Elby, J of Mathematical Behavior (2000)

What students' learning of representations tells us about constructivism

A. Elby, Journal of Mathematical Behavior, 19, p 481-502 (1999). (html version)

Abstract: This paper pulls into the empirical realm a longstanding theoretical debate about the prior knowledge students bring to bear when learning scientific concepts and representations. Misconceptions constructivists view the prior knowledge as stable alternate conceptions that apply robustly across multiple contexts. By contrast, fine-grained constructivists believe that much of students' intuitive knowledge consists of unarticulated, loosely-connected knowledge elements, the activation of which depends sensitively on context. By focusing on students' intuitive knowledge about representations, and by fleshing out the two constructivist frameworks, I show that they lead to empirically different sets of predictions. Pilot studies demonstrate the feasibility of a full-fledged experimental program to decide which flavor of constructivist describes students more adequately.