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.
Table of Contents
Contents: Preface. Introduction. Part I: Knowledge Structures. Learning Rules. Conceptual Understanding. Part II: Problems. Elementary Problems. Multistep Problems. Algebra Problems. Part III: Transfer. Abstracting Solutions. Adapting Solutions. Representing Solutions. Part IV: Important Topics in the NCTM Standards. Wor(l)d Problems. Estimation and Functions. Curriculum Reform.
"This book is one of the most complete and insightful accounts on mathematics education to date....If you are interested in mathematical thinking from a theoretical or an applied point of view, the current standards for math education, and the link between cognitive theory and educational practice, Word Problems will provide an invaluable source of inquiry. This book is comprehensive, provocative, and filled with examples that provide rigor and 'meat' to the discussion."
"Reed's treatment of word problems and the underlying learning theories and research provide a cohesive perspective on the problem-solving task posed by the question, How do students attempt to solve word problems? The evidence Reed provides will enable researchers and curriculum developers to address the question."
—American Journal of Psychology
"This book has many strengths. Research in mathematics learning is placed within the context of cognitive science and fairly equal weight is given to empirical psychology, classroom practice and curriculum reform, and computer modelling. It also emphasises the importance between theory and practice....For students starting a PhD in this area, I can think of no more helpful text than this one. This is particularly true if the emphasis is on how learning research can be used to inform instruction."
—British Journal of Educational Psychology
"Word Problems provides an excellent summary of a great deal of important information about how students solve word problems....The numerous research trials, along with the depiction of current national needs for curriculum reform, offer fertile ground for further research and can serve as a basis to guide mathematics education in the future....It provides food for thought for anyone who wishes to institute reforms in the teaching of mathematics and offers insights into problem-solving approaches."
—Horizon Research, Inc. material is presented effectively through the use of supp