First Advisor
Novak, Jodie
Document Type
Dissertation
Date Created
12-2022
Department
College of Natural and Health Sciences, Mathematical Sciences, Mathematical Sciences Student Work
Abstract
Mathematicians teaching at the university level have a deep understanding and appreciation for the mathematics that they teach. However, they rarely receive much formal training in teaching. Thus, university mathematicians must rely on their mathematical understandings and personally developed ideas of teaching to guide their decision-making. Relatively little research exists on mathematicians’ teaching practices. The purpose of this study was to examine the mathematical knowledge for teaching (MKT) of a university mathematician teaching discrete mathematics and how he leveraged his knowledge to make decisions and develop coherence among mathematical ideas during a semester review. An enactivist perspective examining a mathematician’s decision-making in planning, enacting, and reflecting upon their lessons in this study shed light on how this mathematician practically approached his teaching duties. By enacting four distinct coherence strategies, the mathematician in this case study revealed a personal standard for mathematical storytelling which guided his decision enactment. These strategies fostered rich connections among mathematical ideas and among topics from earlier in the semester meaningfully with a single culminating topic: the chromatic polynomial. Implications of this study for research include recognized advantages of graph theoretic visualizations for the analysis of teacher decisions and coherence, benefits of dual coding for the Knowledge Quartet MKT framework, and a stance on inactivism's consideration of cognitive actions. For teaching, this research supports the benefits of mathematical storytelling and review units which feature a new context to reframe previously seen topics.
Extent
473 pages
Local Identifiers
Lang_unco_0161D_11064.pdf
Rights Statement
Copyright is held by the author.
Recommended Citation
Lang, Julie, "Mathematical Knowledge for Teaching as Decision-Making for the University Mathematician Developing Coherence in Review of Discrete Mathematics" (2022). Dissertations. 902.
https://digscholarship.unco.edu/dissertations/902