Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair…

This dissertation reports on three studies about students' conceptions and learning of the idea of instantaneous rate of change. The first study investigated 25 students' conceptions of the idea of instantaneous rate of change. The second study proposes a hypothetical learning trajectory, based on the literature and results from the first study,…

Mathematical notations not only contribute to but also confound the development of the understanding of mathematical concepts (Leinhardt, Zaslavsky & Stein,1990). Inaccurate use of calculus notations is likely to have a significant influence on student conceptual understanding and student assessment scores in the Calculus 1 course. This…

Despite the standardization of calculus education as a Calculus and Analytic Geometry course after the 1950s, curriculum updates have been slow to penetrate the undergraduate mathematics classroom practice, taking decades to manifest. Common struggles with the teaching and learning of calculus, such as relying on a procedural understanding of…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

In recent years, diversity, equity, and inclusion (DEI) have gained increasing importance in the field of physics. Despite efforts to enhance DEI, physics still faces numerous challenges in this area. This dissertation is divided into three main chapters, aiming to investigate the significance of learning-related emotions and physics identity as…

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…

This action research study used data from multiple assessments in Mechanics and Electricity and Magnetism to determine the viability of Modeling Instruction as a pedagogy for students in AP Physics C: Mechanics and Electricity and Magnetism. Modeling Instruction is a guided-inquiry approach to teaching science in which students progress through…

This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using…

The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks…

This dissertation examines the relationship between an instructional style called Interactive-Engagement (IE) and gains on a measure of conceptual knowledge called the Calculus Concept Inventory (CCI). The data comes from two semesters of introductory calculus courses (Fall 2010 and Spring 2011), consisting of a total of 482 students from the…

The purpose of this study was to determine (1) strategies students use when solving composition problems and the difficulties they encounter; (2) conceptions and/or misconceptions students have with respect to composition of functions; and (3) the effect of using dynamic visualization during instruction on students' understanding of composition of…

Sfard and Thompson (1994) state that what matters most is that educators develop ways of thinking, teaching, and learning mathematics. This study introduced constructive habituation, a new strategy developed to aid both students and teachers in the thinking, teaching, and learning of mathematics. Constructive habituation attempts to unite…