Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis
Date
2016-09-28
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0000-0003-4620-7202
Type
Thesis
Degree Level
Doctoral
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.
Description
Keywords
Mathematics, Indigenous Worldview, Traditional Western Worldview, Transreform Approach, Indigenous, Philosophy of Mathematics, Math Wars, Ethnomathematics, Risk, Theoretical Worldview Framework, Socio-cultural Gap
Citation
Degree
Doctor of Philosophy (Ph.D.)
Department
Curriculum Studies
Program
Curriculum Studies