Why is there an athema in mathematics? : a philosophical investigation in mathematics education : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Education at Massey University

Abstract

This work is a Wittgenstein-based philosophical analysis of mathematics education, primarily in the context of New Zealand secondary curriculum. In Chapter 1.00 the aims of the Forms I-IV Syllabus are examined in detail with respect to the possible meanings of the statements contained there-in. The consequences and hidden assumptions of these meanings are elucidated. Chapter 2.00 examines eight specific assumptions arising from Chapter 1.00 and from observation of mathematics teaching. Their consequences for mathematics education are discussed. Alternative assumptions are also considered. Finally the history of mathematics and mathematics education in the United Kingdom, United States of America and New Zealand are summarised and then used to investigate the origins of the assumptions above.