**Why Change?**

The past twenty years have witnessed a growing and
intensified public demand to raise academic achievement for all students. This
demand reflects the historic shifts from an agricultural-based economy and
society in the 19^{th} century, to an industrial economy and urbanized
society in the early and mid 20^{th} century, to a knowledge-based
global economy and data driven digital society in the late 20^{th} and
21st centuries.

Mathematics has been valued for its applications in
national defense, industrial processes, financial management, medicine and all
of the social sciences. For these reasons, student achievement in mathematics,
along with English language arts, has been used as one indicator of the general
health of schools as well as of the nation’s general intellectual capacity.
Periodically, startling statistics and events have awakened the public’s
interest in students’ mathematics competence.
For example, in 1941, at the beginning of America’s involvement in World
War II, in a test of 4,200 candidates for naval officer, 62% failed math
reasoning---a critical faculty for navigation at sea. The general population
was not much better. In 1950, only 35% of persons over 25 years of age finished
four years of high school, and less than 14% of African-Americans did. For many
of those students who did manage to graduate high school, only two math courses
were commonly required. Those courses often consisted of business math,
consumer math, or general math, all of which were basically arithmetic at a middle
school reading level dressed as a high school text.

Despite massive support for higher education offered by the
GI Bill, by the late 1950s less than 8% of the population had completed four
years of college, and less than 4% of African- Americans had. (The GI Bill did
much more for high school graduation rates than college.) High-level
mathematics achievement was reserved for a small elite group. But in 1957, the
Soviet Union’s launch of Sputnik shocked the country. In the midst of the nuclear-tipped Cold War, fear swept the
nation that America’s best and brightest in math and science may not be the
world’s best and brightest. The First International Mathematics and Science
Study conducted during the 1960s documented America’s lackluster performance in
mathematics and science as compared to other First World countries.

By the late 1980s and early 1990s, the mathematics
education community responded with a host of reports that called for
fundamental changes and upgrades in mathematics education. These reports
advocated not only more years and higher levels of mathematics for students to
graduate high school, along with better trained and paid teachers, but also a *re-conceptualization* of what constituted
important mathematics content, effective teaching practices and authentic
assessments^{[1]}. These upgraded learning goals required
students to acquire a deeper understanding of the core concepts of mathematical
and scientific content. Students needed
to become comfortable, confident and competent with the processes of scientific
inquiry; no longer was it sufficient merely to master mindless robotic
mathematical tasks akin to the factory assembly line.

All of these reports delineated an expanded concept of
"basic math" found in the elementary grades to include higher-order
algebraic and geometric thinking, statistical inference, probability, modeling,
and use of calculator and computer technology to solve multi-system problems
with large data sets. Moreover, rather
than organizing mathematics education into an amalgam of isolated topics, these
reports advocated the integration of mathematics topics into fewer core concepts
to delve deeply into mathematics’ "big ideas." The 1989 National Council of Teachers of
Mathematics *Curriculum and Evaluation*
*Standards*, for example, stressed the
importance of mathematical reasoning and communication skills for the purpose
of fostering “mathematical power," for *all*
students. NCTM’s *Professional Teaching
Standards* have called for changes in the traditional
"teacher-telling/student-listening" teaching paradigm. Teachers are urged to lecture less and
facilitate more inquiry-based learning activities. By stimulating students' active experimentation with engaging
mathematical problems in interesting contexts, teachers can instill in students
a deeper understanding of mathematics.
Accordingly, assessment of a student's mathematical knowledge must
extend beyond computational proficiency to include non-routine problem solving
embedded in an application context.

While there has been widespread
acknowledgment and acceptance of the *NCTM*
*Standards*, how to actually implement
change in the classroom on an everyday basis remains problematic. The NCTM *Standards*
are learning goals. They are not a curriculum detailed enough to enable regular
classroom mathematics teachers to implement *standards*-based
lessons on an everyday basis, 180 days a year. Recognizing this problem, the National Science Foundation responded in 1989 by
supporting the development of thirteen NCTM standards-based mathematics
curricula materials projects, K-12, that are intended to be "full replacement"
texts. At the high school level, these
texts include:

§
*The Interactive
Mathematics Program (IMP), *

§
*CORE-Plus Mathematics Project, *

§
*Applications Reform in Secondary Education (ARISE),*

§
* Math Connections, and
*

§
*Systemic Initiative for Montana Mathematics and Science
(SIMMS* ).

(For a
synopsis of the common features of these NSF-sponsored mathematics curricula
and their rationale, see Appendix A. Common
Features of an NSF Curriculum)

** **

**The Interactive Mathematics program (IMP) **

This report details the research results on student
achievement using the* Interactive
Mathematics Program (IMP)* in Philadelphia public schools*.
IMP *was one of the first NSF-sponsored, standards-based,
full-replacement, high school mathematics curriculum projects. Like other new curricula sponsored by the
NSF, IMP is a high performance curriculum requiring instructional practices
that deeply embody *NCTM's Curriculum,
Teaching and Assessment Standards. *IMP
consists of 20 highly contextualized thematic units built around large
problems. (See Appendix B, Detail
of IMP Math Topics)

The IMP writing team consisted of two mathematicians from
San Francisco State University, Dan Fendell and Diane Resek, and two
mathematics educators from the EQUALS program at University of California at
Berkeley, Sherry Fraser and Lynne Alper. The design parameters for this new
curriculum were as follows:

1.
It had to fully embody the
content recommendations and spirit of the 1989 National Council of Teachers of
Mathematics *Curriculum and Evaluation
Standards.*

2.
It had to be mathematically
challenging for the best and the brightest students.

3.
It had to be a curriculum
accessible to all students.

The first IMP units were written in 1989 and were field
tested in a limited number of classrooms in three high schools in the Berkeley,
California area. Over the next several years, as more units were written, other
pilot sites were added. Subsequent feedback from IMP teachers, including
Philadelphia teachers, resulted in numerous rewrites for each unit prior to the
finished product. The 9^{th} grade level, or first year of IMP, became
commercially available in August 1996. The fourth year of IMP became
commercially available in August 1999.
In short, it has taken ten years to fully write and field test the
complete four years of IMP.

IMP in Philadelphia

In March 1992, a four and one half year contract was
awarded by San Francisco State University Foundation (SFSUF) to PATHS/PRISM: The Philadelphia Partnership
for Education, a local education fund, for the purpose of administering the
dissemination of the pre-publication pilot version of *The Interactive Mathematics Program.* The contract was funded by a
grant from the National Science Foundation to SFSUF.

IMP in Philadelphia began in the 1993-94 school year with
nine teachers representing six out of thirty-five public high schools. Approximately 300 9^{th} grade
students out of a total Philadelphia 9^{th} grade student enrollment of
15,000--roughly 2%--were enrolled in IMP the first year. (See Appendix for a time line of IMP’s
implementation in Philadelphia. Philadelphia
Expense Timeline)

Because the IMP authors retained
copyright control over the dissemination of the pre-publication IMP unit
booklets, the implementation standards of IMP could be set very high. All
initial IMP teachers received the following:

1.
ten days of training per year
in each level of IMP (240 hours total),

2.
on-going classroom mentoring,

3.
a course load reduction of
1.5 periods,

4.
a period where two IMP
teachers would team-teach,

5.
a classroom set of graphic
calculators and LCD overhead,

6.
a classroom set of
manipulatives and other supplies,

7.
regular citywide follow-up
teacher meetings.

The above implementation standards were fairly uniform
wherever IMP was being piloted in the country. The IMP authors would not grant
any school permission to use the pre-publication copyrighted materials unless
they agreed to these standards. In addition, in Philadelphia, four part-time
co-directors facilitated the implementation of IMP. These local co-directors
performed a variety of tasks which included: co-teaching IMP classes, mentoring
other teachers, helping to procure materials, collecting and analyzing student
achievement data, helping to prepare school budget for the program, and
generally ensuring district fidelity to the implementation model. (See Appendix
under Implementation
Standards )

Prior to 1996, there existed neither Philadelphia nor
Pennsylvania State math standards, nor any standards-based testing. There were
also neither Philadelphia nor Pennsylvania accountability systems. In short,
there were no external sanctions/incentives based on student achievement
data. As a result, despite the many
national reports released during the 1980s that documented the deficiencies in
mathematics education as it was currently being taught, principals and other
administrators had difficulty advocating the local need for change among their
mathematics teaching staffs. In this environment, teacher recruitment for IMP
relied on “heroic volunteers.”
Recruiting new IMP teachers proved difficult in part because, in order
to take part in the program, teachers were required to undergo extensive
professional development and additional preparation. The reduction in teacher load was at best a mild incentive for
teachers to participate, as this was the only way to compensate them for the
considerable increase in preparation time associated with being the first to
pilot a new program.

The cost of training a teacher in IMP for four years in the
early years in Philadelphia was approximately $102,000. Roughly 80% of this cost was for the 1.5
teaching period reduction in course load. Later, the 1.5 period reduction per
teacher was discontinued. By the 1999-2000 year, neither the School District of
Philadelphia nor any of the surrounding suburban districts were providing their
teachers with a reduction in course load. Many schools adopted various models
of intensive block scheduling, which provided a reduction in teaching load.
Nonetheless, even without a course load reduction of 1.5 periods per teacher,
the costs of implementing a new standards-based curriculum are considerably
greater then merely purchasing a new textbook series. (See Appendix on Four
Year Implementation Cost )

Over the years, the number of Philadelphia IMP teachers has
steadily grown to involve nearly 20% of all the high school staff. However, the
first school to adopt IMP for its entire student body was in the Philadelphia
suburbs—not the city. Strath Haven High School in the Wallingford/Swarthmore
school district was the first high school to go all IMP in 1996-97. By
September 2000, approximately 20 Philadelphia suburban districts were using IMP
or other NSF standards-based materials in both their middle and high schools.

^{[1]}These reports
include: the National Council of Teachers of
Mathematics' (NCTM), *Curriculum and
Evaluation Standards for School Mathematics* (1989); the National
Research Council's (NRC) *Everybody
Counts: A Report to the Nation on the Future of Mathematics Education*
(1989); NRC's *Reshaping School Mathematics: A Philosophy and Framework for Curriculum
*(1990); NRC's *Summit on Mathematics
Assessment* (1991); and NCTM's *Professional
Standards for Teaching Mathematics* (1991).