Table of Contents

**What is IMP?**

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.

**How Does IMP Address the Common Core State Standards?**

With the use of IMP, teachers can be confident that they will meet the Standards for Mathematical Practice as outlined in the Common Core State Standards for Mathematics. Teachers can quickly see that their students will be problem solvers through the use of “Problems of the Week.” Students will model mathematics and attend to precision by investigating situations and generalizing the mathematics embedded in each problem. The use of logic and proof will allow students to practice being persuasive writers as well as critics of arguments set before them.

The IMP curriculum consistently employs the Standards for Mathematical Practice throughout the four-year program. Students will see the value of these practices in all the assignments, activities, and investigations that they perform. These include Problems of the Week, classroom investigations, presentations, alternative assessments, and portfolios.

Teachers will also see their teaching of IMP mirror the eight Standards for Mathematical Practice. Teachers will discover a multi-faceted approach to teaching that reaches all learners.

**Why is a Change Needed in Mathematics Education?**

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.

IMP integrates traditional areas of mathematics with new topics such as probability, statistics, discrete mathematics, and matrix algebra. It also includes the use of graphing calculators and computers, encourages cooperative learning, and is accessible to all students.

**How Does IMP**** differ from Traditional High School Mathematics Courses?**

**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 textbook. 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.

**What happens in an IMP Classroom?**

**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 a 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 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.

**Does IMP Prepare Students for College?**

**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.

**Case Study: Comparison of IMP Students’**

**Progress to Peers in Traditional Mathematics**

While a formal, five-year evaluation of IMP is currently

underway, schools with IMP classrooms have conducted

their own research as well. In the Colorado study, sample

SAT tests were given to IMP Year One and Algebra I

students at the beginning and end of the academic year

(1991–92). The average gain of IMP Year One students

was significantly higher than that of Algebra I Students.

**SAT Average Raw Scores***

**Eaglecrest High School, Aurora, Colorado**

*Average raw scores of IMP Year One students increased by 2.92,

while average raw scores of Algebra I students increased by only

1.25. The difference in growth was significant at the .025 level.

**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 the sample SAT and other competency exams.

**IMP Nationwide**

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, call 1-888-698-TIME (8463).

**IMP Curriculum Content: A Summary**

**Year 1**

Revised to better help you prepare your students for algebra-based standardized tests, the second edition of Year 1 provides a broader introduction to algebra and more formal work with linear functions and algebraic symbol manipulation. 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, linear programming, and quadratic functions—and learn a variety of approaches to solving equations. Problem contexts include a statistical comparison of populations, the geometry of the honeycomb, and maximization of profits from a cookie store.

**Year 3**

Students extend their understanding of the material studied in preceding years of the curriculum while learning about and applying new topics such as combinatorics, derivatives, and the 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**

Revised to complete the four-year IMP curriculum, the second edition of fourth-year IMP has a more varied subject matter than a calculus-focused course and includes topics such as circular functions, computer graphics, statistical sampling, and the Fundamental Theorem of Calculus. Units build on the strong knowledge base of students who have completed three years in the program; further, the modified unit The Diver Returns completes the solution of the High Dive problem from Year 3, while the all-new unit How Much? How Fast? follows up on the Year 3 unit, Small World, Isn’t It? by looking at the issue of accumulation of change. Problem settings in Year 4 include a Ferris-wheel circus act, election polling, and a solar energy collector.

**IMP Co-Directors**

**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), andCurriculum and Evaluation Standards for School Mathematics(National Council of Teachers of Mathematics, 1989)