ABSTRACT
As usual, Vygotsky has spurred Western psychologists to take a radically different perspective on the process of academic development…
… their separation [intellect and affect] as subjects of study is a major weakness of traditional psychology since it makes the thought process appear as an autonomous flow of “thoughts thinking themselves,” segregated from the fullness of life, from the personal needs and interests, the inclinations and impulses of the thinker.
(Vygotsky, 1962, p. 8) Research on mathematical teaching, learning, and knowing has a long and impressive history, investigating cognitive processes, developmental trajectories, and pedagogical techniques that explain and predict mathematical achievement (Grouws, 1992). In a parallel history, the research on beliefs, affect, and motivation has seen considerable recent development, especially in explaining why, despite our best efforts, these processes, trajectories, and techniques seem to have a broad impact on only a narrow and privileged portion of our society, and leave the rest out (Middleton & Spanias, 1999). Perhaps we have ignored a key purpose of education in our desire to create the next generation of scientists and mathematicians, and, in our attempts to enhance intellectual development, perhaps we have ignored Vygotsky’s notion of the “fullness of life.” If mathematics learning is portrayed as “thoughts thinking themselves,” and if curriculum activities are thought of as “deeds doing themselves,” then we are not likely to attend to the place of the child as both an intellectual and affective being, situated within a community of intellectual and affective beings, attempting to coordinate their actions to enhance their personal success and happiness. The purpose of this chapter is to describe a way of thinking about the activity of doing mathematics that treats the affective and motivational (i.e., dispositional) state of the child as integral, and indeed inseparable, components of children’s mathematical interpretations of learning and problem solving experiences (i.e., models). This perspective is crucial, we think, to understanding why children do what they do, what the nature of their knowledge is given a particular set of processes that may impinge upon their learning experience, and why they sometimes (despite all of our good intentions) fail to do what we want them to do. The route through which we came to this particular stance reflects the history of the authors as psychologists, our gradual conversion by innovations in the learning sciences, and especially by means of our experiences as designers of mathematics tasks and curriculum. Through successive phases in our own learning histories we have come to view learning as constituting more than change in behavior potential, knowledge as more than configurations of neural firings, and motivation as more than either incentive or coercion. In brief, our chapter sums up this history and projects a research agenda on modeling that allows students to take an active role in behaving intelligently in complex quantitative and spatial tasks.