Date of Award

2016

Document Type

Thesis

Degree Name

Bachelors

Department

Humanities

First Advisor

Edidin, Aron

Keywords

Mathematics, Philosophy, Pedagogy, Cognition

Area of Concentration

Philosophy

Abstract

This thesis takes two issues which crop up in mathematics in general, but which are specifically invoked through examples drawing on mathematical pedagogy. Chapter one focuses on the problem of what it means to understand mathematics, and what it means to have different levels or kinds of understanding. Chapter two then takes up a similar question regarding mathematical cognition, focusing on what sense can be made of different kinds of mathematical cognition from a philosophical standpoint. More specifically, this thesis takes up three thinkers who represent two opposing ontological camps in the philosophy of mathematics. For each thinker, the goal is to extract notions of understanding and cognition which operate on the philosopher's own grounds. The resulting notions of understanding and differences in cognition are novel both in their contribution to continuing commentary on the thinkers and conceptual tools of potential value to fields which might want to take up these notions in practice, if such adoption is possible without issue.

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