In this paper, I report on doctoral research in which I investigated the relationships between student approaches to learning, conceptions of mathematics, mathematical self-efficacy, personal factors and examination results. Using seventy-three post-secondary mathematics students, some pertinent findings were: self-belief in selection processes…

Imagine a large randomized controlled trial study of a mathematics educational intervention planned in two large urban districts. District 1 gets a new administrator and drops out. In the meantime, the state test changed, so one of the planned outcome measures is no longer usable. Teacher dropout is high. And, as the analysis is being completed,…

In this paper, we address the variety of ways in which students conceive of binary operations and the metaphors they might leverage when working with binary operations in group theory. We use open-ended surveys paired with interviews to qualitatively explore student's conceptions of binary operation. Through this analysis, we identified three…

This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

This study aims to explore undergraduate mathematics students' difficulties in their initial encounter with the subgroup test, and in particular in the proof of closure under operation. Subgroup test is one of the first results in an introductory course of Group Theory where students need to cope with the characteristic, for novice students, high…

This study employs a cross-case analysis in order to explore the demands and opportunities that arise when information problem-solving tasks are introduced into college mathematics classes. Professors at three universities collaborated with me to develop statistics-related activities that required students to engage in research outside the…

Though there has been limited empirical research on the cost component from the expectancy-value model, a recent interest in the construct has spurred advances in theory and measurement. We present a longitudinal analysis of four types of cost: effort, loss of valued alternatives, emotional, and outside cost. We focus on how cost changes over time…

This paper considers what students attend to as they first encounter R[superscript 3] coordinate axes and are asked to graph y = 3. Graphs are critical representations in single and multivariable calculus, yet findings from research indicate that students struggle with graphing functions of more than one variable. We found that some students…

The role of mathematical education in everyday life, professional activities, attitude towards the role of mathematical knowledge in the labour market is widely discussed in the literature. To improve the studies of mathematics according to the trends in society development, it is necessary to find out the mathematics teaching philosophy as well…

Cognitive Load Theory's Four Component Instructional Design (4C/ID) Model has been used in mathematics education but not confirmed as an instructional theory. Using the Factors Influencing College Success in Mathematics (FICSMath) project and confirmatory factor equation modeling, we empirically validated the model and created the 4C/IDMath Model.…

Learning analytic models are built upon traces students leave in technology-enhanced learning platforms as the digital footprints of their learning processes. Learning analytics uses these traces of learning engagement to predict performance and provide learning feedback to students and teachers when these predictions signal the risk of failing a…

Most community college students in the U.S. must complete at least one developmental class, such as elementary algebra, before they can enroll in a college-level mathematics course. Increasingly common in such courses is the use of a web-based activity and testing system (WATS). This report presents initial results of a mixed-methods study of…

Trigonometry is one of the fundamental topics taught in high school and university curricula, but it is considered as one of the most challenging subjects for teaching and learning. In the current study Mason's theory of attention has been used to examine undergraduate student's perception of the transformation of sinusoidal functions. Two types…

Feedback on assessed work is invaluable to student learning, but there is a limit to the amount of feedback an instructor may provide. Peer feedback increases the volume of feedback possible, but potentially reduces the quality of the feedback. This research proposes a model of collaborative peer feedback designed to increase quality of peer…

The Merriam-Webster dictionary defines "transition" as: (a) the passage from one state, stage, subject, or place to another: change; or (b) a movement, development, or evolution from one form, stage, or style to another. The word transition can refer to an active shift of the person in space and time or status, for example; it can also…