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Ilhan M. Izmirli

philosophy of mathematics education

2013

27

In this paper our main objective is to interpret the major concepts in Wittgenstein’s philosophy of mathematics, in particular, language games and forms of life, from a social constructivist point of view in an attempt to show that this philosophy is still very relevant in the way mathematics is being taught and practiced today. In the first section we briefly introduce the social constructivist epistemology of mathematics – a perspective that reinstates mathematics, and rightfully so, as “… a branch of knowledge which is indissolubly connected with other knowledge, through the web of language” (Ernest 1999), and portrays mathematical knowledge as a process that should be considered in conjunction with its historical origins and within a social context. In section two, we give a telegraphic overview of the main points expounded in Wittgenstein’s two books, Tractatus Logico-Philosophicus and Philosophical Investigations, as well as in his “middle period” that is characterized by such works as Philosophical Remarks, Philosophical Grammar, and Remarks on the Foundations of Mathematics. In the third and last section, we highlight the connections between social constructivism and Wittgenstein’s philosophy of mathematics.