeder schools.

* One second-year CPMP teacher arranged a 2-day IMP workshop for his entire department of veteran teachers.

* Teachers continued to be active in the professional organization, attending state and national meetings; one teacher served on the Board of Directors of ICTM.

* CPMP teachers headed Chicago's Urban Systemic efforts in their schools.

* Eleven teachers from the five schools conducted several sessions on the model classroom at a Chicago area CSI Conference, February, 1995.

* By 1996, three out of five DePaul schools had CPMP teachers as department chairs.

These acts illustrate the empowerment of the teachers to take leadership in their schools.

Where We Are Now

In the Chicago Public Schools the influence of CPMP, IMP and other NSF-funded projects have had a positive impact on student achievement in mathematics and science. In some cases, these other programs are adding or replacing the support that CPMP has initiated. Full participation in this reform movement has been assumed by many of our DePaul teachers. Looking back at the last three years, there are several outstanding strengths that typify the DePaul CPMP experience.

* Teacher Awareness: By the end of the third summer, the teachers were able to distinguish and find exemplary activities and materials. Students were showing their work on chart paper and making more presentations, and open-ended problems were becoming a standard component in the classrooms.

* Shift in Curriculum: Using the IMP Patterns and Shadows units during the 1994 Summer Institute made a great impact on many of the teachers. They have moved to another phase of change; all see the need for a quality curriculum to match the shift in pedagogy.

* Network of Empowerment: DePaul teachers became committed and empowered to make CPMP an ongoing reality in their schools, regardless of the degree of support from their administrations. In every school, teams have increased the number of teachers involved in CPMP. This commitment resulted largely from the trust, strength and support of the network of CPMP teachers.

Where Do We Go From Here?

Four of the five DePaul schools are now designated as CSI schools and are busy with meetings and workshops. These teachers are recognized as valuable resources and are leading the change brigade in their schools. What can we do to support these change agents in their schools?

* Teacher Ownership: Enhancement activities must be structured to insure that teachers develop ownership of the group. This is crucial for growth to continue when external support declines. DePaul teachers have not yet participated enough on this level.

* Administrative Support: Administrators must facilitate support of the DePaul teachers in various stages of change. Important ways this can be accomplished are through common preparation periods of teachers and encouraging and funding teachers to attend workshops and meetings.

* Individual Teachers: Teachers need to constantly be aware of the uneven path to growth. Change varies between teachers and in most cases is not linear. According to NCTM (1992), reversion, or backsliding, may occur even in light of superior performance, to relieve the tension of change. Thus the see-saw behavior observed in some DePaul teachers was not uncommon.

As the year 2000 approaches, more organizations are realizing the benefits of supporting and enhancing teachers. The powerful dynamics that result when this happens means success for all students as well as teachers. CPMP has laid the groundwork for the DePaul teachers to move to a crucial and important phase of reform: system institutionalization.

The above essay was written by Slaughter, Teacher Coordinator, and Narasimhan, PI and Co-Director at DePaul.

Difficulties affecting the DePaul cluster

The struggles the teachers had with the materials was mentioned; there were also complaints about the meeting schedule, since the schools were widely spread, etc. But the cluster faced more serious obstacles.

Roger Jones, the other mathematics faculty member, was enthusiastic but was not available during the summer when the most intensive work was done. Narasimhan, though strongly committed to the goals of CPMP, was an Associate Dean working to improve the university in many aspects and was greatly overextended.

In recruiting schools, there was a preference for teachers who had participated in DePaul's Master's in Mathematics Education (MAMED) program, both as participants and to fill the position of Coordinator. This may have excluded participants who might have been more committed or prepared. One of the schools was in another city, Evanston Township; its participation, subject to the difficulties mentioned in the UWP chapter (conflicts involving distance, a second bureaucracy, schedules and personnel) only lasted a year. [48]

But far worse was the district-wide crisis that occurred in Chicago just as the DePaul cluster was getting under way. Academic year 1993-94 was the worst year in Chicago public high schools in decades, according to veteran CPS teachers. Within the context of an especially severe fiscal crisis, a relatively new superintendent, and an incomplete implementation of Illinois' School Reform Act, events occurred that were especially detrimental to CPMP.

Due to an across-the-district change in the school day (from 9 periods to 7 periods), CPMP lost the second period of the double-period freshman algebra course, the centerpiece of the academic year program. Most CPMP teachers lost their common planning time at the school level, so valuable to them for exchanging ideas and nurturing their CPMP team.

This crisis affected the UIC cluster deeply also. Some of the first CPMP seniors, Class of 1994, lost the upper-level mathematics and science courses for which they were registered. Other students lost a semester of instruction, spending their mathematics class time with substitutes.

With teachers cut or given inappropriate reassignments, morale across the system was dismal. Over time the CPMP schools adapted to the changes along with the rest of the system, but most schools did not regain their extra algebra period.

During Fall 1993, CPMP staff spent considerable effort in lobbying the Board, helping problem-solve in the schools, and attempting to maintain the teachers' support network across the clusters. The first seven schools were going into their fourth year together, and most teachers were plugged into the support network. In spite of their short time in the program, DePaul schools hung together, and tried to implement ideas from CPMP.

Here is an instrument given to the DePaul teachers near the end of the second semester, Spring 1994. Handwritten responses of those present (8 of the 10 teachers) are collated:

DePaul cluster survey

1. On the line below, mark where you think your classroom was as the semester ended.

-----x------x-----x----------x------x-----------------------------------------x-x--x-------------------

student-centered traditional

cooperative teacher-directed

2. Please explain why you marked it there:

90% of in-class work is done cooperatively. Even some individual work is done cooperatively. Yesterday I was called out of Algebra-with-support. We were going over an exam review sheet. I asked them to do their best to complete on their own as 1 big group! They were successful with it.

I have been working on cooperative techniques and my students finally ran with the ball. When I did discovery lessons, they worked particularly well. I could leave my classroom if I wanted and the students would keep working. A common comment the last few weeks -"Is that the bell already?"

90% of the time my students in groups. They must work together on most assignments. They are allowed and encouraged to have an opinion. I encourage them to value each others' opinions.

I am becoming much less teacher-centered and more student-centered. A lot of the things I used to do for my students now I don't

I have the students working in groups but I don't use a formal "Role" method. I have a way to go before I can say that my classroom is student-centered-cooperative.

I was still spending a lot of time and effort talking to (at) my students , and/or trying to get them to be quiet so I could talk to them. I had them sitting in table-groups of 3 or 4, and told them to help each other, but most of my assignments were still typical textbook work and their roles in groupwork were very informal, really optional. If they chose to work together they did and chose their own ways of doing it.

I did some cooperative learning, some hands on activities and some computer activities. Some, I'd like to do more and do them better.

Review at end was teacher-directed but with a lot of student work. Pressed for time-during the year, a lot of group work toward the end to help understand topics.

3. Please write below the concerns you have about cooperative learning:

Time and energy to do this the way I'd really like to do it.

None, I think it is a very positive program.

I don't have any major concerns or minor concerns.

That I will fall back into old habits. That I will talk too much, instead of giving kids space and time to think for themselves. I need to discipline myself to make them think for themselves. Also to cut back on the volume of work I give them so that they do have enough time to achieve some competency.

My students tend to spend more time being concerned about if they are the recorder or the facilitator etc. than doing the problem.

Organization of groups, scoring of activities, writing good cooperative lessons.

how to properly set groups

how to effectively evaluate groups/groupwork

Extreme ?? (can't read) levels sometimes get "lost" in the solving and discussion processes.

need more info on alternative assessment

discuss different theories by different authors of co-op learning

how to handle absenteeism in classroom with co-op groups

While staff observers might not have agreed with those who put their X's on the far left, all would agree that these teachers were conscientious and were reflecting on their teaching practices.

DePaul had no new CPMP teachers for Summer 1994, but furnished the student program at each school. As suggested by Narasimhan, the DePaul and UIC clusters conducted a large part of the afternoon training jointly. The training during the past summer was coordinated with UIC. Instead of maintaining the cluster identities during training, staff grouped the teachers according to subject: pre-algebra or pre-geometry. Much of the training for use of the IMP materials was led by Margaret Small, who had taught IMP Year 1 at Lake View High School . Every Friday afternoon during the Summer Institute, the entire DePaul and UIC staff met to confer on the program.

DePaul's 1994 Eisenhower report [49] includes outcomes of the final evaluation given to all students in the program: ]

Generally, students enjoyed the program, and felt that working with their classmates in groups was a good experience. Here are some selected responses to two questions:

The two most important things about the summer math program were:

We all learned something.

We all had fun.

We all learned to trust each other.

Solving different kinds of problems.

How do you feel about working with your classmates in groups?

I like it because we help each other out.

It makes me work harder.

It's okay because we share our thoughts.

I liked it. I felt more independent.

DePaul teachers still seemed to have mixed feelings about the program and whether it was meeting their needs, or perhaps some felt a rivalry between the two groups. In a typical questionnaire, teachers were asked to rate the major joint activities. The UIC teachers responded more positively than the DePaul teachers to all but one of the activities, the time set aside for planning with partners. The complete tally of the Teacher Ratings of Program Activities is given in Appendix 19, CPMP at DePaul.

In Fall 1994, Narasimhan made these remarks in her report to the Eisenhower Foundation, which had funded the summer teaching for DePaul teachers:

In many ways, the distinction between clusters is artificial. CPMP is truly a collaborative venture among the three universities now participating. Most of the planning has been done in joint staff meetings between two of the three universities, or among all three. There were several all-day workshops in which teachers from all eighteen schools participated. Within Illinois, there are more frequent joint in-service meetings for UIC and DePaul teachers. The combined training last summer was a natural result of this phenomenon. Thus, we are building a growing network of high school mathematics teachers who are using cooperative learning techniques in activities that engage students in significant mathematics.

In light of these remarks, I should say that we are approaching a new stage in the evolution of CPMP. Although the plan to expand CPMP into "satellite clusters" was a good idea in 1991, we have now reached the point where we need a new model for further expansion. One unlooked-for result of the expansion was a tripling of the paper work necessary for such a complicated project. Therefore, during the next stage of CPMP, all the administration will be handled by UIC. I personally will participate in some of the training, and the DePaul schools will maintain their cluster identity by occasionally meeting at DePaul.

DePaul was able to recruit eight new teachers for Summer Institute 1995, when the in-services were completely integrated. Teacher teams had a choice of the IMP unit, The Game of Pig, or the Enriched Curriculum for math and science.

DePaul continued to have activities for students as a cluster, however, and teachers at the DePaul schools asked Narasimhan if they could continue CPMP for their third academic year, [50] thus ensuring their support through classroom visitations and monthly meetings. Narasimhan made this request of NSF as part of CPMP's formal budget revision process in Spring 1995 and was granted the extension for Academic Year 95-96.

Update

Effect on the university

Narasimhan and Jones say that their own classes are more interactive, and efforts to share with other faculty members are ongoing.

With the ending of the NSF grant, Narasimhan continues to lead reform in math and science instruction at DePaul, and has employed Jean Biddulph, a CPMP Coordinator who retired from full-time teaching, as instructor for elementary and middle school pre-service mathematics classes; a program for middle school teachers is under construction.

DePaul's relationship with CPMP has continued. CPMP teachers at Wells High School asked for and received classrooms at DePaul for classes for juniors in Summer 1996.

Systemic effects

When CPMP began at DePaul, Orr High School already had an established network consisting of itself and its feeder schools. Teachers and counselors met on a regular basis for articulation and to ease the transition of eighth graders into high school. (Orr also had a former CPMP staff member, Dr. Cynthia Felton, as principal.) Orr's good idea was shared in the cluster, and the DePaul teachers subsequently focused on such contacts with middle school teachers much more than UIC teachers did.

In 1996 DePaul and UIC collaborated with CPS on Summer Bridge 1996 (documented in Chapter 12, the Epilogue to this report). Two DePaul CPMP teachers were "trainers," with the guidance of Slaughter and Biddulph.

In Fall 1996, Slaughter has joined the faculty of a new CPS "small school," and is teaching IMP along with another CPMP teacher.

Conclusion: This cluster implemented an excellent adaptation of the CPMP model. The DePaul CPMP teachers and staff have the ability and are in a position to help lead the mathematics reform movement in Chicago.

In project negotiations, NSF asked for consistency of programs across the three clusters (See the organization diagram in Figure 6), that is, assurance of quality of staff and quality of experiences that teachers would have. UIC CPMP has been asked to evaluate how well the program has been implemented in the new clusters.

As mentioned, formative evaluation was an integral part of the program. As CPMP evolved, changing times and economic constraints forced decisions about which features and activities of the program were "the basics." End-of-project reflections lead to this summation of CPMP:

What is CPMP?

The cluster model

One university, with certain permanent faculty (2 or 3)

Several schools, with at least one teacher team of 2 from each school

Individuals concerned share important goal(s)

With mutual respect they make a compact/formal agreement to work together toward the goal(s)

The commitment is long term--like friends or family, it does not end or go on break at the end of the semester.

The view of students

Teachers implement the mutual respect model in their classrooms.

Teachers come to believe that given a reasonable choice, students would rather learn than not learn.

This view enables teachers to give up some control in order to engage the students and get them to commit to each other and to the learning process. Seeing them work together and learn induces more trust. The resulting classroom environment is student-centered; teachers encourage both freedom and responsibility.

The framework: the Summer Institute with its essential elements

Preparation begins in the spring

Team teaching

3-hour class with flexible schedule, materials

Interesting, challenging materials

Afternoon meetings to share and reflect with other teachers

The approach is cooperative learning.

Gives freedom within a structure

Rationale (theory and techniques) for the procedures

The content: significant mathematics

This minimal list of components is assumed in the following discussion.

Student outcomes

Summer 1993

The Summer Institute, the first for DePaul and UWP and fourth for UIC, was exciting. In 28 classrooms, teacher teams were working toward more student-centered classrooms. The majority of students' journal entries and responses to questionnaires looked familiar--

I like working in groups... you learn more that way.

I used to hate math, but now I don't.

Student surveys at the end of the Summer Institutes showed a remarkable consistency across schools, teachers and years within the UIC cluster, and across clusters as well from 1993 onward.

AVE was defined in Chapter 3 as a variable that could be used to compare attitudes of groups of students. In Figures 7 and 8 below, a subset of the survey results in UIC and the new DePaul cluster, consider the two stimulus statements, "Classes were boring," and below it, "We worked together a lot," discussed in Chapter 3. For the first stimulus, a higher AVE, for the level of Disagreement, is desired, and the opposite, a smaller number, for the second one, showing greater Agreement.

In spite of the different number of the students and new vs. established cluster, Figures 7 and 8 show almost identical patterns of increasing Disagreement on "boring" and increasing Agreement on "worked together."

Student Survey Excerpt, UIC Cluster 1993

Responses available from 225 Students in 12 of 17 Classes

Pre-Algebra, 144; Pre-Geometry, 60; Pre-Math/Sci 14; UIC-Math, 26

Circle the number which tells how much you agree (1 is the most) or disagree (5 is the most):

Agree Disagree

My math classes in             1     2        3        4        5        AVE      
grade/high school                                                                 
were boring                   27     40       37       57       61       3.40     
worked a lot in groups        103    27       22       29       44       2.50     

This summer math class         1     2        3        4        5        AVE      
was boring                    11     18       48       47       94       4.00     
worked a lot in groups        191    14       6        5        2        1.20     

Student Survey Excerpt, DePaul Cluster 1993

Responses available: 27 Students in 2 of 5 Pre-algebra Classes

Agree Disagree

My math classes in  grade      1     2        3        4        5        AVE      
school                                                                            
were boring                    4     2        6        6        7        3.40     
worked a lot in groups        13     1        5        2        5        2.42     

This summer math class         1     2        3        4        5        AVE      
was boring                     3     0        3        9        11       3.96     
worked a lot in groups        26     0        0        0        1        1.15     

Both in Chicago, the DePaul and UIC clusters had a special relationship; similarities and differences between the beginning DePaul teacher enhancement program and the ongoing UIC program were discussed in Chapter 8.

Academic Year 1993-94

As the UIC cluster entered its fourth year, three new academic year programs were to begin Fall :

* the UWP cluster (discussed in Chapter 7)

* the DePaul cluster (Chapter 8)

* the first IMP curriculum implementation in a UIC school (Chapter 5).

IMP and the first CPMP algebra classes at eleven new schools were all to include the centerpiece of our academic year program, double-period freshman classes. But in Fall 1993, schools were in crisis. In Chicago, due to an across-the-district change in the school day, CPMP lost the second period of the double-period freshman algebra course. Because of NSF funding, Lake View High School retained its double-period classes for IMP, but other double-period CPMP classes were reduced to one period in most schools. A few teachers tried to hold the extra period before or after school or at lunch, but most gave up by midyear.

With the changed schedule, the teachers also lost their common planning time at school, which was valuable to them for exchanging ideas and nurturing their CPMP team. For DePaul schools this also meant a reduction in the amount of time teachers could try out newly learned activities, cooperative learning teaching strategies, and get feedback from their CPMP teammates. Thus the DePaul schools did not have the complete CPMP model.

In Fall 1993, teachers were let go or reassigned, classes were broken up and redistributed, students' schedules were changed arbitrarily. Some CPMP students were never "found;" some transferred out of the system, going to private schools or suburban districts.

Teacher morale was poor in the UIC cluster, where the CPMP network had already been in place for three years. DePaul had only held one Summer Institute in which to build their support group for such disasters. Nevertheless, by the end of the second year, most of the schools had added two new teachers to their CPMP team.

The schools in the UWP cluster had similar problems. Chapter 7 explains difficulties that occurred because of crossing district lines and involving different teacher and school cultures and different teaching schedules and calendars, both in summer and the academic year.

Student performance across clusters, 1993-94

DePaul's teachers attempted to carry out the planned student testing program, but UIC received incomplete data on the CAP Algebra and Geometry tests. The State of Wisconsin had previously given these or similar skill-based tests but has now changed to its own Wisconsin State Assessment Program, given in spring of the tenth grade. Consequently, no standardized test results are available for the Wisconsin ninth or tenth grades.

The PSTest is the only achievement measure that was given in all three of the new programs. In most of the Chicago schools, the double-period algebra class was not possible, so comparison of students' gain scores with those of previous CPMP ninth grade classes would be inappropriate; in Wisconsin there were other difficulties. Still, here are the results that are available, more or less following the format in Chapter 3's discussion of PSTest.

UIC Cluster PSTest 1993-94

Data is available for CPMP students only, so the two groups were:

*Group A: CPMP students Summer 93 through Spring 94, and

*Group B: CPMP students, academic year only, Fall 93 through Spring 94.

The Core score

The total score possible was 21. The core score is the total over the similar superitems 3, 4, 5 and 6 (highest possible core score = 12).

Table 34. PSTest Score and Gain Score Means for UIC CPMP Students, 1993-94

                           Group                                                       
        Variable            A: Sum, Fall, Spr in CPMP    B: Fall, Spr in CPMP        
                                       n=99              n=54                        
      Summer Score                    15.74                                          
       Fall Score                     16.12              12.67                       
      Spring Score                    16.94              14.72                       
   Fall - Summer Score                 0.38                                          
   Spring - Fall Score                0.82*              2.05*                       
  Spring - Summer Score               1.20*                                          
    Summer Core Score                  8.64                                          
     Fall Core Score                   8.84              6.52                        
    Spring Core Score                  9.48              8.04                        
Fall - Summer Core Score               0.20                                          
Spring - Fall Core Score              0.65**             1.52**                      
Spring - Summer Core                  0.85**                                         
Score                                                                                

Table 34

The unsettled school situation and loss of the extra period in CPMP freshman algebra were expected to have an effect (less gain on this and other measures), but the students tested in the Spring still made significant gains, shown in Table 34. Group B, interestingly, had lower incoming scores than Group A but made greater gains. No adjustment for school effect has been done, so it is not clear what is happening.

UWP PSTest, 93-94

The same students were not all present for pre and post tests, and there is no information available on which students were present for each of the tests. The available data in given in Table 35.

Table 35. PSTest Mean Scores for UWP Comparison Students, 1993-94

  Variable    N           Mean        Std Dev     S. E.       Minimum       Maximum       
Fall Score        95      12.36       4.44                    0             20            
Spring Score      30      12.53       4.66        .85          0            20            

Performance on the pretest in Fall 1993 indicates that incoming CPMP and comparison students were similar. The mean score of the spring comparison group of 30 was not significantly different from the mean score for the group that took the test in the Fall, but the drop-off in numbers from Fall 93 to Spring 94 has not been accounted for (Table 35).

Table 36. PSTest Mean Scores for UWP CPMP Students, 1993-94

  Variable    N           Mean        Std Dev     S. E.       Minimum       Maximum       
Pre-Summer       118      12.16       4.12        .38         1             21            
Score                                                                                     
Fall Score       177      13.64       3.43        .27         6             21            
Spring Score     137      14.42       35.0        .26         4             21            

The mean scores of the CPMP groups (Summer, Fall and Spring) are increasing, as usual (Table 36). But because the gain scores with appropriate n's are not available, no inference is suggested.

DePaul PSTest results 1993-94

Table 37 shows mean gain scores for DePaul CPMP students:

Gain S3F3 = Summer to Fall 93

Gain F3S4 = Fall 93 to Spring 94

Gain S3S4 = Summer 93 to Spring 94

Table 37. PSTest Mean Gain Scores for DePaul CPMP Students, 1993-94

Variable           n        Mean          Std Error     T             p value       
Gain S3F3          48       0.63          0.47          1.34          0.1860        
Gain F3S4          42       0.74          0.45          1.63          0.1103        
Gain S3S4          36       1.75          0.64          2.73          0.0097        

For those students who took all three tests, and therefore participated in the entire program, the gain (S3S4) in the PSTest score is significant even without the double period. However, no conclusion is drawn from the above data, because, of the 153 students in the CPMP summer program, less than a third also took the test in Fall 93. It is known that one school did not test at all during the academic year, and some classes did not remain intact.

IMP1 PSTest Results 1993-94

The IMP1 group that began in Fall 1993, around 80 students in three freshman classes at Lake View High School, did have a double period, due to the financial support of this NSF grant. The IMP1 class contained a number of students who would normally have been registered for pre-algebra rather than algebra (the remainder of the incoming freshmen class were tracked), and none of the IMP1 students had participated in a CPMP Summer Institute. So even if the mathematics topics taught had been comparable, there was no appropriate comparison group available, neither "regular" CPMP or other class.

However, the PSTest had been designed to be independent of specific mathematics content, specifically algebra skills, so two forms were administered to IMP1 students as pre and posttest. The Fall and Spring scores are given in Table 38 and the gain scores for those who took both tests in Table 39.

Table 38. PSTest Score Means, IMP1 Classes, Fall and Spring 1993-94

   Variable     n               mean (of 21)    s.d.            range           
Fall score            74        11.58           3.17            5, 20           
Spring score          70        13.10           3.20            6, 19           

Those IMP students who took both tests made a statistically significant gain in scores on the PSTest, according to a t-test, p < 007 (Table 39).

Table 39. PSTest score differences, IMP1 classes, Fall and Spring 1993-94

  Variable    n          mean       s.d.       range      T          p<         
Gain             64      1.4        3.16       -5, 8      3.56       .0007      

This mean gain score exceeded that of many of the CPMP algebra classes tested over the years, some of whose students had had the 4-week CPMP summer program as well as the double period.

Interpretation: This success with students not self-selected to a special program, and many not even selected by the school as ready to take algebra, is an illustration of the skill of the teachers and also of IMP's strength as a problem-based curriculum.

Teachers outcomes

The joint cluster meeting of December 16, 1995, had as a major agenda item an interim evaluation report to be presented by CPMP staff and reacted by the teachers. Attendance was down due to conflicts, but the teachers present expressed appreciation for the opportunity to receive and discuss the information.

Various staff members presented information about different components--student outcomes, teacher enhancement outcomes, the IMP implementation and the DePaul and UWP clusters. The teachers were asked for written feedback on each presentation. The complete collated responses are in Appendix 12. Teachers classified the information as interesting and useful. Here are a few comments, chosen for variety, that will illustrate their commitment to the task.

Questionnaire: Choose one or more of the following, and add comments or questions in the space provided. This information . . .

was very interesting to me.

would be useful for future proposals.

would be useful to administrators.

would be interesting to parents.

is new to me.

* This would be useful to students to show how active involvement in class will lead to improved performance and love for the class.

* More needs to be said about transitional periods from 40 min. to 50 min. effect on students completing 4 math classes rather than 5 ('93-94' school crises). This presentation should be given to principals of schools with CPMP programs. Given to them by our head people.

* I like the way Regeta articulated teachers' empowerment to take leadership roles and "feeling empowered." Thanks Regeta for those inspirational words on leadership & to CPMP for taking us there.

* Need more information. I hadn't seen a plan of the number of schools involved in IMP & CPMP for the future. If all goes as planned, how long will it be before all CPS high schools will have CPMP & IMP teachers?

* We don't know where we are going. After we get a new principal...?

* Important - ongoing support/collaboration/ team teaching/ time to plan - the strength of CPMP.

Teachers were also asked to take 10 minutes to write a letter to NSF, evaluating CPMP. The results were difficult to choose among, but here is a sample.

I appreciate the support that I have received from the directors of and other teachers in the CPMP program. I know I'm fortunate to have been introduced to the program as I began teaching. Very few teachers have so many resources readily available to them. It has been helpful to try activities and discuss concerns with other teachers. What strikes me most about the CPMP program is the focus on solving problems and doing things to resolve issues rather than dwelling on the negative. I get tired of hearing people complain rather than talking about how to improve situations. I have heard very little negativism in this program except to bring up issues. The conversation then immediately turns to resolving these issues. The meetings have been constructive rather than destructive. I think that this is a major reason for the success of the program.

Conclusion: Except for context it would be difficult to determine from their responses which cluster a teacher "belonged to." Commonalities seen in the volumes of material written by teachers across the program, as well as the hours of conversation in many settings, included dedication, concern for students and a feeling of responsibility to the group.

If CPMP is so successful, why do you need IMP?

Much of Chapter 5 was in answer to this frequently asked question. The following two statements written by a teacher, over three years apart, illustrate how the IMP curriculum has fulfilled many of the original goals of CPMP for the teachers who are participating.

Q. What do you want for yourself professionally out of CPMP this year?

June 26,1991, after her first Spring Training and at the beginning of Summer Institute

A. I would like to be able to teach in a classroom where cooperation and working together in groups is a main aspect. I would hope to gain the skills and techniques necessary to have such a classroom from the CPMP program. I would want a knowledge of cooperative education both in theory and practice.

A second goal I have from the CPMP program is to enhance my abilities in classroom management so that the learning environment can be most effective. I feel I will learn from this program how to do various activities with the least amount of description.

The tremendous amount of materials available that incorporate cooperative learning will be of great benefit to me professionally. I will not be a slave to the textbook but intend to take advantage of other resources available. The amount of sharing that goes on in the CPMP meetings is very helpful. I am able to learn from other teachers what works and what doesn't work and I'm encouraged to try things that work for others in my classroom.

Finally, I see that in order to make the CPMP program work, I need to do much more planning and preparation. I see the other teachers working extremely hard and being totally prepared for the class. I feel I will grow professionally by working harder to make my classes more interesting and stimulating and I will be a much better teacher for it.

Q. Have far have you progressed on your professional goals?

November 12, 1994

I have progressed from a mostly teacher-dominated lecture-type classroom to a student-centered cooperative classroom. Teaching the IMP curriculum has been the main way I have moved toward my professional goals. The IMP material is rich in hands-on, cooperative problems and experiences. I see the benefits that come from students doing, discussing and writing about solutions to problems and presenting the solutions to the class. This is a great improvement over being "shown" how to do a problem by the teacher.

I have a long way to go towards giving students the tools and confidences necessary for success in the curriculum. I hope my continued involvement in CPMP will encourage that growth.

The first statement illustrates how a teacher might be very enthusiastic and want very much to have the idealized CPMP classroom, and also how overwhelmed that teacher might feel ("working hard" being a big part of the program for her). The second statement shows how the IMP curriculum assisted her by providing the interesting material and the effective methods needed for the successful classroom she wanted. And together the statements illustrate how an effective teacher enhancement/support program, can prepare teachers to learn and teach a modern, Standards-based curriculum.

Summary and conclusions

When the CPMP clusters crossed school district lines, there were serious complications. Some were logistic, such as different calendars and teaching schedules, different unions and payroll policies. Other difficulties came from the necessity to learn about and interact with more than one school board and set of traditions.

Still, when the program was minimally implemented, as described at the beginning of this chapter, certain outcomes were consistent, as reported by a majority of students and teachers and witnessed by staff and other observers. There was a qualitative improvement in the classroom, with benefits to students and teachers including, for students:

* better attendance and positive behaviors

* a decrease of discipline problems

* improved attitude toward mathematics, or at least math class

* improved performance on various measures of mathematics achievement

CPMP teachers, many for the first time, had opportunities to talk to other teachers about math. The schools, or at least the math departments, were opened up so that information was disseminated more widely, even to people who were not directly involved, and support developed for the people who were trying new things.

Regardless of the cluster or the curriculum used, by the third summer that teachers participated, they were able to distinguish and find exemplary activities and materials that they felt comfortable with and that seemed to bridge the gap between the traditional and the student-centered classrooms.

These factors contributed to increased job satisfaction in the short term, and many teachers were inspired to develop themselves professionally and/or take leadership in working for further changes in their school and system.

Introduction

During Spring 1996 the teacher leadership of UIC IMP/CPMP planned with the new Board of Education of the Chicago Public Schools for a combined 1996 summer program.

Teachers in six new CPMP schools and six new IMP schools, as well as new IMP teachers in current IMP schools, participated in Summer Institute, including spring training. Teaching in CPMP's Summer Institute was funded by a new grant from State of Illinois' Eisenhower Fund. The proposal was prepared by the CPMP teacher leadership, assisted by the UIC's Institute for Mathematics and Science Education (IMSE), which now houses CPMP as part of its secondary school reform effort.

CPMP also agreed to be responsible for a subset of a larger CPS Summer Bridge program, with goals of teacher enhancement and remediation for rising eighth graders. The CPMP proposal for both programs called for contributions from at least six different funding sources, including CPS and the Chicago Systemic Initiative. (The Summer 1996 program is described in Chapter 12.)

This is an excellent example of the collaborative work of DePaul and UIC staff and teachers over the past three years, but perhaps a first illustration of what might be accomplished in working with the new Board. CPMP has a reputation for effective teacher enhancement, and supporters of Standards-based curricula now may have more authority; two former principals of CPMP schools now hold administrative positions with the Board, for example.

This section will discuss some interactions of CPMP with other systems and agencies, such as individual schools and school systems, CPS and the Urban Systemic Initiative in Chicago, the three participant universities, other universities, and the local mathematics education community.

Systemic change, or impact on school systems, in general

Many educators now recognize that change affecting an entire school and all its students cannot be accomplished through isolated projects that train X teachers or bring Y students into a university for a two-week math camp; it is complex, time-consuming, difficult.

Universities must have the permission of school districts before entering schools in any capacity. But the two groups of educators, from school and university, do not have a common culture nor (usually) much understanding of each other. Sometimes university faculty members look down on public school staff, and many school personnel are suspicious of the motives of university faculty when they attempt an intervention.

Systems targeted for change by CPMP, beginning with the most basic level, were:

* Teacher team of two

* Mathematics department

* School

* School district

This report has included some effects of CPMP on teacher teams and mathematics departments, and now addresses schools and school districts.

The school as system

CPMP was designed as a school program: School change was to be achieved by beginning with the first CPMP team of two teachers. It was intended that this team would become part of a peer support group that would continue to work together for reform.

CPMP teachers were mathematics department heads in 4 of the 7 original schools, but this fact alone did not guarantee acceptance or spread of the program. Within the schools, teachers need the support of the power structure to do the hard work of CPMP. Whoever is able to make decisions at the school (principal, assistant principal, or other) must support the CPMP teachers in scheduling, providing resources, and in relating to the parents and other school staff. The schools where the program has been the most robust had strong initial support of significant school administrators, including the programmer. But turnover is high -- of the original seven 1990 principals, only one remained in Spring 1996.

During the operation of CPMP, schools have been subject to strong external forces. Under the Illinois School Reform Law, Chicago Public Schools were ordered by the state legislature to change to site-based-management in 1988. Schools were to assume considerable autonomy over their own operation, through their principals, guided by their Local School Councils (LSCs). But in 1990, no effective structure had been generally implemented to transfer power from the district to the seventy-odd public high schools in Chicago. Even the most progressive principals were confused about what they were allowed or could afford to do.

School change

But at the school level, change occurred. It was perhaps noticed first at Lake View High School that the culture was changing: it was no longer totally un-cool to like mathematics and do well in it. A summary of school change during the first three years, written by Horn, the CPMP Coordinator and former teacher and department head at Young High School, begins:

In a typical school which was part of CPMP, certain changes could be observed.

Year 1: The first two teachers to be trained collaborated on a broad range of issues . . .

Year 2: The second year brought at least two more teachers on board. There was a beginning awareness in the rest of the math department that the traditional "gatekeeper" mentality of mathematics was being eroded by the "quality mathematics for the largest number" mentality. Some department members felt that the quality and integrity of the mathematics courses in the school were being threatened by the new mentality. There was a struggle within the department over definition of quality mathematics. With the inclusion of more teachers in the monthly CPMP meetings and planning for the summer institute, the scales were finally tipped. The dominant view within the department was now the view that all students have a right to succeed in quality mathematics.

The Lake View story

The videotape, The College Preparatory Mathematics Program: The First Four Years, [51] shows a representative from UIC Public Relations at Lake View, talking to CPMP teachers and students and the math department head. In a lengthy interview, excerpted for the tape, principal Donna Macey clearly stated her support for CPMP, IMP and the mathematics department as a group. [52]

Lake View was chosen to highlight in the tape because of the degree of institutionalization of the program there. In this neighborhood school, with a large portion of minority and/or poor students, the program principles were evident, especially the group spirit of the CPMP teachers.

At an all-cluster conference at DePaul, February 1995, each school's CPMP team was to make a presentation, in the format of their choice, to tell how things were going at their school. One teacher did a straight presentation by herself; other CPMP teams shared the task. The most unusual presentation was Lake View's. It was the largest group to take the stage, around eight teachers, and they sat in a circle. They presented their report in the form of a CPMP team meeting, in which teachers took turns sharing how things were going for them and concerns they had.

Here are some of Lake View CPMP's successes:

* of the 7 schools, the largest number of CPMP teachers, and largest proportion of the department,

* IMP implementation,

* involvement of the department in the selection of new hires, textbook decisions, and scheduling,

* extra time for the CPMP geometry class, 8 times per week (in addition to extra algebra time), and

* advanced courses offered in the summer enabling students to take calculus as seniors

What is their secret? During Fall 1995, Slaughter and Dees asked Lake View CPMP teachers to host a focus group meeting in connection with the program evaluation. Slaughter and Dees had prepared questions for the teachers, hoping to answer the following question: In addition to beginning with two dedicated and charismatic teachers and a supportive principal, assistant principal and department head, were there other identifiable factors contributing to Lake View's success?

The meeting unfortunately conflicted with an IMP training session, which involved about five Lake View teachers. The four teachers who were in attendance at the focus group brought a range of experience: a CPMP 6-year veteran and now department head, teachers in fourth year and second year, and a young teacher who had just completed his first semester. Notes of the discussion and focused writing of the teacher participants are given in Appendix 18, School Changes.

One question was:

Despite many changes in the Chicago Public Schools (i.e., the 1993 scheduling change from a 9-period to a 7-period day, personnel cuts, administrative changes, etc), your math department has managed to remain cohesive and continue to expand the number of teachers involved with CPMP or IMP. Why do you think this has happened? List what you think are the most important factors.

The response from a second-year CPMP teacher follows:

1) Depth of CPMP experience among staff who believe in CPMP.

2) Established notion among administration that the math dept. does these things.

Asking for an explanation of the second factor brought on a discussion of how entrenched the idea was that the math department just "does these things.' Perhaps this teacher's phrasing could be an operational definition of a program's being institutionalized.

Changing the school system

Activities designed to raise awareness of mathematics teaching reform efforts continued and were expanded with the resources of NSF. Here are examples.

Associate teachers: To accommodate more teachers already at the awareness level, but not in CPMP schools, staff began an "Associate" program in 1994. A lone teacher from a non-CPMP school could partner with a CPMP teacher and thus participate in the spring training and Summer Institute at a current CPMP school. During the summers of 1994 and 1995, there have been 22 CPMP associates, who are helping to improve mathematics instruction in their home schools. Over 20 Chicago public high schools have at least one CPMP-trained teacher (i.e., attended at least one Summer Institute).

World Wide Web and E-Mail listservs: From late 1995 to Fall 1996, CPMP's pages on the Math Department's World Wide Web site have shown highlights of the program and introduced the IMP curriculum being implemented in the three participating schools. This material will be incorporated into the Web presence of IMSE's more comprehensive Center for Secondary School Mathematics Reform (CSSMR), the new home base of IMP at UIC. (The URL is http://www.math.uic.edu/IMSE/)

Cpmp@uic.edu is a Listserv intended to provide a forum for CPMP teachers to share ideas amongst themselves. Most teachers needed assistance and encouragement from the program to get online at home, since Internet access was not available at most schools in the program. There were eventually about 80 subscribed members during the project. Teachmat@uic.edu, another Listserv, was begun by Baldwin as a forum for anyone interested in mathematics education at the secondary level; it grew to include over 200 subscribers from about a dozen countries.

The Chicago Systemic Initiative (CSI)

Over the years, CPMP found a variety of positive ways to interact with teachers, schools and the Board of CPS. Such efforts have brought some results. Dorothy Strong, former Bureau of Mathematics Supervisor and now CSI administrator, stated that she now had a different view of university professors and no longer mistrusted them automatically. [53]

When Chicago received an Urban Systemic Initiative grant, CPMP contributed as much as possible. The CSI videotaped CPMP teachers in a panel discussion on the Standards, to be used at later in-services.

Since five of the 10 first high schools chosen by CSI for concentration were CPMP schools, staff increased collaborative efforts, holding two afternoon in-services for CSI Design Teams of all 10 schools. Eleven DePaul CPMP teachers conducted several sessions on the model classroom at a Chicago Area CSI Conference, February 1995. CPMP teacher leadership helped organize an April 1996 CSI curriculum conference and presented the IMP curriculum as one session.

Chicago Public Schools

CPMP met the goal of providing a corps of teacher leaders ready to reform the mathematics programs in their own schools, to continue their own professional development and to assist in staff development for other teachers and schools.

In 1995, the State of Illinois gave the Mayor of Chicago authority to "take over" the city schools. The new Board, taking office in Summer 1995, made significant steps to stabilize contracts and calendars so that school could open on time in Fall 1995. CPMP was much encouraged by early moves to reduce bureaucracy and give more authority to educational leaders within the system. CPMP/IMP staff and teachers have assisted as requested, working with students and teachers in a successful summer program. (Discussion of Summer 1996 appears in Chapter 12, the Epilogue to this report.)

However, in Fall 1996 it is hard to predict the effect this board will ultimately have on the gains that the reform movement in mathematics has made. In its haste to show results, the board seems to have given excessive weight to a single measure of students' progress: an external, standardized multiple-choice test. Hopefully, those principals who thoroughly understand and are committed to Standards-based mathematics instruction will be able to maintain their ongoing programs.

Effects of CPMP in the universities

At The University of Illinois at Chicago

CPMP has influenced and been influenced by the involved mathematics faculty at UIC. Besides Dees and Baldwin, the Principal Investigators, eight other mathematics faculty [54] have made significant contributions to CPMP. Three have worked extensively on collection and analyses of various kinds of data resulting from the project. When faculty members have visited classrooms in schools, worked with students, and participated in in-service sessions, teachers and mathematicians came to have mutual respect. CPMP students, teachers and professors became members of a community of scholars that transcended age, level of education, and neighborhood.

]

Effects on university teaching: CPMP has affected the UIC mathematics department in a number of ways: individual faculty attitudes and practices, certain other mathematics programs, and general faculty and departmental commitment to teaching.

For several years the department has conducted the Professional Development Program (PDP), the UIC parent of CPMP, providing students a collaborative workshop experience in which to work on challenging mathematics in calculus and later pre-calculus courses. The CPMP staff has worked closely with PDP faculty and assisted in training Teaching Assistants and tutors. Influenced by the success of this program, now named the Emerging Scholars Program (ESP), the department converted a floor of math classrooms from fixed seating to tables and chairs.

There is a ripple effect even among the faculty not directly involved in CPMP or ESP, according to Judy Baxter, Director of Undergraduate Instruction. She estimates that 30 of the department are now making an effort at least to make their classes more accommodating, and 10 are actually trying some group work or other innovative methods.

Cooperative learning is encouraged in Teaching Assistant sections. Faculty have experimented with more student-centered instruction, notably when converting to "Harvard calculus" during 1995-96. The college version of the Interactive Mathematics Program (IMP) was used in two remedial sections at UIC during Fall 1995. Other innovations include an integrated chemistry-college algebra course. Some implementation of cooperative learning has also taken place in upper level courses.

There has been an increase in discussion of pedagogy and curriculum among the faculty. The department has vastly increased the training program for all Teaching Assistants; a course in teaching methods is mandatory for new teaching assistants, since Fall 1995. These graduate students teaching precalculus meet once per week. Activities, methods, and connections with educational psychology that were developed or learned by Baldwin in CPMP all play a major role in the course.

Institutionalization at UIC: During the course of this grant, CPMP received excellent support from the MSCS Department. Beyond the $100,000 per annum university cost-sharing negotiated in the original proposal (for IMSE support of CPMP), the Department provided $20,000 in computer equipment and several courses released time for Baldwin and Dees. However, this depended on the profound support of John Wood, the Department Head at that time.

At UIC, the negotiated Indirect Cost Ratio is lower for projects in Education, as opposed to "research" grants at UIC. This fact greatly hampers education projects in obtaining necessary space from the university pool. There was a lag between hiring of CPMP staff and finding office space for them, and there was never a satisfactory place to house all the resources for teachers. Funding agencies need to pay attention to these conditions at institutions whose resources are already strained and attempt to negotiate a uniform rate for all projects. This problem is exacerbated by the requirement of "cost-sharing," since for education grants this means at least some cash money spent in ways the university would not ordinarily spend it.

In Fall 1996, however, CPMP has evolved into the Center for Secondary School Mathematics Reform (CSSMR), jointly supported by IMSE and the MSCS Department. Currently the major project of CSSMR is the IMP Regional Implementation Center, which is working with nine schools and seeking funding to continue and expand in Chicago schools.

Interactions with the other university partners

The daily operation of this project has necessitated an increase in communication between the university partners, yielding a qualitative change in their relationship. In the meantime, CPMP staff of DePaul and UIC have developed a bond of mutual trust through joint projects with Chicago Public Schools, including the Chicago Systemic Initiative. The Chicago clusters, especially, have shared responsibilities and resources.

For example, Narasimhan submitted an Eisenhower proposal for DePaul's teaching stipends for 1993 and received $45,000. In subsequent years, UIC and the DePaul clusters merged for most of the Summer Institute sessions, alternating meeting sites between the two campuses. DePaul and UIC CPMP staff "took turns" getting the Eisenhower grants that paid for part of the summer teaching stipends.

* $82,000; Summer 1996 (UIC Cluster)

* $52,000; Summer 1995 (UIC Cluster)

* $51,000; Summer 1994 (DePaul Cluster)

* $45,000; Summer 1993 (DePaul Cluster) [55]

Challenges at DePaul and UWP

Both DePaul and UWP have relatively small mathematics departments (a dozen or less, compared to 70-odd at UIC) and their faculty members carry heavy teaching loads. There was also the usual pressure for non-tenured faculty to concentrate their energies on publishing. At both of these campuses, relations between mathematics and education departments are not yet conducive to joint activities.

The three CPMP mathematics faculty were not able to involve other DePaul and UWP faculty in this time-consuming program , and were themselves overextended during the project.

The support of university faculty members has been valued highly by the teachers in all three clusters, who were able to see them in a new way. However, it was difficult for faculty members, with their other duties, to maintain the intense relationship that contributed so much to the program. Small universities, especially, need more support from their departments and the funding agencies to engage in a comprehensive, long-term interventions such as CPMP.

Conclusion

This school-university collaboration has had significant effects upon at least some subsets of each of its target systems,

* Teacher team of two

* Mathematics department

* School

* School district

The most profound effects have been on individual teachers and students. But especially in Chicago, the High School District, the central administration of CPS, and the CSI are all aware of this new core of teacher leaders who are willing and able to take on responsibility.

Added benefits have been the effects on UIC and the development of a unique collaboration between universities, as exemplified by UIC and DePaul in their leadership of CPMP.

CPMP was one way to energize mathematics reform in the Chicago metropolitan area. Its legacy is a core of teacher leaders organized for change, four classes of students with improved mathematics educations, a continuing program for implementing the Interactive Mathematics Program in Chicago, greater connections between UIC/Depaul and CPS, and effects on the teaching of mathematics at UIC.

A minimalist description of the program in Chapter 9 included this list:

* A special school-university collaboration, based on common goals and mutual respect, embodied in the cluster model: one university and several schools working together in a long term commitment

* A view of students that enables teachers to implement student-centered classroom environment based on mutual respect

* The Summer Institute with its intensive teacher preparation, team teaching, a 3-hour laboratory class for students, and in-service sessions for reflecting and sharing with other teachers

* Cooperative learning as a primary teaching/learning strategy

* Challenging, interesting mathematics

This section summarizes some observations about the six-year program and contains recommendations for other educators seeking similar results. The analysis proceeds in the order of the text of this report.

Student program

CPMP, in the UIC cluster, was successful at its original goal. With CPMP support, students under-represented in mathematics have exhibited greater success and persistence in school and in more advanced mathematics courses than historically expected.

Overall, when compared with similar students not in the program, all CPMP students achieve more in mathematics, have better attendance, take more mathematics courses, and graduate at higher rates.

It is not expected that in a four-week summer program, or even a double-period freshman class, students will learn all the mathematics skills and concepts that they might have missed in grades K-8. But it is possible to involve more students in mathematics and lead them to a deeper understanding. CPMP students learned that they could do math; that math was fun, that math was worth doing. But for many, this was a different math than what they had in elementary school. The success of the student program has been documented through careful analysis of persistence data, done on a school-by-school basis, and by analysis of student accomplishment on a variety of tests.

This comprehensive program, begun to help more minority students succeed in challenging mathematics, has achieved its goal with the students who participated. CPMP has also had other positive effects on students, teachers and faculty who have traveled together in this adventure. The program culminated in great achievement and enthusiasm for students and teachers alike, despite complications in replicating the program across varied school districts. Increased involvement by other school staff and parents produced better achievement for the students.

A comprehensive year-round program-- that involves more time on math during the

academic year -- is needed for students with weak backgrounds .

The standardized test data support a general conclusion that students in the CPMP classes performed better than similar students not in the program, on a variety of tests on traditional college preparatory mathematics courses (algebra, geometry, advanced algebra, AP calculus). These results reflect the impact on the students of the combined, essential features of CPMP: increased time on mathematics, cooperative learning, innovative curriculum materials and high expectations.

Teacher Enhancement

One legacy of the program is a corps of 12 to 15 teacher leaders who are taking leadership roles in their schools and/or system; another 8 to 10 are ready to step up. Many teachers participated in the in-services for several years and gradually took on in-service responsibilities themselves.

The Summer Institute, in which with teachers in teams of two teach a real class, with related in-service in the afternoon, is an effective model. Teachers felt that sharing with each other (in teaching teams of two, in small group work and in whole group discussions) was the most powerful element of the teacher enhancement program. Many teachers entered the program thinking they would find a way to change the students. After immersion in the program some decided that what they needed to "fix" was themselves.

After teachers had done all they felt they could to enrich their mathematics classes using traditional textbooks, some came to feel that there was nothing left to do but to change the entire curriculum. Thus, the program activities laid a foundation on which to implement innovative curricula such as IMP.

The experience of teaching IMP units in Summer Institute influenced teachers, whether they decided to implement the curriculum or not. Students across the project were making more presentations. Teachers were including more open-ended problems in their daily lessons, and `Problems of the Week' were becoming a standard component of their curricula.

It is impossible to underestimate the combined effect of the year-long CPMP experience: summer teaching laboratory and support during the academic year. The changes in teacher attitudes brought about by this intense program should not be expected in a program that provides only 60 hours of in-service per year.

The major impact of CPMP was on pedagogy. Substantial further programs are needed in two areas: remediation of poorly prepared (often not fully certified) teachers of high school mathematics and the provision of a rich mathematical context for the teacher-leaders who are fully competent in the traditional material but don't have enough background to evaluate the contents of various competing curricula. A CPMP-like program can attract teachers to programs that address these issues more directly.

Schools

Changing the role of mathematics instruction at the school was a key aspect of the CPMP approach. Making 3rd and 4th year mathematics a normal part of the students' curriculum has crucial financial and personnel implications that must be understood and supported by the principal. Here are some observations on Lake View High School, by Dees, who had over the years talked to the principal and assistant principal at length, met the counselors and interviewed the head of the math department. She summarizes her opinions of these administrators' contribution as follows:

The principal, programmer, and department head are extremely important to the success of school-based mathematics reform. The persons in these three positions at Lake View during the 1990-1995 were dedicated, educated, smart and approachable professionals. Specific factors in the institutionalization of CPMP at Lake View were:

* The principal, since retired, saw herself as a curriculum leader.

* The assistant principal, in the crucial role of programmer, supported educational goals over convenience.

* The head of the mathematics department, since retired, led a democratic department.

All three had a basic respect for and trust in the teachers and students.

What have you learned about replication?

As NSF moves toward regional centers for support of mathematics reform, including the implementation of the five Standards-based curricula, a number of lessons can be drawn from the CPMP experience across several districts.

Aspects to be considered include:

1) Do the affected districts have similar calendars, school regulations?

2) How stable are the administrations at the District and school level?

3) Does any school have a rule outlawing calculators on school grounds?

4) Dealing with different administrators and different policies, e.g., on teacher release time, increases the administrative difficulties enormously.

5) The outreach persons who will work with the teachers should have had some high school teaching experience.

6) Teachers can best reach the deep understanding needed of the new curricula through teaching the material in conjunction with in-service about the material.

If the effective teaching laboratory in the Summer Institute is not available, at least arrangements should be made to have in-services concurrently with some ongoing teaching schedule, so that teachers can try some new material/approaches and report back to the group. The sharing with other teachers and opportunity to ask in-service leaders specific questions about the material is needed for a full realization of curriculum goals.

Can the program be exported?

Given the intensive support provided by CPMP, virtually all teachers in a continuing CPMP school can improve the classroom for their students. Even very traditional teachers have raised their expectations and become more student-oriented.

For introduction and awareness purposes, CPMP's short-course in-service model proved to be effective in Chicago. CPS granted one lane-advancement credit for fifteen contact hours in "Cooperative Learning in Mathematics," for example, taught by CPMP staff and offered in the afternoons at various school sites across the city.

The success of a program may depend on subtle factors that are in the background of the original implementation. Here are two examples from CPMP.

The double-period algebra class was easy to achieve when the Chicago Public Schools had 7 short periods; it became almost impossible when the system switched to 5 longer periods.

The Chicago teacher culture supports teaching summer school as a "normal" activity; this was not the case in Wisconsin.

Evaluator needed

This document reports the results of evaluating a project that was trying to implement change. If the funding agency will need hard data, it is recommended that they include a line item for at least one strong person, who will be dedicated to overseeing data collection and analysis.

Does site - based management work?

CPMP is a school-based program. It did not begin at a school until some measure of support from the administration had been demonstrated. As expected, it worked best where the principal was an active proponent of the program.

However, turnover has been a problem; it takes some time for new principals to gain understanding of the various programs already functioning at their schools. An empowered, happy mathematics department with a successful program can often find the new principal an ally.

Over the six years there have been cases in which a new administration either refused to honor an agreement of the previous administration or damaged the program through misunderstanding or neglect. But a mathematics program under the attack of a traditional principal with a back-to-basics bent and a central office bureaucracy similarly inclined is in serious trouble. Even supportive principals have sometimes been overruled and plans already made have been vetoed; classes under way have been disbanded. Some CPMP teachers in such situations leave the school or the system; some retreat into their own classrooms, where they take satisfaction in the community they can create with their own students.

CPMP and IMP

CPMP and IMP have been effective partners for the last three years. Current IMP teachers have participated in the Summer Institute, in the model developed by CPMP and with the major portion of curriculum and training materials provided by IMP.

Providers of other innovative curricula may want to consider how to, through general teacher enhancement, provide a similar base of support for their implementation effort.

Conclusion: CPMP has shown that this high school-university partnership has empowered teachers to implement Standards-based instruction in their classrooms and to improve the mathematical performance and persistence of their students. In the long run, it is possible that the influence of such partnerships can improve education for all students.

Originally it was anticipated that Summer 1996 would be used for completing the end-of-project reports and budget documents for submission to NSF. Instead, most of the staff was off and running on an evolution of the program as parts of it became institutionalized in the school system and new schools participated in CPMP/IMP Summer Institute, with John Baldwin, Co-Director, as the overall coordinator. The following summaries, written by the staff members who led these activities, describes CPMP's collaboration with the Board of CPS and other university partners and the 1996 version of the Summer Institute. The last document is the proposal to NSF that led to these changes in the operation of the project.

Contents

Summer Bridge Program

Introduction

John Baldwin

Evaluation, DePaul/UIC Mathematics Staff Development Group,

1996 Summer Bridge

Regeta Slaughter, DePaul Coordinator

Summary of CPMP and IMP Activities for Spring and Summer 1996

Anne Horn, CPMP Coordinator and IMP Co-Director

Proposal: Summer 1996 CPMP/CPS Collaboration

CPMP staff, UIC and DePaul Clusters

Summer Bridge Program

Introduction

John Baldwin

In Spring 1996 the CPS Office of High School Service and Support asked the College

Preparatory Mathematics Program (CPMP) at UIC/Depaul to develop a curriculum and train teachers for 1/3 of the 1996 Summer Bridge Program. [56] We report some observations about the program, suggest some improvements, and request your assistance in obtaining additional data to evaluate our program's effectiveness.

For our segment of the Bridge training, approximately $35,000 from the CPMP grant and Eisenhower funds combined (and an additional $70,000 to the associated Interactive Mathematics Program). Overall, we found that students were learning the mathematics and the teachers were enthusiastic about the methods we introduced.

We provided the students with a coherent set of innovative materials drawn from three NSF-funded curriculum projects:

* Math Trailblazers (produced by UIC's TIMS Project), for about 2/3 of the materials:

* Interactive Mathematics Project, and

* Math in Context [57]

The materials combined review and drill on traditional topics with active investigations by students on basic concepts such as area, fractions, ratios, and functions. Thus, the program tried to serve a true transition role of remediating the students' skills while leading them into ideas necessary for success in high school algebra. Work on extended problems developed both the students' ability to work independently and their realization that mathematics problems can and should take more than a minute to solve.

From grants we paid two coordinators, Regeta Slaughter and Jean Biddulph, experienced mathematics teachers and former mathematics department chairs, who participated in CPMP from its inception in 1990, to coordinate the program and lead the in-service session. Our staff of four CPMP-trained Chicago High School teachers visited classrooms daily and met weekly with the teachers. We concluded that the students (in most classrooms) were intensely involved in the mathematics and were learning the material. Although many of the teachers were initially skeptical of a program which required behaviors so different from the regular routines of both teacher and student, the teachers became increasingly enthusiastic as the summer progressed.

Of the 45 final teacher evaluations, here were their ratings of the overall program:

12 raved about the "great" program,

21 enthusiastic,

6 neutral, and

6 negative.

45 Total

EVALUATION

DePaul/UIC Mathematics Staff Development Group

1996 Summer Bridge

by Regeta Slaughter

Introduction

In March, 1996 Dr. Lynn Narasimhan of DePaul University and Marty

Gartzman of the University of Illinois at Chicago (UIC) were asked by Powhatan Collins and Jacqueline Simmons of the Chicago Public Schools, High School Service and Support to train 75 teachers in a summer program for at-risk 8th graders. Since 1990, UIC and DePaul had worked with some of the math teachers at 12 Chicago high schools in the College Preparatory Mathematics Program (CPMP). The daily operation of CPMP has necessitated an increase in communication between the university partners, yielding a qualitative change in their relationship. CPMP staff of DePaul and UIC have developed a bond of mutual trust, through joint projects with Chicago Public Schools.

CPMP, a teacher enhancement program funded primarily by the National Science Foundation, focused on teacher training. Trained teachers worked with groups of incoming freshmen during a four-week summer school program. The summer curriculum implemented included active and problem-based lessons. With this prior experience, Dr. Narasimhan and Mr. Gartzman were charged with developing an active, problem-solving curriculum for the summer. Unlike the drill oriented curriculum that many of them had failed, Ms. Simmons felt that an active mathematics program was needed.

I. Staff: College Preparatory Mathematics Program

John Baldwin, University of Illinois at Chicago, Professor of Mathematics, CPMP, Director

Lynn Narasimhan, DePaul University, Professor of Mathematics, CPMP, Director

Phil Wagreich, University of Illinois at Chicago, Professor of Mathematics, Institute for Math and Science Education, Director

Marty Gartzman, University of Illinois at Chicago, Institute for Math and Science Education, Outreach Programs, Director

Jean Biddulph, DePaul University, Mathematics Education Instructor, CPMP Coordinator

Regeta Slaughter, Lane Technical High School, CPMP Coordinator

Carolyn Baskin, Fenger High School, Trainer

Ronald Melman, Lake View High School, Trainer

Joan O'Brien,Wells High School, Trainer

Cynthia Sleyko, Orr High School, Trainer

Description:

* University faculty developed and adapted curriculum that was used during the summer. Lynn Narasimhim and John Baldwin worked and met with other trainers implementing the spring training for teachers. John Baldwin continued meeting during the summer with coordinators and trainers to plan weekly curriculum development meetings. Baldwin also supported Bridge teachers with site visitations.

* Jean Biddulph and Regeta Slaughter, who had coordinated the DePaul CPMP cluster for three years, served as coordinators for the Bridge. Their duties included planning training sessions, curriculum planning, developed budgets for summer materials, processed time sheets for training and summer meetings and visitations with Bridge site coordinators and teachers.

* Trainers who had participated in CPMP and had used the curriculum were selected to work in the spring training and summer Bridge. Trainers planned and participated in spring and summer curriculum development sessions. During the summer, trainers supported teachers through classroom visits averaging one hour in length. Trainers often conference with teachers after school, discussing curriculum issues and problems. Afternoons were spent in writing visitation reports and planning curriculum meetings based on their observations in the classrooms.

II. Funding Sources

* CPS

* DePaul and UIC, contributed though grants provided by:

National Science Foundation and the

Eisenhower Foundation, Illinois State Board of Education

III Topics

* Estimation and Measurement

* Patterns and Functions

* Proportional Reasoning

* Using Data to Predict

* Using Fraction, Percents and Decimals

IV Curriculum material taken from/excerpted from:

* Trailblazers, Kendall Hunt Publishers

Based on materials from Teaching Integrated Mathematics and Science (TIMS), a curriculum development and teacher enhancement project founded in the late 1970's at the University of Illinois at Chicago.

* Mathematics in Context, Encyclopedia Britannica

Developed by the Wisconsin Center for Educational Research, School of Education, University of Wisconsin, Madison and The Freudenthal Institute of the University of Utrecht, The Netherlands.

* Interactive Mathematics Program (IMP), Key Curriculum Press

A four-year problem-based mathematics curriculum for high school students IMP began as part of a curriculum development effort funded by the California Post Secondary Education Commission (CPEC). Currently IMP is being used in three Chicago high schools with six additional implementations scheduled for fall, 1996.

Overall Curriculum Structure

Summer Bridge curriculum was designed to be a mixture of drill problems (Daily Problems and Practice), activities imbedded with math concepts that might have not been previously mastered, and extended problems of the week (POW's) that were used to encourage students to explore open-ended problems.

III. Schools and Teachers

About one-third of the Bridge sites, or sixteen high schools and 58 math teachers, were assigned to be trained by the DePaul/UIC group. The schools, representative of the 6 regions, were divided into two clusters of eight schools each. During the 18 hours of spring training from late May to the middle of June, all 16 schools met together at one location. However during the summer, for the weekly two-hour curriculum development meetings, schools met at their cluster sites, either Englewood on the South Side or Wells on the North.

There were 31 elementary teachers and 27 high school teachers. The math background of the teachers varied. Some teachers whose regular teaching assignment was in another subject, but were endorsed in mathematics, had not taught any math classes in several years. High school math teachers while well-trained in high school curriculum, but were not very knowledgeable about approaches to teaching elementary school mathematical concepts.

IV. Training

Due to a late start, some schools were unable to staff their schools at the onset of the 18 hours of spring training. Overall attendance at the five meetings was about 78%. Despite staffing problems at some of the sites, most schools were enthusiastic and ready to begin training, even though they were still unclear about the structure of the summer and the expectations of the program.

Of the 58 teachers:

* 40 attended the entire 18 hours of spring training.

* Eight schools had 100% attendance through the entire spring training and summer curriculum development meetings!

* 6 received four hours of training

* 7 received no training, due to late selection of staffing or changes in Bridge schools that were not supported by DePaul/UIC

* the remaining teachers averaged about 14 hours of spring training

UIC and DePaul were aware that the curriculum that they were asking the teachers to implement was different. Several had doubts that this approach would be successful with this particular group of students. They were also were aware that the teaching style that was required by the lessons would be new and in some cases uncomfortable to some teachers. Another problem was the lack of familiarity that some of the elementary teachers had with some of curriculum concepts that were being used. On the other hand, many high school teachers were rigid and traditional in the method that they felt some of these concepts should be taught.

With these issues in mind, training was planned to model the actual classroom setting and at the same time deal with some of the problems mentioned. Training included teachers actually participating in curriculum lessons and activities as students, processing how they went and planning strategies to make them work successfully with their students. Through modeling, different teaching methodologies such as cooperative learning were introduced in the framework of the curriculum. Teachers were encouraged to work as school teams, plan common lessons, and get feedback from other colleagues

The format of the spring training was repeated at the weekly curriculum development meeting with added feedback of students in classes and their reactions to the curriculum. Weekly blocks of daily lessons and strategies were given to the teachers as a framework for planning. Manipulatives and classroom supplies that were necessary to implement the curriculum were distributed during these meetings or sometimes hand delivered to schools. In the meetings, teachers were able to talk about what went well in their classes, problem areas and possible solutions and share ideas on various teaching strategies. Attendance at these meeting was about 93%.

Classroom support was given through visits and descriptions. At the end some classrooms were videotaped and teachers and students were interviewed, for preparation of this report. Student tutors assigned to teachers performed such tasks as copying, distributing, collecting and managing materials, tutoring individual students. (At some sites, tutors were very effective).

V. Strengths

1. Topics introduced in a hands-on format that allowed students of varying abilities to grasp concepts that previously had not been mastered and be successful.

2. Mixture of elementary and high school teachers working together allowed greater flexibility ranging from mutually shared teaching techniques to better assessment of the students.

3. At a majority of successful schools, teachers working together as school teams as opposed to the usual one-person-in-isolation in the classroom strengthened the program.

4. Curriculum development meetings in which teachers were able to experience the materials prior to using them in class.

5. Feedback and sharing during the two-hour curriculum meetings

6. Ongoing support from trainers through classroom visitations

VI Weaknesses

1. Teachers who received less than 8 hours of training had difficulty implementing the curriculum and sometimes had to rely on their own material.

2. Teachers who were not endorsed or certified in mathematics sometimes had difficulty implementing the curriculum.

3. Teachers worked four hours with only one hour per week to plan and prepare activities. The one hour varied depending on the schedule of the counselor.

4. The 3-1 schedule did not lend itself to uniform teaching in the two classes each day. Also students were not able to stay on task for the three hour blocks of time.

5. Teachers who were not at their home schools were not able to access supplies such as overhead projectors, copying materials or space to secure their materials.

6. There were wide variances at different schools of communication between teachers, site coordinators and counselors.

VII Recommendations

1. Choose Bridge staff and start training of teachers in early spring (March).

2. Select teachers who have endorsements in math or are math certified.

3. Offer on going staff development courses such as cooperative learning, to improve teaching methodologies.

4. Make greater efforts to balance school staffs with equal numbers of high school and elementary teachers.

5. Provide planning time during each day to give teachers the necessary time to plan lessons and get feedback from other teachers in their subject area.

6. Allow materials distributed during the summer to remain with the individual teacher. To truly "bridge" there must be a continuum of reaching and motivating students into the academic school year.

1996 Summer Bridge Math Program

Final Teacher Evaluation

Summary

Part A: DePaul/UIC Summer Math program

1. How did the Bridge Math program enhance your professional growth? Are there any specific changes in teaching style or new materials that you expect to use next year?

* "I developed a better sequencing of teaching blocks during the extended periods."

* "...presented different methods and techniques that will enable me to better relate and present material on a level on which achievement will be higher. The material also helped me to hold the interest level of the students and to keep them focused."

* "Personally, I don't feel that the Bridge Math Program enhanced my professional growth, but I did learn some new techniques to use this year."

* "I did not find this program compatible to my teaching style."

2. In what ways do you feel your students benefited from the program? Specific examples would be helpful.

* "Students benefited from the sharing and cooperative work atmosphere. More hands on activities."

* "If my students learned good study habits and understand teacher expectations such as behavior and conduct, the program would have been more than worthwhile."

* "It made them hate math a little less."

* "They were able to work with math 2 hours a day instead of 50 minutes."

* "They became better thinkers in solving problems. They learned new approaches and approached each problem with new ways."

* "Another way to view problems, but for some students it was frustrating."

* "As a result of using `hands-on' activities and cooperative learning, students realize they can do math and feel proud of themselves. This motivates them to do the next activity, etc. It has a sort of exponential effect on their achievement."

3. Was there any effect on attendance?

* "There were very few students absent in my classes."

* "No. High attendance 95%"

* "Yes! The attendance was excellent. They attended school regularly because of the high interest generated in the program."

4. What were the strengths and weaknesses of our training program (Wednesday meetings, staff visitations, communication)

* "It helped me to see what I was doing wrong, and make appropriate changes if need be."

* "We got the opportunity to use the material (as students would) before we actually had to present it. We were allowed the opportunity to learn the material as learners which gave me a greater insight into presenting it."

* "...some of us were very tired after teaching 4 hours and having to sit for 2 more hours."

* "The staff visitations were good but feedback is needed for the teachers."

5. What is your opinion of the curriculum materials we provided? What concepts or skills were particularly well handled; which not? How did the use of dpp's, pow's and activities work out?

* "I loved the curriculum, great format."

* "The pow's and dpp's were great. The children enjoyed them. The curriculum did not address the children's immediate needs."

* "The curriculum materials were excellent! Some could've been more challenging, especially for those students who had level or above level math scores. Even so, the material was presented in a new format which held their interest and enabled them to grasp concepts that were familiar but not totally understood."

* "dpp's and pow's got the students to thinking."

* "Fractions - the presentation was excellent; it gave a different slant on the subject."

* " I feel the use of the dpp's and pow's did not correspond with the curriculum."

* "The materials should have been combined into one booklet so the students could use them more often."

* "The real problem has nothing to do with the quality of material; the real problem had to do with meeting the needs of so many kids in so little time."

6. Directions: Circle one number that rates how well your students increased their knowledge of the following areas: (1 = Slightly increased to 5 = Much increased)

# responding Average

a. ratio 1 2 3 4 5 40 3.00

b. area 1 2 3 4 5 42 3.26

c. computation 1 2 3 4 5 41 3.41

d. calculator awareness 1 2 3 4 5 45 3.62

e. fractions 1 2 3 4 5 40 3.10

f. interpreting data 1 2 3 4 5 39 3.33

g. graphing 1 2 3 4 5 41 3.65

h. patterns 1 2 3 4 5 43 3.34

i. estimation 1 2 3 4 5 39 3.58

j. problem solving 1 2 3 4 5 40 3.20

Part B: The general CPS Summer Bridge Program

We will incorporate your ideas into our report to the Board.

1. What were the strengths of the Summer Bridge program? What were the weaknesses?

Strengths:

* "To address the fact that social promotion must end."

* "The students learned the importance of good attendance and they began to work in extended blocks of time."

* "The materials of the program, the Wednesday meetings and communication."

* "The strongest point I feel had to reflect on the project coordinators and the thoroughness with which they prepared the instructors and provided materials."

Weaknesses:

* "No prep time for teachers either before or after school."

* "The 3-1 setup could be 2-2 hours."

* "... the total disregard of math and math scores as determined by the board in their criteria for success."

* "Promotion policy was too inconsistent throughout the program."

* "High school teachers need to be consulted in terms of curriculum."

* "Four hours of constant work with immature 9th graders was too long. Their attention span is too short for 4 hours of constant lessons even though the activities were varied."

* "Wishy-washy enforcement of the attendance policy."

2. What specific (policy) suggestions do you have for next year?

* "Students attend Bridge only for deficient subject."

* "Policy enforced pertaining to attendance, discipline, etc."

* "A 2-2 schedule instead of 3-1 or 1-3"

* "Decrease the student/teacher ratio to 15 to 1."

* "The exit test should match the curriculum."

* "Math should be given as much weight as reading in terms of exit criteria."

* "The exit criteria should be clear at the start of the program."

* "We need prep time."

* "Present students with a written copy of requirements."

* "I am not a negative person. I am in this profession for the well-being of the students. I feel the board failed the students. A lot of my students worked very hard and probably not pass the IOWA. What kind of message are we sending?"

Summary of CPMP and IMP Activities for Spring and Summer 1996

by Anne Horn

The CPMP activities during July consisted of three 15-hour workshops for teachers previously involved in summer CPMP institutes or new teachers receiving a first exposure to IMP. They were each conducted by a pair of teacher-leaders. The three workshops were:

Baker's Choice: an introduction to IMP,

Function Probe: using exploratory computer software as an intrinsic part of problem-solving in IMP, and

Activity-based Geometry.

Each workshop enrolled 25 teachers. On the basis of evaluation surveys given to participants, teachers responded that they learned new mathematics and new ways of teaching and that they intended to incorporate these into their classrooms in the fall. Teachers from six schools not previously using the IMP curriculum expressed interest in pursuing the use of IMP for the 1997-98 academic year. Recruitment of eight new schools to participate in the planned 1997 Spring and Summer Institutes preliminary to IMP implementation for fall 1997 will be based on contacts with teachers such as these.

The 1996 Spring and Summer Institutes involved 23 teachers from eleven schools. The 87 hours of teacher staff development and the 60 hours of teaching laboratory focused on "The Game of Pig," a first-year IMP probability unit. The institutes served as part of the preparation for new IMP teachers and an introduction to Standards - based curriculum for teachers from schools not yet committed to using IMP. The staff development curriculum included: changing pedagogy, learning new mathematics, and creating a student-centered classroom environment. Along with two experienced staff members, workshops and classroom visits were conducted by two new teacher-leaders who will continue to work throughout the 1996-97 academic year as intern staff-developers.

The institutes included the three schools which had begun IMP prior to 1996, [58] two schools that had chosen to begin using IMP in fall, 1996, [59] and six new schools participating on an exploratory level with no initial commitment to adopt the program. Teachers from four [60] of the six new schools] were convinced through their practice with students that the IMP curriculum presents a better alternative to the traditional curriculum at their school. They have decided to move forward with IMP implementation beginning in the fall, 1996. The principals at these schools, interviewed by UIC staff, voiced their concerns that mathematics teachers are slow to change, that students are failing or disengaged, and that test scores are abysmal. They stated that IMP and the accompanying staff development is the only possible solution they have been offered.

Date: April 18, 1996

To: Diane Spresser

From: John Baldwin, Roberta Dees, Lynn Narasimhan

Subject: Progress report and proposal for end-of-project budget revision

This letter summarizes plans for completing our NSF grant, #ESI-9253326.

Plans for institutionalization in Chicago

We are optimistic about recent developments in the Chicago Public Schools (CPS). CPMP staff developers have been asked to participate in a summer school program including classes for students and teacher enhancement. We expect CPS to fund around 75 teachers this summer, contributing over $350,000 to this effort.

CPMP proposes to collaborate with CPS on this project. CPMP has secured an Eisenhower grant to partially fund our Summer Institute with heavy emphasis on IMP training. Tentative agreements have been made by CPS and CPMP to share resources and staff developers. The attached proposal and request for budget revision describes how we would like to use the remaining NSF funds.

Attachments:

Proposal: Summer 1996 CPMP/CPS collaboration

Request: End-of-project budget revision

Proposal:

Summer 1996 CPMP/CPS Collaboration

Introduction

The College Preparatory Mathematics Program (CPMP) and Chicago Regional Center for the Interactive Mathematics Program (IMP) have benefited from recent changes in the structure of the Chicago Public Schools (CPS). The CPS leadership was taken over in Summer 1995 by the City of Chicago, and Paul Vallas became the general Superintendent of Schools.

Powhatan Collins, the former principal of Whitney Young High School, one of the Chicago IMP sites, was appointed as the Director of High School Support, the top CPS high school administrative position. Collins moved immediately to formalize a relationship with CPMP/IMP to plan and provide staff development for a larger number of high school mathematics teachers. He had sought the IMP curriculum for Whitney Young, has a fundamental belief in the curricular change it represents, and is pleased with the results of the two years of implementation at Whitney Young.

Collins is an advocate for CPMP/IMP in the Chicago Public Schools, and currently CPS is adopting the key premise of CPMP: a combined program of teacher and student enhancement that allows teachers to develops new pedagogical skills while preparing students for successful high school mathematics.

As in previous summers, UIC has requested and received funds from an Eisenhower grant to run a Summer Institute. The design of this Summer Institute and the preceding spring staff development, now going on, is part of a larger plan for IMP implementation and staff development in the Chicago Public Schools, continuing the work of the current NSF project.

CPS, under Collins, has begun a summer bridge program between eighth grade and freshman year for eighth grade students who score in the bottom three stanines on standardized exams. Due to our successful work with CPMP and IMP, Collins has requested both DePaul University and The University of Illinois at Chicago to provide staff development for approximately half of the 150 teachers in the bridge program and to design the curriculum for the seven week summer school.

The DePaul/UIC consortium proposes to assist CPS and imbed its planned Summer Institute in the larger staff development program for the CPS. This plan will maximize use of CPMP's staff developers and be a significant step toward institutionalizing CPMP/IMP in the Chicago Public Schools.

Expansion of IMP -- current schools and CPMP/IMP awareness

Eleven schools will have a laboratory summer school where the teachers will teach an IMP unit to entering ninth-graders. Participating in this Summer Institute will be 24 teachers: two or more teachers from

* three current IMP schools,

* three new IMP schools, already planning to implement the curriculum in 1996-97 and

* five newly recruited CPMP schools.

The new schools will receive an IMP immersion, designed to give them a basis for deciding whether the curriculum is right for their school. Because of the developments in the CPS, and the support from Mr. Collins, expanded IMP implementation in Chicago high schools is a good possibility.

Collaboration with CPS in Summer Bridge program:

CPMP/IMP at DePaul and UIC have agreed to provide staff development for the 75 teachers of the bridge program. An enriched curriculum will be designed for the students, currently below-grade-level. Pairs of CPMP staff developers will work with the teachers in groups of 25.

Funding for the CPMP/IMP Summer Institute:

In addition to financially supporting the DePaul/UIC staff development for the bridge teachers, CPS has agreed to contribute funds to the planned Summer Institute. Support for the Summer Institute is also being drawn from the new Eisenhower grant and anticipated rollover from unused ACCESS 2000 funds. In order to maximize the effectiveness of our first large-scale IMP immersion Spring and Summer Institutes, we request the accompanying rebudgeting of the remaining project funds.

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