This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis…

Research across five countries has identified inability to pay attention to mathematical detail -- the discipline of noticing -- is an issue in senior secondary school mathematics teachers. The test and questionnaire completed by an Australian cohort further identifies a reluctance to employ non-routine questions in assessments, with teachers…

Inequities in STEM participation for people of color and women are documented extensively, often highlighting issues of representation and/or achievement. This study adds to the literature by looking at participation inequities in a high school calculus class. Equity is conceptualized as a fair distribution of opportunities for students to engage…

We discuss an investigation of students' motivational beliefs and performance on the Force Concept Inventory (FCI) in a calculus-based introductory physics course at a large public university in the U.S. We investigated how students' perception of the inclusiveness of the learning environment (including perceived recognition, perceived…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

Calculus is typically one of the first college courses encountered by science, technology, engineering, and mathematics (STEM) majors. Calculus often presents major challenges affecting STEM student persistence, particularly for students from groups historically underrepresented in STEM. For life sciences majors, calculus courses may not offer…

Ongoing need for adjunct instructor support is a critical aspect for institutions to consider. Through research focused on full-time and part-time faculty job satisfaction, a number of practices for supporting faculty and improving job satisfaction have been suggested. In this article, we present an innovative model of instructor resources and…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

Studies examining gender differences in introductory physics show a consensus when it comes to a gender gap on conceptual assessments; however, the story is not as clear when it comes to differences in gendered performance on exams. This study examined whether gendered differences exist on midterm and final exams in introductory physics courses…

This brief summarizes findings from a study in which we examined postsecondary college transcript and degree records from hundreds of thousands of transfer-intending community college students in three states. Our aim was to explore and test metrics that could be useful in the formative assessment of efforts to improve STEM transfer outcomes. Our…

Reform initiatives in mathematics education have been reluctant to embrace racial equity as a core or guiding principle. The field is replete with studies on Black students' poor performance in mathematics education and of its persistence. Conversely, success in mathematics is rarely associated with groups of African or African American descent.…

Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…

Three years ago our mathematics department rearranged the topics in second and third semester calculus, moving multivariable calculus to the second semester and series to the third semester. This paper describes the new arrangement of topics, and how it could be adapted to calculus curricula at different schools. It also explains the benefits we…

"Mathematics Across the Sciences" is an applications-based course designed to strengthen students' mathematical skills in preparation for calculus or for a major in the sciences. Its development relied heavily on input from faculty members in several science departments. This article describes the course; many of the scientific…

Student perceptions on teaching and learning are investigated in a side-to-side comparison between traditional (closed, CER) non-free course materials and free open educational resources (OER). The primary resources being compared are textbook and automatically-graded web-based homework systems. The results are based on a 32 item survey given to…