The Study of Affect and Mathematics: A Proposed Generic Model for Research

Abstract

During the last 15 years, much understanding has been gained about cognitions in mathematics. Starting with the content area of early number concepts, progressing through rational numbers and algebra, and culminating with problem solving by university mathematicians, scholars have been probing cognitions and determining how human beings think with mathematical ideas. This knowledge is beginning to be useful not only in understanding human thought processes, but also in the development of new paradigms for curriculum development (Carpenter, in press). This knowledge has grown and become useful because a relatively consistent research methodology has been used in relation to a fairly concise theoretical model of cognitive processing. Usually this cognitive science research methodology started with an explicit definition of some specific mathematics content; questions relating to this definition have been formulated; subjects were asked to think aloud (or self-report) as they answered the questions; their responses were studied for patterns of thinking; and, finally, the identified patterns were compared with the overall theory to see if the theory was supported or needed modification.