ERIC Identifier: ED372969
Publication Date: 1994-10-00
Author: Edwards, Thomas G.
Source: ERIC Clearinghouse for
Science Mathematics and Environmental Education Columbus OH.
Current Reform Efforts in Mathematics Education. ERIC/CSMEE
The current reform effort in mathematics education has its roots in the
decade of the 1980s and the national reports that focused attention on an
impending crisis in education, particularly in mathematics and science (e.g.,
"An Agenda for Action," 1980; "A Nation at Risk," 1983; "A Report on the Crisis
in Mathematics and Science Education," 1984). It received further impetus with
the publication by the National Council of Teachers of Mathematics (NCTM) of
"Curriculum and Evaluation Standards for School Mathematics" (1989) and
"Professional Standards for Teaching Mathematics" (1991). The Mathematical
Sciences Education Board (MSEB, 1990) urges that school mathematics programs be
revised and updated to reflect the NCTM "Standards," develop students'
mathematical power, use calculators and computers throughout, feature relevant
applications, and foster active student involvement.
Within this context, dozens of individual reform efforts have been initiated
in recent years. Many have focused on the development of new curricula, others
on teacher enhancement, some on both. Still others have taken the use of
technology in mathematics instruction as their central theme. The projects
listed below are but a small sample of current efforts, but they serve to
illustrate the diversity of programs nationwide.
CURRICULAR REFORM PROJECTS
The "Connected Mathematics
Project (CMP)" at Michigan State University is a five-year National Science
Foundation (NSF)-funded project for the development of a middle school
mathematics curriculum rich in connections. Students solve problems by observing
patterns and relationships, thereby enhancing their understanding of
mathematics. Natural extensions involve conjecturing, testing, discussing,
verbalizing, and generalizing. In addition to student materials, "CMP" is
developing teacher materials designed so that teachers can learn directly from
their use and assessment materials that are extensions of the learning process.
"The Adventures of Jasper Woodbury" is a series of four problem-solving
videodisks developed by the Cognition and Technology Group at Vanderbilt
University, supported in part by grants from NSF and the James S. McDonnell
Foundation. The theory underpinning this work emphasizes the importance of
developing instruction in meaningful, active contexts and is in step with the
Standards recommendation that problem-solving applications should drive
instruction (NCTM, 1989).
The University of Illinois at Chicago NSF-funded project, "Maneuvers With
Mathematics (MWM)" has produced a series of student lab books to supplement or
replace components of the middle grades mathematics curriculum. "MWM" presents
thought-provoking, original problems that utilize manipulative materials.
Students investigate a series of carefully sequenced activities aimed at
hands-on discovery of mathematical concepts that often integrate mathematics
with other content areas.
Mathematics in Context has been funded by NSF to create a comprehensive
mathematics curriculum for the middle grades that reflects the content and
pedagogy suggested by the NCTM Standards (1989, 1991). The University of
Wisconsin--Madison and the Freudenthal Institute at Utrecht University are
collaborating with middle school mathematics teachers to develop the curriculum.
These materials will support teachers' efforts to connect students' previous
knowledge with new ideas, connect conceptual and procedural knowledge, and
connect mathematics with other fields of human endeavor.
The "Quantitative Reasoning Project (QRP)" at San Diego State University is
an NSF-funded project investigating the development of students' algebraic
reasoning in the middle grades following instruction that emphasizes
quantitative reasoning. "QRP" has objectives in three domains: students'
cognitions, teachers' cognitions, and materials development. "QRP" will identify
areas of the middle school mathematics curriculum that can be modified to allow
for direct instruction in quantitative reasoning and will develop activities and
problems to support such instruction.
Since 1983, the "University of Chicago School Mathematics Project (UCSMP),"
funded by Amoco, General Electric, and the Carnegie Corporation, has developed a
six-year secondary mathematics curriculum encompassing a broad scope of content
and emphasizing real-world applications. In focusing on both procedural and
conceptual knowledge, student understanding is developed in four domains:
skills, concepts, applications, and representations. Reading mathematics is
stressed for all students, and appropriate use of computers and graphing
calculators is presumed. "UCSMP" is currently developing a K-6 curriculum
structured as a helix, with skills and concepts developed over time and
revisited in varying contexts. The materials assume the use of calculators and
TEACHER ENHANCEMENT PROJECTS
Some teacher enhancement
projects are aimed at all mathematics teachers of particular grade levels, while
others target teachers of specific student populations, such as minority
students or groups that have traditionally been underrepresented in higher
mathematics courses. Many projects target teachers who work in urban classrooms.
Projects With a General Focus. The "Atlanta Math Project (AMP)" at Georgia
State University is an NSF-funded project operating in 13 school systems in the
metropolitan Atlanta region. "AMP" provides teachers with experiences that
facilitate their construction of knowledge about teaching and learning
mathematics consistent with the NCTM "Standards." Project activities include
summer professional development; on-site school-year support in the form of
planning, teaching, and debriefing sessions; and peer mentoring.
"Teaching to the Big Ideas (TBI)" is a four-year professional development
project involving staff from Education Development Center, Mt. Holyoke College,
and the Technical Education Research Center (TERC), in which teachers address
the big ideas--the central organizing principles--of mathematics. During the
first two years of the project, TBI will engage participants through summer
institutes, bi-weekly after-school meetings, and classroom visits. The last two
years will feature summer institutes, as well as a year-long course geared
toward the development of participants as teacher leaders.
Projects Targeting Specific Populations. California State Polytechnic
University at Pomona, in cooperation with school districts in Southern
California, is conducting a teacher enhancement program called "Integrating
Science and Mathematics Teaching for Middle School Underrepresented Students."
This three-year project will offer hands-on instruction that integrates science,
mathematics, and teaching methods consistent with the NCTM Standards, the new
science standards, and the appropriate California state frameworks.
"Math Matters" is an NSF-funded four-year grant to the California Department
of Education to improve the mathematics achievement of Chapter 1 and migrant
students in the upper elementary grades. "Math Matters" is a comprehensive
professional development program which encourages teachers to share experiences
with their peers. The major components of the project are mathematics for the
professional growth of participants, mathematics for the classroom, management
and content strategies, and assessment practices.
The "New York City Mathematics Project (NYCMP)" is a K-12 staff development
project that responds to the critical problem of providing a quality mathematics
program for all students in urban classrooms. "NYCMP" seeks to produce a
leadership network of teachers, exemplary environments for teaching mathematics
in urban classrooms, and a support system for ongoing staff development. The
four stages in the staff development model used by "NYCMP" are becoming aware of
the need to change, making major changes in teaching practice, becoming a
teacher leader, and finally, teaching in the project.
"Project IMPACT" is a cooperative between the University of Maryland at
College Park and the Montgomery County Public Schools. Partially funded by IBM,
the project is developing a model for elementary mathematics instruction that
enhances student understanding and supports teacher change in predominantly
minority schools. "IMPACT" is a school-based project that includes a summer
in-service program, on-site mathematics specialists, innovative classroom
materials, and a common mathematics planning period for all teachers of a given
grade level in each school.
The Learning Research and Development Center at the University of Pittsburgh
has undertaken the "Quantitative Understanding: Amplifying Student Achievement
and Reasoning (QUASAR) Project" in response to the related crises of low levels
of student participation and inadequacy of student performance in mathematics.
QUASAR addresses the needs of schools serving economically disadvantaged
children, using a coherent set of general principles as guides for reform while
recognizing the importance of tying reform efforts to local conditions.
Instructional practices at all sites feature increased emphasis on mathematical
discourse, the application of mathematics to problems that are meaningful to
students, and the use of physical and mental models to provide concrete
grounding for abstract principles. QUASAR encompasses curriculum development and
modification, staff development and ongoing teacher support, classroom and
school-based assessment design, and outreach to parents and the community.
PROJECTS INVOLVING BOTH CURRICULUM REFORM AND TEACHER
At the University of Wisconsin Center for Educational Research,
Cognitively Guided Instruction (CGI), partially supported by an NSF grant,
structures workshop environments in which teachers synthesize findings of
research on children's mathematical thinking to inform their teaching. As a
result, each teacher can construct a mathematical learning environment that fits
her or his own teaching style, knowledge, beliefs, and students.
At the University of Delaware, an NSF-funded project is developing a model
for implementing the NCTM Standards. Project goals are to develop mathematical
power in teachers and assist them in implementing Standards-based curricula in
their classrooms. To achieve these goals, the Delaware Teacher Enhancement
Project seeks to enhance teachers' knowledge of mathematical content, pedagogy,
and curriculum, and to help them develop a supportive school environment.
The primary goals of the Math Learning Center (MLC) at Portland State
University are to develop curriculum materials and workshops for middle school
teachers who seek to change the way mathematics is learned in their classrooms.
MLC materials emphasize visual thinking, exploration, and experimentation.
Workshops typically engage teachers in hands-on activities that model
independent investigation, small group cooperative learning, and whole class
PROJECTS FOCUSED ON TECHNOLOGY
The Calculator and Computer
Precalculus (C2PC) Project at Ohio Sta te University has produced a curriculum
based on computer/calculator-generated graphs. Students use the power of
visualization to solve realistic, interesting applications through exploration
and experimentation. Because technology enables interactive instruction that
casts teachers in nontraditional roles, C2PC conducts workshops to assist
teachers in mov ing beyond transmission of knowledge to facilitation of
The Computer Intensive Algebra (CIA) Project has capitalized on opportunities
for improving instruction in algebra using computers and calculators. With
support from NSF grants to the University of Maryland and Pennsylvania State
University, CIA has developed a computer-based algebra curriculum featuring
models and representations of algebraic ideas, variables and functions as
unifying concepts, and a balance between conceptual and procedural knowledge in
Because CIA de-emphasizes routine skills in favor of computer-based
explorations, teachers must assume a variety of unfamiliar roles. Empowering
Teachers in Computer-Intensive Environments will construct a series of courses
and practica to prepare teachers to implement computer-intensive curricula by
increasing their mathematics content knowledge through a computer-intensive
course, developing their ability to assess and analyze student understanding in
technology-rich learning environments, assisting them to conduct research in
their own classrooms, and focusing their attention on teaching/learning issues
in computer-intensive learning environments.
One result of an NSF-supported cooperative project among SUNY at Buffalo,
Kent State University, TERC, and Southeastern Massachusetts University is
Geo-Logo, a new Logo environment that emphasizes in-depth exploration of
meaningful mathematical problems, supports construction of the abstract from the
visual, connects different representations, and encourages procedural thinking
to undergird conceptual understanding.
The Graphing Calculator-Enhanced Algebra Project--funded by NSF, the
Interlochen Arts Academy, and Texas Instruments--starts with the premise that
students have access to graphing calculators and teachers have comparable
technology for in-class demonstrations. The curriculum materials feature fewer
problems considered in greater depth, emphasis on small group work, analysis of
graphical representations, and development of mathematical concepts in
real-world contexts accessible to high school students.
The Oregon State University Calculus Curriculum Project has developed a
curriculum that uses supercalculators (e.g., HP-48SX) and emphasizes multiple
representations of functions, graphical interpretations, conceptual
understanding, real-world applications, mathematical modeling, and the
intelligent use of technology with full awareness of its limitations.
In 1992, NSF began funding Statewide
Systemic Initiatives (SSIs) for the purpose of improving school mathematics and
science education. Some SSIs exhibit elements of both curriculum reform and
teacher enhancement (e.g., the Systemic Initiative for Montana Mathematics and
Science), while others are primarily teacher enhancement projects (e.g., Ohio's
Project Discovery). Beginning with the 1993-94 school year, NSF is funding Urban
Systemic Initiatives (USIs), to improve mathematics and science education under
the special circumstances of urban schools.
American Association for the Advancement of
Science. (1984). A report on the crisis in mathematics and science education:
What can be done now? New York: J. C. Crimmins.
Mathematical Sciences Education Board. (1990). Reshaping school mathematics:
A philosophy and framework for curriculum. Washington, DC: National Academy
National Commission on Excellence in Education. (1983). A nation at risk: The
imperative for educational reform. Washington, DC: U. S. Government Printing
National Council of Teachers of Mathematics. (1980). An agenda for action:
Recommendations for school mathematics of the 1980s. Reston, VA: Author.
National Council of Teachers of Mathematics. (1989). Curriculum and
evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (1991). Professional standards
for teaching mathematics. Reston, VA: Author.