Although many policy documents include equity as part of mathematics education standards and principles, researchers continue to explore means by which equity might be supported in classrooms and at the institutional level. Teaching practices that include opportunities for students to engage in active learning have been proposed to address equity. In this paper, through aligning some characteristics of inquiry put forth by Cook, Murphy and Fukawa-Connelly with Gutiérrez's dimensions of equity, we theoretically explore the ways in which active learning teaching practices that focus on inquiry could support equity in the classroom.
This study has two goals: First, to investigate the effectiveness of using a digital game to teach undergraduate-level calculus in terms of improving task immersion, sense of control, calculation skills, and conceptual understanding. Second, to investigate how feedback and visual manipulation can facilitate conceptual understanding of calculus. 132 undergraduate students participated in a controlled lab experiment and were randomly assigned to either a game-playing condition, a practice quiz condition, or a no-treatment control condition. The authors collected survey data and behavioral-tracking data recorded by the server during gameplay. The results showed that students who played the digital game reported highest task immersion but not sense of control. Students in the game condition also performed significantly better in conceptual understanding compared to students who solved a practice quiz and the control group. Gameplay behavioral-tracking data was used to examine the effects of visual manipulation and feedback on conceptual understanding.
A link between proving and problem solving has been established in the literature [5,21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribe pen data from a previous study [13]. I focus on two participants' proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the mathematician and that of the graduate student. This study suggests the feasibility of an expanded framework for the proving process that can encompass both the similarities and the differences found.Keywords: undergraduate mathematics education; problem-solving; proving; proof construction Proof and proving are central to advanced undergraduate and graduate mathematics courses. Yet there is often little systematic discussion in these courses on how proofs are constructed. Since proving and problem solving overlap [5,21], one might look at the problem-solving literature in order to describe some aspects of the proof construction process. Here I use the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2], coupled with a data collection technique [13] specifically aimed at collecting the real-time actions that a prover takes, to examine the proving actions of a topologist, Dr. G, and a mathematics graduate student, L. I discuss the adequacies and limitations of this framework for describing the observed proof
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