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.
II Essential Features
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
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.
III IMP at ARHS
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.
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.
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.