Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis

Abstract

This dissertation is a theoretical investigation of the kinds of knowledge and ways of knowing that are valued within mathematics and the teaching and learning of mathematics. Central to this research is a theoretical framework based upon the Traditional Western Worldview and an Indigenous Worldview. This research is based upon a collage of three methodologies: auto/ethnography, Gadamerian hermeneutics, and grounded theory. The initial data source within this dissertation is a personal one, namely the story of how I, the author, have related to mathematics and the teaching and learning of mathematics from my earliest memory up to the moment of genesis for the theoretical worldview used within my research. Analysis of this data gives rise to the collection and analysis of further data, until a theory can be, and is, proposed. In doing this research, I, the author, am most interested in the points of conflict and tension that exist within the different arenas of mathematics and the teaching and learning of mathematics, how these trouble spots relate to the valuing of different kinds of mathematical knowledge and ways of knowing, and ultimately theorizes about how to rectify these problems. In addition to proposing a new theory of mathematics and the teaching and learning of mathematics, this dissertation also proposes a new philosophy of mathematics in support of that theory.