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 mixed-methods study examines the conceptual understanding of limit among 22 undergraduate engineering students from two different sections of the same introductory differential equations course. The participants' concepts of limit (concept images and personal concept definitions) were examined using written tasks followed by one-on-one…

Prevalent characteristics of effective mathematical discourse in the literature include student autonomy, a positive social environment, and a degree of perceived mathematical competence. These characteristics are also found in Self-Determination Theory (SDT), which posits that actions are self-regulated when students' autonomy, competence, and…

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

The purpose of this study was to explore middle grade mathematics students' uses of scaffolding and its effectiveness in helping students solve non-routine problems. Students were given two different types of scaffolds to support their learning of sixth grade geometry concepts. First, students solved a math task by using a four square graphic…

This mixed methods study describes the effects of a "minute contextual experience" on students' ability to solve a realistic assessment problem involving scale drawings and proportional reasoning. Minute contextual experience (MCE) is defined to be a brief encounter with a context in which aspects of the context are explored openly. The…