This mixed methods study investigated undergraduate elementary grades pre-service teachers' (PSTs) mathematical reasoning. In the context of combinatorics, we examined two aspects of mathematical reasoning, namely, the processes of enumerating and generalizing, and sought to understand the relationship between them through analyses of 150 PSTs'…

This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

Past research has investigated students' epistemologies while they were taking courses that required an integrated understanding of mathematical and scientific concepts. However, past studies have not investigated students who are not currently enrolled in such classes. Additionally, past studies have primarily focused on individuals who are…

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

The gap between young Indigenous and non-Indigenous children's capability within mathematics is widely acknowledged. This gap is conjectured to exist at all levels of schooling, including pre-school, and widens as children mature. Most of these findings are based on research relating to children's understanding of number and space. Little is known…

This dissertation study examines the experiences of four Latina/o pre-service teachers (PSTs) as they learn about teaching mathematics for understanding (TM4U) and integrating a child's out-of-school mathematical knowledge and experiences during instruction. Studying the knowledge and experiences of Latina/o PSTs is necessary because PSTs…

This paper reports on a study that explored the use of cognitively challenging tasks with low-attaining mathematics students and in particular, their teachers' attempts at scaffolding. A major finding was that responding appropriately to scaffolding opportunities was challenging for the teachers. In this paper two main factors are discussed which…

There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students' understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus…

Does speed provide a "model for" rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the "model for" rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14-15 year old students at…

Concerns about students' difficulties in statistical reasoning led to a study which explored form five (14- to 16-year-olds) students' ideas in this area. The study focussed on descriptive statistics, graphical representations, and probability. This paper presents and discusses the ways in which students made sense of information in graphical…