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