I often elicit an emotional reaction when I tell people that I do research on solving algebra word problems. Some people are quite good at doing this and enjoy the challenge. More typically, people moan. They never did very well at solving word problems, and may feel helpless when their children need assistance with their homework. Gary Larson's cartoon (see Fig. 1.1) captures this typical reaction.
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. My perspective is that of a cognitive psychologist who does research on mathematical problem solving. Until recently, I had not paid much attention to curriculum reform in mathematics education, which is starting to find its way into classrooms across the country ( Alper, Fendel, Fraser, & Resek, 1995; Heid & Zbiek, 1995; Kysh, 1995). But the current debate regarding the reform of mathematics education has brought these issues to the front pages of our newspapers. As newspaper articles continued to appear on this controversy between teaching basic skills and teaching concepts, I decided that research on mathematical problem solving would be of greater interest to me and my readers if I embedded it within the context of this ongoing debate. Therefore, I begin by giving a brief overview of the debate, which was stimulated by the publication of Curriculum and Evaluation Standards for School Mathematics ( National Council of Teachers of Mathematics [NCTM], 1989).