Date of Award

5-2019

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

First Advisor

Joo Young Park

Second Advisor

Thomas J. Marcinkowski

Third Advisor

Samantha R. Fowler

Fourth Advisor

Ada Harvey

Abstract

Based on the socio-critical perspective of mathematical modeling this research investigated a tool termed MESH (Mathematics Expressing Society’s Hopes) designed to stimulate reflexive discussions about the role of mathematics in society. Constructivist grounded theory (Charmaz, 2014) methods were used to collect and analyze data from 27 students enrolled in two college algebra classes at a community college in the southernmost U.S. state. The research questions were: 1. How does the MESH tool stimulate reflexive discussions about the role of mathematics in society during and after the technological, mathematical, and reflection activities, respectively? 2. How do students understand the role of mathematics in society before and after the MESH tool? The findings suggest that reflexive discussions were produced by (a) personalizing modeling activities, (b) challenging taken-for-granted beliefs and values about the social issue at the mathematical level, (c) prescribing reflections beyond the mathematical level, and (d) reflecting individually on the learning process. Additionally, students understood the role of mathematics as a practical tool as well the role of mathematics in technological and societal development. However, students saw very little connection between mathematics, citizenship, and democracy. These findings have been conceptualized as the core process of unboxing mathematics which is described as a process of deliberately opening mathematics in school to questions from the realm of students’ experiences for empowerment and establishing the relevance of mathematics in society. Unboxing mathematics includes the sub-processes of personalizing mathematics, challenging mathematics, voicing mathematics, and negotiating mathematics. The purpose of unboxing mathematics is establishing the relevancy of mathematics in everyday life. The major contribution of this research is a substantive theory grounded in the empirical data. The substantive theory of unboxing mathematics represents one interpretation of how reflexive discussions are stimulated and identifies classroom mathematical practices specific to the socio-critical modeling context of this study. It provides a framework for creating a culture of modeling as critic that may develop students’ reflective competence to see the role of mathematics in society. Implications and recommendations for research, teaching and teacher education are provided.

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