In 1989, the National Council of Teachers of Mathematics[NCTM] issued a visionary document titled, Curriculum and Evaluation Standards for School Mathematics. The Standards called for a high quality core curriculum for all high school students and for changes in the way mathematics is taught. More than 50 professional organizations of educators, mathematicians, scientists, engineers and industry leaders are on record supporting the vision and recommendations in the Standards. Updated in 2000, the Standards have stood the test time; still, today, they define the terms of math discussion and debate nation-wide. At ARHS, our aim is to realize, for all our students, the vision of math articulated in the Standards.
The National Science Foundation (NSF) embraced the Standardsand set out to ensure that they were fully implemented in math classrooms throughout the country. To this end, they funded the development of a number of mathematics curriculum projects in the early 1990’s that sought to capture and operationalize the NCTM standards. The Interactive Mathematics Program, begun in 1989, was one of about a dozen high school curriculum projects to receive NSF funding.
In 1996, after several rounds of field testing, revision and independent research commissioned by NSF establishing its effectiveness, the four-year integrated IMP program was published by Key Curriculum Press, making it one of first high school programs specifically designed to realize the full vision of the Standards.
IMP differs from a traditional approach to high school math in a number of important ways:
IMP is problem-centered. IMP units typically involve a central problem that is too complex to solve initially. Students work on smaller problems over a number of weeks developing the concepts and skills needed to solve the central problem. These problems give mathematics learned on a daily basis a purpose for students and highlight the connections between different mathematical concepts and skills.
IMP is integrated. Mathematical ideas and skills from strands such as algebra, geometry and trigonometry are integrated through the central unit problems, enabling students to see how important mathematical ideas are related to one another. Over four years, the various strands are developed more and more deeply and students come to understand and apply them in more complex and sophisticated ways.
IMP expands the content scope of high school mathematics. Following the recommendations of the NCTM Standards, IMP includes significant work with probability, statistical reasoning and discrete mathematics. Despite the widespread recognition of the need for all students to develop statistical literacy, data analysis and probability are almost completely absent from the traditional course sequence.
IMP focuses on developing understanding. By giving students experiences resembling the inquiry method used by mathematicians and scientists in their work, students develop in-depth understanding of mathematical concepts and techniques and the ways to apply them. Students regularly gather and organize data, search for and express patterns, and make, test and prove conjectures.
IMP includes long-term, open-ended investigations. Each IMP units contains several Problems of the Week (POWs). These problems are designed to require a sustained effort over time to make meaningful progress. Working about 50 such problems over 4 years, IMP students develop thoughtfulness, perseverance and a wide range of problem-solving strategies. Extensive written reports help students develop their reasoning and communication skills, two more pillars of the NCTM standards.
IMP can serve students with varied mathematical backgrounds in heterogeneous classrooms. Segregating students by ability, a practice commonly known as tracking, reflects, deepens and reinforces the divisions and inequities in the world outside of school. On the other hand, simply mixing everyone together without taking into account how the needs of all students will be met is equally irresponsible. At ARHS, we chose IMP because equity through differentiated instruction in heterogeneous classes was a central goal and design principle of the program and the record, as will be described below, indicates that IMP is capable of meeting that goal.
The ARHS Math Department spent two years researching and discussing IMP prior to proposing this addition to the School Committee. Teachers and administrators visited three schools with IMP programs, observed classes and interviewed students and teachers. We also reviewed the extensive research that has been conducted on IMP’s effectiveness, covering a variety of measures. We looked carefully at the available evidence of effectiveness before choosing to offer IMP. The information and studies cited below contributed to our confidence that, with adequate support for implementation, IMP would help many of our students achieve greater access to high quality mathematics.
In 1999, at the direction of Congress, the US Department of Education convened a panel of experts to identify exemplary mathematics programs. IMP was one of only five programs to receive the ‘exemplary’ designation. In order to receive the “Exemplary” designation, the panel had to find convincing evidence of effectiveness in realizing the vision of the NCTM Standards in multiple sites with multiple populations. More information can be found at http://www2.ed.gov/PressReleases/10-1999/mathpanel.html and at www.edpubs.ed.gov.
In 1993, Dr. Norman Webb of the Wisconsin Center for Educational Research (WCER) was commissioned by the NSF to evaluate the impact of IMP on student learning. The study looked at the following measures:
Completion of College-Preparatory Mathematics Courses. The level of high school mathematics is a better predictor of college completion than high school grades or standardized test scores. The study found that IMP students took more math courses, especially advanced math courses, than their counterparts in traditional math programs and that the difference was statistically significant at the .01 level.
Achievement on Traditional Standardized Tests. In every part of this study IMP students performed as well as or better than their peers in traditional programs on the Comprehensive Test of Basic Skills (CTBS) and the Scholastic Aptitude Test (SAT). While in only one comparison was the difference statistically significant at the .01 level, we found it important that IMP students did at least as well on standardized tests at the same time that IMP students spent significant time on non-traditional topics like probability and statistics that are recommended by NCTM.
Student Performance on Probability, Statistics and Quantitative Reasoning. These studies suggest that IMP students are learning mathematics in areas emphasized by IMP. In all studies, IMP students did as well or better than their peers in traditional programs. In several comparisons the differences were statistically significant at the .01 level.
Dr. Webb’s full report can be found in the book, Standards Based School Mathematics Curricula, What Are They? What Do Students Learn? A copy of this book is available in the ARHS library. Some of these studies can also be found at Dr. Webb’s website: http://facstaff.wcer.wisc.edu/normw/IMP%20Page1.htm. A report to the NSF based on Dr. Webb’s research and titled The Impact of the Interactive Mathematics Programby Harold Schoen of the University of Iowa can also be found at http://facstaff.wcer.wisc.edu/normw/NSF%20IMP%2093%20Scan.pdf.
The Greater Philadelphia Secondary Math Project (GPSMP) has conducted extensive research on a variety of measures (see http://www.gphillymath.org/StudentAchievement/Reports/SupportData/StudentAchievMeas.pdf) and on schools representing a variety of demographics. The executive summary of a five year research program states:
When IMP students were taught by teachers who had been properly trained, IMP students consistently out-performed similar students who were taught using a pre-NCTM standards curriculum and subjected to lecture style instruction. The superior performance results of IMP were found using a variety of measures and across different student ability levels, when measures for achievement are controlled for 8th grade cohort effects. That is, lower ability IMP students did better than their lower ability counterparts while higher ability IMP students did better than their higher ability counterparts.
The full report can be found at http://www.gphillymath.org/StudentAchievement/Reports/AssessCostIndex.htm.
The GPSMP website also contains links to other studies and data related to IMP’s effectiveness: http://www.gphillymath.org/StudentAchievement/Reports/Initial_report_Greendale.pdf.
An NSF-funded study by Dr. Jo Boaler titled, Stanford University Mathematics Teaching and Learning Study: Initial Report – A Comparison of IMP1 and Algebra 1 at Greendale School, (http://www.gphillymath.org/StudentAchievement/Reports/Initial_report_Greendale.pdf) found, among other results, that IMP Year 1 students did as well as traditional Algebra 1 students on a test of algebra, even though IMP 1 covers topics in probability, statistics, geometry and trigonometry not covered in the traditional course.
As part of the NSF-funded development, the Interactive Mathematics Program disseminated information about the program to every college admissions office in the country. The IMP website contains a partial list compiled from information reported by teachers of colleges and universities where IMP students have been accepted for admission (http://www.mathimp.org/research/colleges/index.html.) We were impressed that MIT, Cal Tech, RPI and many other highly selective technical schools are included in this list as well as all of the Ivy League schools. In the past two years our first IMP students have graduated from ARHS and have been accepted at schools like Amherst College, Skidmore and Brandeis among many others.