Stephen K. Reed - Word Problems: Research and Curriculum Reform

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 Psychology of Mathematics Education conventions. These are typically presented by faculty in mathematics education who reference other work in mathematics education.

There are a few exceptions, of course. A chapter by Putnam, Lampert, and Peterson (1990) in the Review of Research in Education on knowing mathematics in elementary schools has a wonderful section on how work in cognitive psychology has contributed to our understanding of understanding. I use this section in my cognition seminar in place of articles written by cognitive psychologists. But these kinds of articles are difficult to find. I therefore wanted to write a book in which I could bring together some ideas from both cognitive psychology and mathematics education.

Another reason for writing this book is that 1 have become interested in developing computer software that would help students solve word problems. I have been disappointed by the lag between the development of multimedia computers and the development of theory-driven software to run in the machines. We need software that is built on sound theory and experimentally tested to determine whether it is doing the job that it was designed to perform. But I needed to see a much bigger picture before I could begin this kind of work.

I once before had this urge to see a big picture. Late in my junior year as a psychology major at the University of Wisconsin I began to realize that obtaining a Ph.D. in psychology would likely make me a specialist in some small area of psychology. I thought that obtaining a Ph.D. in the History of Science would allow me to see the bigger picture by working in both the sciences and humanities. After consulting with the Chairman of the History of Science Department, I told a fellow student of my plans to obtain a doctorate in this area. His reply was Why would anyone want to study the history of science when they could do science? I didnt have an answer to that question and so went off to do science in a rather narrow area of psychology. Thirty years later my urge to see a bigger picture has returned.

A third reason for writing this book is to learn more about the mathematics reform movement that is occurring in our schools. Several months before I began writing this book there was a meeting of parents and educators at the middle school where our son was attending seventh grade. The purpose of the meeting was to discuss implementing a new mathematics curriculum in the San Diego Unified School District. I am embarrassed to admit that I was not among the approximately 200 parents who attended that meeting, many of whom were adamantly opposed to the new curriculum plans. However, I later talked to some of the parents who were at the meeting and obtained literature distributed by groups on both sides of the issue.