Word Problems: Research and Curriculum Reform

Word Problems: Research and Curriculum Reform

Word Problems: Research and Curriculum Reform

Word Problems: Research and Curriculum Reform

Synopsis

Research by cognitive psychologists and mathematics educators has often been compartmentalized by departmental boundaries. Word Problems integrates this research to show its relevance to the debate on the reform of mathematics education.

Beginning with the different knowledge structures that represent rule learning and conceptual learning, the discussion proceeds to the application of these ideas to solving word problems. This is followed by chapters on elementary, multistep, and algebra problems, which examine similarities and differences in the cognitive skills required by students as the problems become more complex. The next section, on abstracting, adapting, and representing solutions, illustrates different ways in which solutions can be transferred to related problems. The last section focuses on topics emphasized in the NCTM Standards and concludes with a chapter that evaluates some of the programs on curriculum reform.

Excerpt

The purpose of this book is to try to bring together ideas from the fields of cognitive psychology, mathematics education, and educational technology to achieve a better theoretical and practical understanding of how students attempt to solve word problems. I am a cognitive psychologist who has used algebra word problems in my research over the past 15 years. But like most other cognitive psychologists, my research interests have not focused as much on how students solve algebra word problems, as on more general theoretical issues such as how students transfer a solution from one problem to another problem. Algebra word problems just happened to be a convenient source of problems for my research, in large part because students have so much trouble solving them.

Nonetheless, when I began working with algebra word problems I naively thought that my work would be of some interest to professionals in the field of mathematics education. After all, I was working with word problems and transfer has always been a central issue for educators as well as for psychologists. But my work has had little influence on mathematics education, and work in mathematics education has had little influence on my work. Unfortunately, this is typical. Look at the reference section of any article published by a cognitive psychologist on mathematical problem solving and you will see mostly references to the work of other cognitive psychologists. Look at the reference section of any article published by a mathematics educator on mathematical problem solving and you will see mostly references to the work of other mathematics educators. The odds are not improved much by looking at the references of papers presented at the Psy-

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