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Thursday

2:05 - 2:35 pm

Session 2 – Contributed Reports

Marquis A

Students’ explicit, unwarranted assumptions in “proofs” of false conjectures

Kelly Bubp

Although evaluating, refining, proving, and refuting conjectures are important aspects of doing mathematics, many students have limited experiences with these activities. In this study, undergraduate students completed prove-or-disprove tasks during task-based interviews. This paper explores the explicit, unwarranted assumptions made by six students on tasks involving false statements. In each case, the student explicitly assumed an exact condition necessary for the statement in the task to be true although it was not a given hypothesis. The need for an ungiven assumption did not prompt any of these students to think the statement may be false. Through prompting from the interviewer, two students overcame their assumption and correctly solved the task and two students partially overcame it by constructing a solution of cases. However, two other students were unable to overcome their assumptions. Students making explicit, unwarranted assumptions seems to be related to their limited experience with conjectures.

Paper

11

Marquis B

Physics: Bridging the symbolic and embodied worlds of mathematical thinking

Clarissa Thompson, Sepideh Stewart and Bruce Mason

Physics spans understanding in three domains – the Embodied (Real) World, the Formal (Laws) World, and the Symbolic (Math) World. Expert physicists fluidly move among these domains. Deep, conceptual understanding and problem solving thrive in fluency in all three worlds and the facility to make connections among them. However, novice students struggle to embody the symbols or symbolically express the embodiments. The current research focused on how a physics instructor used drawings and models to help his students develop more expert-like thinking and move among the worlds.

Paper

41

Marquis C

Inquiry-based learning in mathematics: Negotiating the definition of a pedagogy

Zachary Haberler and Sandra Laursen

Inquiry-based learning is one of the pedagogies that has emerged in mathematics as an alternative to traditional lecturing in the last two decades. There is a growing body of research and scholarship on inquiry-based learning in STEM courses, as well as a growing community of practitioners of IBL in mathematics. However, despite the growth of IBL research and practice in mathematics, wide uptake of IBL remains hamstrung in part by the lack of a sophisticated discussion of its definition. This paper offers a first step toward addressing this problem by describing how a group of IBL practitioners define IBL, how they adopt IBL to fit their specific teaching needs, and how differences in definitions and perceptions of IBL have constrained and enabled its diffusion to new instructors.

Paper

55

Grand Ballroom 5

Student resources pertaining to function and rate of change in differential equations

George Kuster

While the importance of student understanding of function and rate of change are themes across the research literature in differential equations, few studies have explicitly focused on how student understanding of these two topics grow and interface with each other while students learn differential equations. Extending the perspective of Knowledge in Pieces (diSessa, 1993) to student learning in differential equations, this research explores the resources relating to function and rate of change that students use to solve differential equations tasks. The findings reported herein are part of a larger study in which multiple students enrolled in differential equations were interviewed periodically throughout the semester. The results culminate with two sets of resources a student used relating to function and rate of change and implications for how these concepts may come together to afford an understanding of differential equations.

Paper

124