Operationalizing figurative and operative framings of thought

Abstract

<p>In this chapter, we discuss Piagetian notions of figurative thought and operative thought. Consistent with many of the ideas introduced by Piaget, characterizations of figurative and operative thought have evolved in different ways since their introduction. Specifically, mathematics educators have adapted Piaget’s ideas in order to develop models of students’ mathematics. Evolutions in the use of these constructs typically stemmed from researchers’ needs to adjust them—in ways faithful to particular aspects of the original distinctions—in order to yield more viable and generalizable models of students’ mathematics. Here, we provide a summary of these evolutions. In doing so, we draw from our own work to provide concrete examples of researchers’ uses of figurative and operative thought in order to illustrate distinguishable aspects of the two forms of thought in multiple settings. We also discuss methodological implications of figurative and operative thought including how the constructs can be used in task design during empirical studies and can inform researchers’ claims regarding students’ mathematical meanings. We close with suggestions for future research in the hopes this chapter can be a springboard for pursuits in constructing viable models of students’ mathematics.<br></p>