What Is an IMP Unit?

A New Look for the Curriculum

The IMP curriculum probably looks different from any textbook you have worked with before. Instead of being organized into courses called Algebra, Geometry, and Trigonometry, it comes in "units" that are part of each "year" of the program.

That's because the IMP curriculum is integrated and problem-centered. Most units begin with a central problem that is explored and solved over the course of six to eight weeks. As you guide students through a variety of smaller problems within the unit, they develop the mathematical concepts and techniques they need to solve the central problem. A particular unit may combine several branches of mathematics so that students see how important ideas are related to each other.

Some of these central problems are based in practical real-world situations, such as maximizing profits for a business or studying population growth. Others are more fanciful, involving situations like a pennant race or a circus act. Central problems may have connections with history, science, or literature. Because the curriculum is organized around such "big problems," students get a rich look at how mathematics is actually used--a feature that is often lacking in traditional textbooks.

The Student Text

The student text contains the mathematics assignments and activities through which students develop the concepts and skills of each unit. It also contains reference material on major new ideas and a glossary of important terms.

Basic assignments

There are three main types of student assignments:

• In-class activities
• Daily homework
• Problems of the Week (POWs)

Generally speaking, students will examine new concepts through an in-class activity. By starting in class, students have each other as resources. You are there to provide guidance and direction as they begin their exploration.

In homework assignments, students reinforce and extend concepts that are introduced in class and sometimes explore new ideas. Some of these assignments provide opportunities for students to reflect on and synthesize what they have learned over a longer period of time. Problems of the Week (POWs) let students explore mathematical ideas without the constraints and time pressure of needing to know something tomorrow or next week. These are open-ended problems, often mathematical classics, that cannot be solved easily in a very short period of time. In POW write-ups, students describe how they worked on the problem and explain their reasoning; these problems are a vehicle through which students improve their mathematical writing. Though POWs are embedded within the units, the mathematics of these problems is usually independent of the unit problem.

Supplemental problems

Each student unit also includes a collection of supplemental problems, both for reinforcement of concepts and skills and for extending ideas beyond the basic curriculum. These problems provide you with a way to tailor the curriculum to the needs of individual students. The special role of supplemental problems in the heterogeneous classroom is discussed later in this handbook.

A Teacher's Guide for Each Unit

For each unit, there is a teacher's guide that explains in detail how to present the material of the unit. This guide organizes the material as a series of daily lesson plans; it discusses how the mathematical concepts should evolve from the student activities and discussions. The guide suggests specific hints you can give or questions you can ask to promote student dialogue, and provides additional mathematical background for your reference. It also contains specific suggestions as to how you can use the supplemental problems.

Overview

Each teacher's guide begins with an overview that gives a summary of the unit, a list of the main concepts and skills that students will be learning, a description of any special materials you will need to provide, and specific grading suggestions for the unit.

Collegial support

Because this curriculum represents a major change for most teachers, you should look to your colleagues for support as much as possible. The developers of IMP recommend that as teachers present each year of the curriculum for the first time, they have a common preparation period in which to discuss their achievements, frustrations, and questions. In many schools, teachers have been provided with an extra preparation period for this professional sharing.

Teachers around the country have described this type of collegial support as one of the most useful forms of professional development in their teaching careers. I certainly know how valuable and productive this time was for me when I began teaching the IMP curriculum. Each teacher's guide includes suggested topics--geared to the specific issues of the unit--for you to discuss with your colleagues during this shared time.

A Complete Four-Year Curriculum

This four-year curriculum includes the fundamental ideas that have been part of the high school syllabus since before we went to school--concepts and skills from algebra, geometry, and trigonometry. Although this material is organized in a new way and embedded in problem-based units, the key ideas are all there and students will use them and revisit them throughout the four years. The individual units of the curriculum are described in an Appendix to this handbook. In addition to this traditional material, students will also learn about branches of mathematics, such as statistics or matrix algebra, that are new to the high school curriculum but are used throughout business and industry today. These additions to the mathematics content of the curriculum are consistent with the recommendations of NCTM's Standards.

By combining traditional concepts and newer material in an integrated setting, the IMP curriculum meets the needs of both college-bound students and those headed directly into the workforce. By putting these ideas in context, the curriculum prepares students to use problem-solving skills both in school and on the job.