The emphasis in the preceding chapters has been on research that has focused on particular topics related to mathematics education. Some of the educational implications of these studies have been occasionally discussed, but this book would be incomplete without saying more about the curriculum reform efforts that were mentioned in chapter 1. This final chapter is concerned with new curriculum that is consistent with the NCTM Standards. Is it working? Are students developing a deeper understanding of mathematics? Are they losing their ability to perform basic computations? I will try to answer these questions by reviewing the evaluation of several programs that have implemented curriculum changes.
In chapter 1, linking instruction with theory was discussed by giving an overview of work done at Northwestern by Fuson, Hudson, and Pilar ( 1997), which used a theoretical model to guide the design of instruction. That discussion emphasized the model rather than the instruction, so this chapter begins by looking at the instruction-side of the program. A second program is the Purdue Problem-Centered Mathematics Project, which is based on the constructivist belief that students learn mathematics most effectively if they construct meanings for themselves, rather than simply listen to the instructor ( Cobb, Yackel, & Wood, 1992). From this point of view, learning is seen as involving extensive interaction and exchange of ideas between students and teachers. A third program is the Cognitively Guided Instruction program at the University of Wisconsin, which tries to help teachers to better understand their students' thinking ( Carpenter & Fennema, 1992). All three of these programs focus on instruction at the lower elementary grades and use research on elementary word problems (discussed in chapter 4) in the design and evaluation of instruction.