The opportunity to innovate, experiment, and take chances in the classroom should be accessible to all students regardless of the social identities they hold; however, white women and women of color (WOC) in male-dominated physics, engineering, math and computer science (PEMC) learning environments, and STEM broadly, have been expected to take…

Undergraduate mathematics education research focused on Introduction to Proofs courses has gained traction as more students are experiencing challenges in their proof-based courses. While studies have analyzed the teaching and learning of proofs, there is a growing need for research in students' understanding of mathematical logic and set theory…

Guided by constructivism, which posits that students assimilate new knowledge into what has made sense to them previously, we researched student conceptualizations of proof. We used the qualitative research methods of thematic analysis and phenomenography to learn and categorize student conceptualizations of proof, and of mathematization more…

Historically, girls and women have experienced gender disparity in access to, and persistence in, STEM education. Though women comprise 50% of the total workforce, they occupy only 25% of STEM-related occupations. STEM degrees and occupations have been linked to economic prosperity, both for individuals and the nation as a whole. However, women…

The purpose of this study is to present some of the classical concepts, definitions, and theorems of calculus from the constructivists' point of view in the spirit of the philosophies of L.E.J. Brouwer and Errett Bishop. This presentation will compare the classical statements to the constructivized statements. The method focuses on giving…

This thesis is about a design process for creating "educationally relevant" tools. I submit that the key to creating tools that are educationally relevant is to focus on ensuring a high degree of alignment between the designed tool and the broader educational context into which the tool will be integrated. The thesis presents methods and processes…

Over the past decade, three rationales have emerged for emphasizing the reinforcement of the United States' science, technology, engineering, and mathematics (STEM) pipeline. The first rationale pertains to U.S. global competitiveness, the second revolves around the benefits of a diverse workforce, and the third argument points to social justice…