Theories of Mathematical Learning

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

27 On the Nature of a Model of Mathematical Learning

Leslie P. Steffe Heide G. Wiegel University of Georgia

In mathematics education, we often take for granted that students can and do learn mathematics. But it is quite difficult to specify an account of this process of learning, an account detailed enough for a teacher to recognize particular types of mathematics learning and general enough to provide an orientation for action in future teaching situations. We need a general model of learning and particular models of mathematics learning ( von Glasersfeld & Steffe, 1991). Each particular model constitutes a major achievement on the part of the model builder, and we make no pretense to offer such models in this chapter. Our goal is more modest. We focus our comments on the nature of a particular model of mathematics learning: its relation to theory, its constitutive elements, its relation to mathematics teaching, and how it might be built.

Several of the preceding chapters are of a general nature and depict certain world views either explicitly or implicitly (e.g., Goldin & Kaput, chapter 23; Hatano, chapter 12; Marton & Neuman, chapter 19; van Oers, chapter 7; Vergnaud, chapter 13; Voigt, chapter 2; von Glasersfeld, chapter 18). One might say that these chapters have to do with basic theoretical principles that underpin general as well as specific models of mathematical learning. In fact, these authors explicate, in part, what Lakatos ( 1970) has called hard-core principles of scientific research programs, principles that could be used in building models of mathematical learning. This distinction between a model and theoretical principles used in building the model is not an idle one and goes to the heart of some very old problems in mathematics education.

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