Introduction and Implementation Strategies for the Interactive Mathematics Program: A Guide for Teacher-Leaders and Administrators

IMP's Record of Success

It stands to reason that before teachers or districts would undertake the kind of changes described in the previous section, they would want some assurance that the program is successful. The record provides this assurance on many levels.

The IMP™ curriculum has been thoroughly field-tested.

This is probably the most carefully and thoroughly field-tested program you will ever see. Beginning in 1989, IMP began a testing and evaluation process that has involved hundreds of teachers and tens of thousands of students throughout the United States.

• Almost every activity was used at teacher workshops and evaluated by participants before ever being used in the classroom.
• Initial drafts of each unit were reviewed by subject-matter experts before field testing.
• Field testing involved schools with widely varying demographics.
• During field testing, the IMP directors sat in classrooms every week, talking with students, observing their reactions to the activities, and meeting with teachers to hear their insights.
• Two of the IMP directors team-taught the first three years of the program in its initial draft.
• Each unit was revised after its first field testing; the revised units were field-tested in hundreds of classrooms over a four-year period. A few units were revised again during this period.
• The entire program was classroom-tested in real time as a four-year sequence, so that each unit could build on what students had learned earlier in the program. Units were never tested in isolation.
• After this extensive field testing, and with the full curriculum written, every unit underwent a thorough reexamination with a team of experienced classroom teachers, based on the longitudinal experience of the extensive field test. This reexamination led to yet another revision.
• These revised versions were retested in several classrooms (an IMP director was one of the teachers testing this version); once again, the feedback of teachers was incorporated into the curriculum.

The IMP curriculum is mathematically sound.

IMP directors Dan Fendel and Diane Resek, who are the authors of the curriculum, are professors of mathematics at San Francisco State University. They hold doctoral degrees in mathematics and have written mathematics research articles and college mathematics textbooks.

IMP's Advisory Board includes nationally recognized mathematicians and mathematics educators:

• David Blackwell, Professor of Mathematics and Statistics, University of California at Berkeley
• Andrew Gleason, Hollis Professor of Mathematics and Natural Philosophy, Department of Mathematics, Harvard University
• Milton Gordon, President and Professor of Mathematics, California State University, Fullerton
• Shirley Hill, Professor of Education and Mathematics, University of Missouri, and President of the National Council of Teachers of Mathematics, 1978–1980
• Steven Leinwand, Mathematics Consultant, Connecticut State Department of Education, and President of the National Council of Supervisors of Mathematics, 1995–1997

The IMP curriculum is pedagogically sound.

IMP directors Lynne Alper and Sherry Fraser, who field-tested the program, are highly regarded mathematics educators with extensive experience in the classroom as secondary teachers. For many years, they developed and led workshops at the Lawrence Hall of Science of the University of California at Berkeley; they have been in the forefront of efforts to improve the teaching and learning of mathematics.

The IMP curriculum is based solidly on the experiences of hundreds of teachers in IMP classrooms, who provided extensive feedback throughout the formal developmental process described earlier, as well as through informal conversations, by telephone, at workshops, and through electronic mail. These teachers have reported to the authors what did or didn't go well in each unit, identifying potential trouble spots and sharing the solutions they have found to classroom difficulties. Their ideas have been incorporated into the final published materials and their teaching hints have been used in creating a detailed Teacher Guide for each unit.

Formal evaluations show documented success.

Numerous studies have documented the success of the Interactive Mathematics Program. These include a major evaluation funded by the National Science Foundation (NSF), as well as local studies conducted by individual districts. The NSF study is led by Dr. Norman Webb of the Wisconsin Center for Education Research (WCER) at the University of Wisconsin, Madison. Dr. Webb is in the forefront of evaluation of mathematics education programs, such as the Urban Mathematics Collaboratives and other successful NSF mathematics and science programs.

Here are a few highlights of IMP's evaluation successes.

• A detailed WCER study of all 1993 graduates at IMP's three pilot schools showed that IMP students took significantly more mathematics courses than their counterparts in traditional programs.
• The same study showed that IMP students had significantly higher overall grade point averages than students in traditional programs.
• Another component of the WCER evaluation examined both IMP and non-IMP students at a large urban high school who had scored in the upper 25th percentile (based on national norms) on the seventh-grade level Comprehensive Test of Basic Skills. On the average, IMP students in this study of "high achievers" finished high school with higher overall grade-point averages and got higher SAT mathematics scores than non-IMP students with equivalent seventh-grade scores.
• In every one of many local studies of scores on standardized tests, IMP students have done at least as well as students in traditional programs. Because IMP students learn not only the material in the traditional curriculum but also other mathematical topics not covered on these tests, this represents an important achievement.
• A study in Philadelphia showed a 17% increase in attendance among IMP students as compared to their counterparts in traditional programs.
• In a 1995 study of innovative programs in inner-city schools by the Consortium for Policy Research in Education, students in an IMP course showed the highest gains in mathematics achievement among all programs evaluated.

  IMP has developed a series of Evaluation Updates on the WCER study and local evaluation data that provide more details on these and other results.

IMP students are achieving success in college.

IMP students have been admitted to and are succeeding at a wide variety of colleges and universities, including some of the most selective schools in the nation.

When the program began in California, the curriculum had to undergo careful scrutiny from mathematicians in the University of California system. It has been officially approved as meeting University of California admission requirements, and other universities have followed suit.

Many students have written about their IMP experience as part of their college applications; admissions officers have responded enthusiastically.

IMP graduates have also been writing to their teachers about their experiences after they leave high school. They talk about how well prepared they are for more advanced mathematics.

They also talk about the differences they see between their attitudes toward learning and the approaches taken by students with traditional preparation. IMP students describe themselves as more inquisitive, more confident, and better able to apply what they know in new situations.

Appendix C: College Acceptance of IMP Students lists colleges and universities that have accepted IMP graduates for higher education.

Teachers endorse this curriculum.

Change is not easy; moving from a skill-based curriculum to a deep, problem-based curriculum is an enormous amount of work. The willingness of so many teachers to accept this challenge and all the extra work it entails is a stirring endorsement of the program.

What motivates a teacher to switch to IMP?

Teachers are unequivocal in stating that the enormous rewards make it worth the effort. They report that they are energized and rejuvenated by the effect of IMP on their students -- amazed by what students can achieve, by their insightful and innovative thinking about mathematics. Many of those who have used the IMP curriculum have always been innovative in their teaching; they come to IMP because it supports them in what they have been trying to accomplish on their own. Others are simply frustrated by the inability of their existing programs to meet the needs of their students.

Many teachers say teaching IMP has resulted in a change in their perception about themselves. They have come to perceive themselves as mathematicians as well as mathematics educators. They cite two reasons.

First, they are learning mathematics they never studied before, such as complex concepts from statistics. Second, even some veteran teachers of 25 and 30 years exclaim that they really understand for the first time why some of the procedures they have taught over and over again work the way they do. This enthusiasm about mathematics is infectious, and their willingness to keep on learning affects their students positively.

Business and industry support this kind of change.

Business and industry have been strong advocates of the kind of change in mathematics education that IMP provides; leading private foundations are putting dollars behind their words of support. For example, The Noyce Foundation, the Intel Foundation, and the David and Lucile Packard Foundation are major funders of IMP. These organizations promote the dissemination of IMP's work because they regard the program as successfully preparing students to think, to reason, to communicate clearly with others, and to work effectively as members of a team.