The Interactive Mathematics Program

Statement of Philosophy

The following is a summary of the fundamental underlying principles behind the development of the IMP curriculum:

1. Curriculum Principles

2. Problem-centered units

   Mathematics is best learned in the context of meaningful and interesting problems. Therefore, each unit of the curriculum is organized around a central problem or theme. The study of the many branches of mathematics are thus interconnected both with each other and with their applications, including such areas as social science, physics, and music. Concepts and skills are learned in the context of the unit's central focus, through a variety of smaller problems, both routine and non-routine.

   Content changes

   Today's student needs more than algebra and geometry. The IMP curriculum provides students with experience in such areas of mathematics as statistics, probability, curve-fitting, and linear programming. There is an emphasis on broad principles, and methods of investigation, and a de-emphasis of mechanical skills.

   Investigations and Projects

   Students need opportunities to work both independently and cooperatively on long-term projects and investigations. These opportunities are provided through Problems of the Week as well as through one to two-week projects in which students apply key ideas and methodologies learned in a given unit.

3. Equity Principles

4. Greater access

   Our educational system needs to broaden who learns mathematics. The IMP curriculum is designed to make the learning of a core mathematics curriculum more accessible, especially to those groups, such as women and minorities, who traditionally have been under-represented in college mathematics classes.

   Heterogeneous classes

   The IMP curriculum is designed to be used with heterogeneous classes. The developers of the program believe that virtually everyone can gain a deep understanding of the curriculum and can make valuable contributions as a member of the learning group.

5. Instructional Strategies

6. Group learning

   In the real world, learning is often a shared process. Progress toward a goal comes about through the combined efforts of many people. Students need to experience this cooperative process, and be given opportunities to learn from each other. Therefore, students are organized into small groups (usually four students to a group), and much of the classroom learning is done in the context of these groups.

   The role of the teacher

   Within this group learning framework, the role of the teacher changes from that of "imparter of knowledge" to that of observer and facilitator. The teacher asks challenging questions and helps students support each other to get through difficulties. The teacher does not give answers but helps prod students to do their own thinking, to make generalizations, and to go beyond the immediate problem by asking themselves "What if?" The teacher also brings the whole class together after group work, leading a discussion in which students can share insights and correct misconceptions.

   Communication skills

   Communication in mathematics is more than the presentation on numerical answers. Students need experience in explaining both their successes and their frustrations in working on mathematical problems. The IMP curriculum provides students with many opportunities to write about their mathematical thinking, to reflect on what they have done, and to make oral presentations to each other about their work.

   Technology

   The last decade has revolutionized the tools that are available for mathematics problem solving. The IMP curriculum provides meaningful contexts for students to use graphing calculators and computers as components of their problem-solving strategies.

7. Assessment

8. The Interactive Mathematics Program involves a major change in how we define mathematics and mathematical learning. Along with that change must come a complete overhaul in how we measure student success. The IMP curriculum provides teachers with ongoing opportunities to evaluate what their students are learning, through such assessment tools as student's written and oral presentations, teacher observation of student interactions during group work, and student's evaluation of themselves and each other, including student portfolios. Evaluation of student learning cannot be judged simply by correctness of numerical answers, but must reflect our belief that the tools of mathematics have only been learned when they can be appropriately used in a meaningful context.

9. Teacher Support

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