Culture and Context: How Frames of Teaching and of Learning Mathematics Form and Change for Graduate Student Instructors

Authors

Johan Benedict A. Cristobal, University of Nebraska-LincolnFollow

First Advisor

Yvonne Lai

Committee Members

George Avalos, Joshua Brummer, Elaine Chan, Christine Kelley

Date of this Version

5-2025

Document Type

Dissertation

Citation

A dissertation presented to the faculty of the Graduate College at the University of Nebraska in partial fulfillment of requirements for the degree of Doctor of Philosophy

Major: Mathematics

Under the supervision of Professor Yvonne Lai

Lincoln, Nebraska, May 2025

Comments

Copyright 2025, Johan Benedict A. Cristobal. Used by permission

Abstract

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, and decide how to appropriately proceed. While research has affirmed the utility of frames in understanding instructors’ actions, the concept of frames has yet to be examined in the specific context of teaching and learning mathematics. This dissertation argues that more can be understood about why mathematics instructors teach the way they do when frames of teaching and of student learning are explored deeply.

Using a mix of grounded theory and narrative analysis, I investigated the experiences of three mathematics graduate student instructors and their frames of teaching and of student learning during their first semester of teaching as the main instructor. Salient aspects of frames of teaching and of learning mathematics surfaced in the interviews, classroom observations, and written reflections. I produced a novel analytic framework for mathematics instructors’ frames of teaching and of students’ learning. Then, using this framework, I reconstructed narratives of these instructors’ frames and how they began, changed, crystallized, or strengthened as the semester progressed. Lastly, aspects of culture which shape instructors’ frames of teaching and of student learning were extracted from these narratives, interviews, observations, and reflections. Thus, this dissertation gives one answer to the opening question.

These narratives and insights have implications for the professional development of future mathematics instructors, including how instructors might be better oriented to manage classroom events. By detailing how frames may change and naming the aspects of culture which shape frames, instructors better understand how to adopt asset-based frames and practices which can empower students in mathematics courses.

Advisor: Yvonne Lai