• Michigan State University
  
• University of Missouri-Columbia
  
• Western Michigan University
  
• University of Chicago
  
• Horizon Research, Inc.
  
• Columbia MO Public Schools
  
• Grand Ledge Public Schools
  
• Kalamazoo MI Public Schools
  
  

• Chris Hirsch (Western Michigan University): christian.hirsch@wmich.edu
  
• Glenda Lappan (Michigan State University): glappan@math.msu.edu
  
• Barbara Reys (University of Missouri): reysb@missouri.edu
  
  

Guiding Principles:

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. Most recently the No Child Left Behind (NCLB) federal legislation requires states and school districts to articulate curriculum standards for mathematics learning and to regularly (annually in grades 3-8) assess the extent to which students are learning the mathematics outlined in the standards. "Curriculum standards" as used here refers to a set of written learning expectations for the focus of school mathematics instruction. 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.

A principle underlying the work of the Center is that 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 that 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 also 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 that teaching 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 curriculum 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).

A fourth principle governing the work of the Center is that research addressing mathematics curriculum can inform policy and practice and in so doing narrow the gap between the ideal and the achieved curriculum.

CSMC Goals:

The CSMC serves the K-12 educational community by focusing scholarly inquiry and professional development around issues of mathematics curriculum. Major areas of work include understanding the influence and potential of mathematics curriculum materials, enabling teacher learning through curriculum material investigation and implementation, and building capacity for developing, implementing, and studying the impact of mathematics curriculum materials. The work of CSMC is not driven by a particular philosophy or ideology. Instead, Center staff maintain a healthy skepticism throughout all phases of its activities considering both international and multiple U. S. perspectives with an ultimate goal to produce research-based knowledge and products that will enlighten and serve the range of users of mathematics curriculum materials. The primary goals of CSMC are:

1. Develop leadership capacity related to K-12 mathematics curriculum design, analysis, implementation, and evaluation through:

a. Doctoral program development with curriculum emphasis
b. School/district curriculum leadership development

2. Advance a research agenda related to K-12 mathematics curriculum, including the impact of curriculum materials on student and teacher learning.