Some Reflections on the philosophy of Mathematics Education: A Denunciation of the Time and Content Arguments

Ilhan M Izmirli

doi:10.29333/pr/7854

Abstract

Of all the arguments directed against presenting mathematical topics within a cultural and historical context, the most serious ones are those that we will refer to as the time and the content arguments. In this paper, after briefly describing these stances, we will endeavor to evaluate and refute their rationales using a social constructivist line of reasoning. To this end, we will first discuss the basic tenets of radical and social constructivism and then, through some simple concrete examples, show how social constructivism organically heralds the pedagogical methodology that imparts mathematical concepts in conjunction with their historical and cultural contexts.

Highlights

The intensification of the efforts to isolate mathematics from its cultural and historical contexts, that is, its core essences, has rendered, once again, the justification for such a conflation a much needed obligation, a prodigiously exigent one
Following Ernest (1998), with the added assumptions of the existence of social and physical reality, we extend the principles of radical constructivism to elaborate the epistemological basis of social constructivist philosophy of mathematics: (i) The personal theories which result from the organization of the experiential world must ‘fit’ the constraints imposed by physical and social reality; (ii) They achieve this by a cycle of theory-prediction-test-failure-accommodation-new theory; (iii) This gives rise to socially agreed theories of the world and social patterns and rules of language use; (iv) Mathematics is the theory of form and structure that arises within language
Let us contend with this predicament using the social constructivist approach