Inside IMP™

What is IMP?

Why is a change needed in mathematics education?

How does IMP differ from traditional high school mathematics courses?

What happens in an IMP classroom?

Does IMP prepare students for college?

IMP Nationwide

IMP Curriculum Content: A Summary

IMP Co-Directors & Advisory Board

The Interactive Mathematics Program (IMP) is an exciting new way for high school students to learn mathematics. IMP's four-year program of problem-based mathematics replaces the traditional Algebra I-Geometry-Algebra II/Trigonometry-Precalculus sequence. This new curriculum meets college entrance requirements and prepares students to use problem-solving skills at school and on the job.

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The IMP™ curriculum was designed in response to national reports pointing to the need for a major overhaul in mathematics education.* These and subsequent reports agreed that the current high school curriculum has changed very little in the last century. Yet society has changed, and so have its technological tools.

As students enter the professions and trades, demands will be placed on them that focus on their problem-solving and communication skills. Preparing students for the challenges of business and industry requires a shift in instruction away from routine manipulation of symbols and procedures toward an in-depth, conceptual understanding of mathematics.

The reports call for a mathematics program that integrates traditional areas of mathematics with new topics such as probability, statistics, discrete mathematics, and matrix algebra and including those that use graphing calculators and computers, that encourage cooperative learning, and that are accessible to all students.

IMP fulfills all of the above reforms.

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Conceptual Understanding
The IMP curriculum challenges students to actively explore open-ended situations, in a way that closely resembles the inquiry method used by mathematicians and scientists in their work. While the traditional curriculum emphasizes rote learning of isolated mathematical skills, IMP calls on students to experiment with examples, look for and articulate patterns, and make, test, and prove conjectures.

Updated Mathematics
IMP integrates algebra, geometry, and trigonometry with the additional topics recommended by the national reports, using calculator and computer technology to enhance student understanding.

Problem-Based Units
The IMP curriculum is problem-based, consisting of five- to eight-week units bound into a single techbook. The units are each organized around a central problem or theme. Motivated by this central focus, students solve a variety of smaller problems, both routine and non-routine, that develop the underlying skills and concepts needed to solve the central problem in that unit.

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Interactive Learning
The "interactive" aspect of IMP refers, in part, to the program's emphasis on students working with each other in collaborative groups. Students discuss problems, use writing to clarify, and express complex mathematical ides and present findings to the rest of the class. Students share many different and valid approaches, expanding everyone's thinking. Together, they tackle problems that are usually too complex to be solved by any one individual.

Flexible Curriculum
The curriculum design offers complex problems that can be explored at many levels of sophistication. A typical first year IMP class includes accelerated students who have taken algebra in the 8th grade, those who would begin a college preparatory sequence in the 9th grade, and students who might have otherwise been excluded from challenging mathematics classes. A varied collection of supplemental problems gives teachers the flexibility to meet individual student needs. Special features include extensions (for students who want to pursue a specific topic in greater depth) and reinforcement experiences (for student who need to reflect on and synthesize what they have already learned).

Homework
Students complete daily homework assignments that focus on challenging their ability to think mathematically rather than drilling them on the computation skills. They also work on "Problems of the Week," open-ended investigations in which they must write and illustrate their strategies and solutions to complex problems, and deliver oral presentations to the class.

Assessment
IMP Students are evaluated according to a variety of criteria. Student grades are based on class participation, daily homework assignments, Problems of the Week, portfolios, and unit assessments, including a two-hour semester exam rather than on weekly quizzes and chapter tests.

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College Acceptance
The curriculum has been accepted as fulfilling mathematics requirements for admission to the University of California system as well as to other schools throughout the country. Students who have completed the IMP curriculum have been admitted to top schools, including Yale University, Stanford University, Howard University, Carnegie Mellon University, Columbia University, University of Michigan, and all campuses of the University of California. Click here for a complete list of schools.

SAT Performance
IMP students studied at the original three California test sites were given sample SAT tests, and their scores were compared to control groups of students in traditional mathematics classes. These sample SAT results indicate that although IMP students spend less time on traditional algebra and geometry skills they are doing as well as, and in some cases better than, students in traditional mathematics classes.

Studies of IMP classrooms in Colorado, Oregon, and Texas also indicated that IMP students are doing as well as or better than students in traditional classes on sample SAT and other competency exams.

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In 1989 IMP began as part of a curriculum-development effort funded by the California Postsecondary Education Commission (CPEC) and the California State Department of Education. With additional funding from the National Science Foundation, IMP is currently involved in disseminating the curriculum in high schools in over half the states across the United States and in Canada.

For more information, contact
IMP Outreach Coordinator
1-888-MATH-IMP

View a list of IMP Regional Centers.

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Year 1
The first-year curriculum contains an introduction to problem-solving strategies, the use of variables, and the meaning and use of functions and graphs, as well as concepts from statistics, geometry, and trigonometry. These mathematics ideas are set in varied contexts, such as the settlement of the American West, games of chance, Edgar Allan Poe's The Pit and the Pendulum, and measurement of shadows.

Year 2
Students work with powerful mathematical ideas, including the chi-square statistic, the Pythagorean theorem, and linear programming, and learn a variety of approaches to solving equations. Problem contexts include statistical comparison of populations, the geometry of the honeycomb, and maximization of profits from a cookie store.

Year 3
Students extend their understanding of material studied in preceding years of the curriculum, while learning about and applying new topics such as combinatorics, derivatives, and algebra of matrices. A baseball pennant race, population growth, and decision-making on land use provide some of the contexts for the mathematical concepts.

Year 4
Fourth-year IMP has a more varied subject matter than a calculus-focused course, and includes topics such as circular functions, computer graphics, and statistical sampling. Units build on the strong knowledge base of students who have completed three years in the program. Problem settings include a Ferris-wheel circus act and election polling.

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Lynne Alper, Sherry Fraser
Mathematics Educators, Interactive Mathematics Program

Professors Dan Fendel, Diane Resek
Mathematics Department, San Francisco State University

IMP Advisory Board

David Blackwell
Professor of Mathematics and Statistics, University of California, Berkeley

Constance Clayton
Professor of Pediatrics, Chief, Division of Community Health Care, Medical College of Pennsylvania

Tom Ferrio
Manager, Professional Calculators, Texas Instruments

Andrew Gleason
Hollis Professor of Mathematics and Natural Philosophy, Department of Mathematics, Harvard University

Milton A. Gordon
President and Professor of Mathematics, California State University, Fullerton

Shirley Hill
Curator's Professor of Education and Mathematics, School of Education, University of Missouri

Steven Leinwand
Mathematics Consultant, Connecticut Department of Education

Art McArdle
Northern California Surveyors Apprentice Committee

Diane Ravitch (1994 only)
Senior Research Scholar, Brookings Institute

Roy Romer (1992–1994 only)
Governor, State of Colorado

Karen Sheingold
Research Director, Educational Testing Service

Theodore R. Sizer
Chairman, Coalition of Essential Schools

Gary D. Watts
Educational Consultant

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* Everybody Counts (National Research Council, 1989), Reshaping School Mathematics (Mathematical Sciences Education Board, 1990), Science for All Americans (American Association for the Advancement of Science, 1989), and Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989)