Theories of Mathematical Learning

By Leslie P. Steffe; Pearla Nesher et al. | Go to book overview

12
A Conception of Knowledge Acquisition and Its Implications for Mathematics Education
Giyoo Hatano
Keio University, Tokyo JapanIn this chapter I discuss characterizations of knowledge acquisition offered by recent cognitive studies, how these characterizations can be applied to mathematical cognition, and what implications for mathematics education can be derived from them. Such an attempt may no longer be appealing to the mathematics education community, who may contend that:
General theories of learning or acquisition, of either the behaviorist or cognitivist varieties, have not been as informative to mathematics educators as approaches specifically focused on mathematics.
So-called general theories of learning are in fact about the acquisition of knowledge regarding aspects of the actual world (e.g., physics, biology, and psychology), and thus not relevant to the acquisition of logicomathematical knowledge.
The course and process of development in the domain of mathematics are unique, so that studies in other domains of expertise cannot be instructive.
What one has to acquire to become an expert or master in mathematics is radically different from other domains, and also the domain of mathematics is expected to embody a different set of innate constraints.

However, most, if not all, mathematics educators would agree that students' mathematical cognition constitutes a theory-like knowledge system, that is, an organized body of knowledge that concerns a specific set of objects or entities and that, like scientific theories, involves coherent explanations. The acquisition of a mathematical knowledge system will share, at least to some extent, features common to all other theory-like knowledge systems, such as naive physics,

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