Interactive Mathematics Program (IMP)

The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools, designed to meet the needs of both college-bound and non-college-bound students. It was one of several curricula funded by the National Science Foundation and designed around the 1989 National Council of Teachers of Mathematics standards. The curriculum replaces the traditional Algebra I-Geometry-Algebra II/Trigonometry-Precalculus sequence. The IMP books were authored by Dan Fendel and Diane Resek, professors of mathematics at San Francisco State University, and by Lynne Alper and Sherry Fraser.

Designed in response to national reports pointing to the need for a major overhaul in mathematics education, [ [http://www.nap.edu/books/0309039770/html/] "Everybody Counts: A Report to the Nation on the Future of Mathematics Education", Mathematical Sciences Education Board, National Research Council, 1989] [ [http://books.nap.edu/openbook.php?isbn=0309041872] "Reshaping School Mathematics: A Philosophy and Framework for Curriculum", Mathematical Sciences Education Board, National Research Council, 1990] [ [http://www.project2061.org/publications/sfaa/online/sfaatoc.htm] "Science for all Americans", American Association for the Advancement of Science, 1989] the [http://www.mathimp.org/ IMP curriculum] is markedly different in structure, content, and pedagogy from courses more typically found in the high school sequence. ["Introduction and Implementation Strategies for the Interactive Mathematics Program: A Guide for Teacher-Leaders and Administrators", Key Curriculum Press, 1997]

* Each book of the curriculum is divided into five- to eight-week units, each having a central problem or theme. This larger problem serves as motivation for students to develop the underlying skills and concepts needed to solve it, through solving a variety of smaller related problems.

* Each year of the IMP curriculum integrates the algebraic, geometric, and trigonometric topics traditionally taught in separate courses, as well as topics from statistics and probability that are not included in many traditional programs.

* There is an emphasis on students working together in collaborative groups. Together, they tackle problems that are usually too complex to be solved by any one individual.

* The development of communication skills is embedded throughout the curriculum, through the use of group and whole class discussions, the use of writing to present and clarify mathematical solutions, and formal oral presentations.

* The IMP curriculum expects students to make nearly daily use of a scientific graphing calculator. Students become comfortable with the calculator to such an extent that a Year 4 project tasks students with using their knowledge of trigonometry, matrix algebra, geometric projections and transformations, and computer programming to design and present an animated cartoon on the screen of the graphing calculator. [Fendel, R., Resek, D., Alper, L. and Fraser, S: “An Animated POW”, page 160, "Interactive Mathematics Program: Year 4", Key Curriculum Press, 2000.]

Debate

Nearly every one of these distinctive characteristics has generated controversy and placed the IMP curriculum right in the middle of the “math wars,” the conflict between those that favor more traditional curricula in mathematics education and the supporters of the reform curricula that were largely an outgrowth of the 1989 NCTM standards.

IMP is among the reform curricula that have been heavily criticized by organizations such as Mathematically Correct. That organization’s Internet site begins with a statement that “advocates of the new, fuzzy math” (focus) “on things like calculators, blocks, guesswork, and group activities and they shun things like algorithms and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement.” [ [http://www.mathematicallycorrect.com/] Mathematically Correct, www.mathematicallycorrect.com] Former NCTM president Frank Allen states, “Trying to organize school mathematics around problem solving instead of using its own internal structure for that purpose … (is destroying) essential connections….” [ [http://mathematicallycorrect.com/allen1.htm] Allen, F: “A Critical View of NCTM Policies with Special Reference to the Standards Reports”]

Criticism often includes anecdotal evidence including stories of school districts that have decided to discontinue or supplement use of the IMP curriculum [ [http://www.thenewstribune.com/news/local/story/6051712p-5310251c.html] Abe, D: "Back to Basics on Kids’ Math: Alarmed by Low Scores, Tacoma School Officials OK Added Saxon Textbook,” "The News Tribune" (Tacoma WA), August 25th, 2006 ] and of students who did not feel they had been prepared adequately for college. [ [http://mathematicallycorrect.com/impsf.htm] Datta, S: “Interactive Mathematics Program: Manifesto on an Experimental Concept Gone Awry”] "Regular math is much better, it makes much more sense," says Aimee Lynn Stearns, a student at Taos High School in Taos, New Mexico.

On the other hand, some IMP students describe the program in positive terms. "It's fun, but it makes you really think," according to Ziouck Gonzalez, a student at Wells High School in Chicago, Illinois. Looking beyond student response, IMP was one of five mathematics education programs designated "exemplary" by the US Education Department in 1999, for "outstanding quality and demonstrated effectiveness." [ [http://findarticles.com/p/articles/mi_puca/is_199910/ai_2981414283] "Expert Panel Selects Exemplary, Promising Mathematics Programs," US Education Department Press Release, October 6, 1999] Key Curriculum Press, the publisher of IMP, points out “the IMP first edition was published after more than 10 years of research, pilot testing, evaluating, field testing, revising, and detailed reviewing.” [ [http://www.mathimp.org/downloads/IMPWhitePaper.pdf] “Research Supporting the Interactive Mathematics Program”]

Supporters point to statistical studies that compare the performance of students enrolled in IMP courses with their peers enrolled in traditional high school mathematics courses. Merlino and Wolff, two such researchers, report that in their several studies IMP students consistently outperformed traditionally taught students on both the math and verbal sections of the PSAT, as well as on the SAT-9. [ [http://www.gphillymath.org/StudentAchievement/Reports/SupportData/Part1Intro.htm] Merlino, J. and Wolff, E: "Assessing the Costs/Benefits of an NSF “Standards-Based Secondary Mathematics Curriculum on Student Achievement", Philadelphia, PA: The Greater Philadelphia Secondary Mathematics Project, 2001] Kramer reported that grade 12 IMP students in his study performed better on all areas of mathematics tested by the NAEP test, [ [http://lmt.mspnet.org/media/data/IMP_block.pdf?media_000000002049.pdf] Kramer, S: “The Joint Impact of Block Scheduling and a Standards-Based Curriculum on High School Algebra Achievement and Mathematics Course Taking” (doctrinal dissertation), University of Maryland, 2003] and Webb and Dowling reported IMP students performed significantly better on statistics questions from the Second International Mathematics Study, on mathematical reasoning and problem solving tasks designed by the State of Wisconsin, and on a quantitative reasoning test developed by a university to administer to entering students. [Webb, N. and Dowling, M: “Comparison of IMP Students with Students Enrolled in Traditional Courses on Probability, Statistics, Problem Solving, and Reasoning,” "Project Report 97-1", University of Wisconsin – Madison, Wisconsin Center for Education Research, 1997]

Notes

Links

* [http://www.mathimp.org/] Publisher’s IMP web site
* [http://www.mathematicallycorrect.com/] Mathematically Correct home page