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Guided Reinvention As A Context For Investigating Students' Thinking About Mathematical Language And For Supporting Students In Gaining Fluency, Kristen Vroom

Dissertations and Theses

Fluency with mathematical language is important for students' engagement in many disciplinary practices such as defining, conjecturing, and proving; yet, there is growing evidence that mathematical language is challenging for undergraduate students. This dissertation study draws on two design experiments with pairs of students who were supported to encode their mathematical meanings with more formal language. I aimed to investigate the teaching and learning of mathematical language, and particularly the language in statements with multiple quantifiers, by engaging students in this type of activity. In the first paper, I investigated the complex ways in which the students in my study …

Mathematical Silences, Matthew Nathan Petersen

Dissertations and Theses

Previous studies have shown that mathematicians employ lengthy silences in their collaborations, contrary to the norms that govern every-day collaborations. Such results shows the relevance of an investigation of silence in mathematical collaboration. This dissertation builds off these results in a series of three papers. The first paper describes a methodology that can be employed in the investigation of silence in mathematical collaboration. The second paper analyses silence in the mathematical collaboration of students in junior-level introductory proof classes. It identifies two forms of mathematical activity, reading and ruminating, that students regularly engage in, and which violate the norms of …

Identifying A Starting Point For The Guided Reinvention Of The Classification Of Chemically Important Symmetry Groups, Anna Marie Bergman

Dissertations and Theses

The study of abstract algebra is both required for most mathematics majors and notoriously difficult. Much of the mathematics education literature on investigating student thinking in abstract algebra highlights student struggles with understanding even the most fundamental concepts. The abstract nature of the content of the course has been credited as one of the contributors to student difficulties. While there have been various instructional innovations designed to support students in better understanding abstract algebra, and group theory in particular, they have not specifically focused on the issue of the abstract nature of the content. My dissertation study aimed to develop …

Teacher Learning In The Context Of Students’ Mathematical Thinking, Mary Sherrett Duden

Dissertations and Theses

Currently mathematics education is undergoing substantial changes so that students may experience mathematics in intellectually engaging, equitable, and relevant ways. More specifically, I am referring to a teacher stance of centering student thinking and allowing students to make sense of mathematical ideas. Proponents of reform efforts in mathematics argue that this is the path to helping elementary students develop a deep and conceptually sound understanding of mathematics. This is critical because a strong mathematical foundation has increasingly become a gateway for access to many career opportunities and citizenship in the United States.

Unfortunately, these ambitious changes present a challenge for …

Establishing Foundations For Investigating Inquiry-Oriented Teaching, Estrella Maria Salas Johnson

Dissertations and Theses

The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe …