Alternative Perspectives of the Nature of Mathematics and their Influence on the Teaching of Mathematics

Abstract

This article reports on a doctoral dissertation that examined the current state in the philosophy of mathematics, with a view to identifying possible connections with, and influences upon, mathematics education. Recent work in the sociology of knowledge, proposing a strong case for a fallibilist epistemology, can be seen as one perspective, counterposed against absolutist epistemologies. It is proposed that these two views are reflected in the practice of mathematics education, in teaching, research and attitudes to current issues. A field study was carried out, not to provide empirical support but to examine some of the consequences of the theoretical framework proposed, and part of this is described. Finally, some implications of the research are discussed.

Korean Primary School Teachers' Conceptions of Foundations and Creativity in Mathematics

“…mathematics is either absolute or fallible), whereas the other concepts usually appear as continua (Hoz & Weizman, 2008). Lerman (1990) suggested a continuum of conceptions of mathematics, where one pole is seeing mathematics as an immutable body of knowledge, which teachers transmit in replicable ways and the other as a social construction learnt through an engagement in problem solving. In this study, I took a position that the conception of mathematics is rather the other concepts usually appear as continua.…”

“…Beswick, 2004;Strauss, 1993), and teachers' beliefs about the nature of knowledge would impact their teaching plans and practices (Hofer & Pintrich, 1997;Lerman, 1990;Thompson, 1984). Studies on foundations and creativity in mathematics have been conducted in many countries (e.g., Aljughaiman & Mowrer-Reynolds, 2005;Andrews & Hatch, 1999;Fryer & Collings, 1991;Kampylis, Berki, & 401 Saariluoma, 2009;Wong (2007).…”

Elementary Teachers’ Mathematics Subject Knowledge: the Knowledge Quartet and the Case of Naomi

“…Thirdly, teachers hold different beliefs about the conditions under which pupils will best learn mathematics. In fact, there is compelling evidence to suggest that experiences as a learner of mathematics, beliefs about the nature of mathematics and instructional practices as a teacher of mathematics are interconnected (Lampert, 1988;Lerman, 1990;Sanders, 1994;Thompson, 1984Thompson, , 1992.…”

Relationship Between Classroom Authority and Epistemological Beliefs as Espoused by Primary School Mathematics Teachers From the Very High and Very Low Socio-Economic Regions in Thailand

“…Drawing from Lakatos's (1978) notions of Euclidean and Quasi-empirical, Lerman (1990) distinguishes two major perspectives of the nature of mathematics, namely absolutism and fallibilism. In terms of the former view, mathematical knowledge is seen as "timeless truths" (Lerman, 1990, p. 54) and as an "objective, absolute, certain and incorrigible body of knowledge, which rests on the firm foundations of deductive logic" (Ernest, 1995, p. 451).…”