||The Center for the Study of Mathematics Curriculum (CSMC) was funded in 2004 by the
National Science Foundation (Award No. ESI-0333879) under the "Centers for Learning and Teaching" (CLT) program.|
The CSMC serves the K-12 educational community by focusing scholarly inquiry on issues related to the development,
implementation, and use of mathematics curriculum. Major areas of work include understanding the influence and potential
of mathematics curriculum standards and textbook materials, enabling teacher learning through curriculum material
investigation and implementation, and building capacity for developing, implementing, and studying the impact of mathematics curriculum.
- Advance a research agenda related to K-12 mathematics curriculum materials and standards focusing on the relationship between curriculum and student learning.
- Develop capacity related to K-12 mathematics curriculum design, research, and evaluation.
Project Management Team:
- Michigan State University
- University of Missouri-Columbia
- Western Michigan University
- University of Chicago
Mathematics curriculum - what it should be, what it is, how it is organized and sequenced, how it is taught, and what students learn - is the core around which mathematics education revolves. It is the mathematics of mathematics education.
Curriculum standards for school mathematics developed by the National Council of Teachers of Mathematics (NCTM) in the late 1980's (NCTM, 1989) and refined over the next decade (NCTM, 2000) launched a standards movement in the U.S. More recently, the adoption of the Common Core State Standards for Mathematics (CCSSM) by all but a few states (e.g., Alaska, Minnesota, Texas, Virginia) represents a revolution. For the first time in the U.S., a large majority of schools, teachers and students will focus on common, specific and grade-level focused learning goals for mathematics. Coupled with mandated common annual grade-level assessments aligned to CCSSM, this initiative is likely to impact other important systems and factors critical to student learning including instruction, curriculum materials, teacher training, and course-taking/graduation policies.
Curriculum standards guide what has been called the ideal curriculum, what should be taught and when various mathematical content and processes should receive emphasis in the school program.
Four principles underlie the work of the Center. First,
A well-articulated, coherent, and comprehensive set of K-12 mathematics learning goals/standards is necessary to
large-scale improvement of school mathematics.
To be effective, curriculum standards must be translated into materials that guide the day-to-day decisions of teachers and help
them focus on the important mathematical learning goals in significant ways. Teachers and publishers utilize curriculum standards
to build lessons and instructional materials to implement the intended curriculum. Instructional materials include textbooks
typically designed for a semester or academic year of study, modules focusing on smaller amounts of mathematical content,
workbooks, and computer software. Tyson-Bernstein and Woodward (1991) describe as ubiquitous the role of textbooks in
American schools, and as a prominent, if not dominant, part of teaching and learning. This phenomenon is not limited to the
U. S., as is evident from international studies:
Teachers of mathematics in all countries rely very heavily on textbooks in their day-to-day teaching,
and this is perhaps more characteristic of the teaching of mathematics than of any other subject in the curriculum.
Teachers decide what to teach, how to teach it, and what sorts of exercises to assign to their students largely on the basis of
what is contained in the textbook authorized for their course. (Robitaille & Travers, 1992, p. 706)
Mathematics curriculum materials are a strong determinant of what students have the opportunity to learn and what they do learn.
Their potential was recognized early on by the National Science Foundation in their funding of curriculum development projects,
including the University of Illinois Committee on School Mathematics (UICSM) and the School Mathematics Study Group (SMSG) in the late 1950s.
Summarizing lessons learned by SMSG, Edward Begle reported that "The textbook has a powerful influence on what students learn."
(Begle, 1973, p. 209). In spite of this finding, only recently (c.f. Schoenfeld, 2002; Senk and Thompson, 2003) has there been
research to extend our understanding of the effects of textbooks on students' learning of mathematics. Kilpatrick (2002) calls
for additional scholarly work in this critical area and Pellegrino (2002) makes the case for establishing design principles for
instructional materials that draw on research on how students learn (Donovan, Bransford, and Pellegrino, 1999).
A second principle guiding the work of the Center is:
Mathematics curriculum materials play a central role in any effort to improve school mathematics and that their development is a
scholarly process involving a continual cycle of research-based design, field-testing, evidence gathering, and revision.
Research has shown that while teachers rely heavily on textbooks, they also often make major alterations to the textbook lessons
resulting in an enacted curriculum that looks very different from the intended curriculum (Ball, 1988; Cohen, 1990; Lloyd, 1999; Remillard, 2000).
It is essential to keep in mind the way teachers use curriculum materials and the factors that influence this use. For example, the
interaction of teacher knowledge and the enactment of the curriculum is not well understood. Specifically, we need to learn a great
deal more about what curricula and associated instructional practices work for which children in what kinds of circumstances with
what level of support for teachers. Progress on understanding the complex role that curricula play in the learning of both teachers
and students will help advance the development of future generations of mathematics curricula, of professional development strategies
for supporting teacher learning around curricula, and of mathematics teacher education practices. A third principle on which the work
of the Center rests is:
Teaching decisions and actions and curriculum materials are highly interdependent and increasing opportunities for
student learning rests on better understanding the relationship between curriculum and instruction.
State assessments and assessments like the National Assessment of Educational Progress,
the Second International Mathematics Study (McKnight et al, 1987), and the Third International
Mathematics and Science Study (Schmidt, McKnight, and Raizen, 1997) provide benchmarks to judge
the extent to which students are learning the intended mathematics. The writing and selection of
test items and the analysis of results from the assessed curriculum play increasingly important
roles in making policy decisions concerning school mathematics. It is critical, therefore, that
increased attention be given to the creation of tools and methodologies for evaluating the impact of
urriculum on teacher behavior and student learning.
Results from standardized assessments, from district-based tests, and from informal and formal classroom assessments,
provide measures of what students know and are able to do, an indication of the achieved curriculum. Students and teachers
are varied in their understandings and practices, and even the same curriculum presented to different classes of students
results in a range of learning. For example, the 2000 National Assessment of Educational Progress results revealed continuing
gender and ethnicity differences in achievement in grades 8 and 12 (U.S. Department of Education, NCES, 2001). Finally, the fourth
principle governing the work of the Center is:
Research addressing mathematics curriculum can inform policy and practice and in so doing narrow the gap between the ideal
and the achieved curriculum.
Center staff have collaborated in constructing and refining a conceptual framework for understanding the influence and
impact of curriculum on teaching and learning