# The Psychology of Mathematics for Instruction

# The Psychology of Mathematics for Instruction

## Excerpt

This book is addressed to psychologists, educators, and mathematicians who are interested in the mental processes involved in learning mathematics. The book traces the history of psychologists' efforts to inform mathematics instruction, from the associationist work of Edward L. Thorndike to today's information-processing studies of mathematical thinking--with consideration of Gestalt, Piagetian, and various branches of American behavioral and cognitive psychology along the way. The book can thus be read as a history of psychologists' efforts to discover and explicate the nature of learning and thought processes in mathematics. But it is meant to be more than that. It is, above all, an effort to give shape and direction to an emerging branch of study concerned with how expert thought in mathematics proceeds, how that expertise develops, and how instruction can enhance the process of mathematics learning.

For many decades mathematicians and educators committed to improving the intellectual power of mathematics instruction were unable to find much of interest in the work of psychologists. This is not surprising, for psychologists--if they attended to mathematics at all--generally were attempting to make mathematical subject matter fit general laws of learning rather than trying to understand the processes of mathematical thought in particular. This is now changing. An emerging psychology of mathematics is focusing directly on the processes of mathematical thinking and on the ways in which people come to understand the structures of mathematics. This new line of investigation joins cognitive psychology's concern for the processes of thought with traditional learning psychology's interest in how new abilities are acquired. Increasingly it includes explicit attention to the role of instruction in the development of mathematical thinking. The groundwork is thus being laid for a theory of mathematics instruction rooted . . .