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10:15 – 10:45 am

Session 21 – Contributed Reports

Marquis A

A framework for examining the 2-D and 3-D spatial skills needed for calculus

Nicole Engelke, Marjorie Darrah and Kristen Murphy

Having well developed spatial skills is critical to success in many STEM fields such as engineering, chemistry, and physics; these skills are equally critical for success in mathematics. We present a framework for examining how spatial skills are manifested in math problems. We examine established spatial skills definitions and correlate them with the spatial skills needed to successfully solve a standard calculus problem – find the volume of a solid of revolution. This problem is deconstructed into steps and analyzed according to what 2-D and 3-D spatial skills are necessary to visualize the problem. The results of a pilot study in which we examine the spatial skills that first semester calculus students possess are presented along with the potential implications the studentsŐ skill level could bring to bear on the problem. We conclude with suggestions for remediation of these spatial skills in the calculus classroom and directions for future research.



Marquis B

Ways in which engaging in someone elseŐs reasoning is productive

Naneh Apkarian, Chris Rasmussen, Hayley Milbourne, Tommy Dreyfus, Xuefen Gao and Matthew Voigt

Typical goals for inquiry-oriented mathematics classrooms are for students to explain their reasoning and to make sense of othersŐ reasoning. In this paper we offer a framework for interpreting ways in which engaging in the reasoning of someone else is productive for the person who is listening. The framework is the result of analysis of 10 individual problem-solving interviews with 10 mathematics education graduate students enrolled in a mathematics content course on chaos and fractals. The theoretical grounding for this work is the emergent perspective (Cobb & Yackel, 1996), which views mathematical progress as a process of active individual construction and a process of mathematical enculturation. The framework captures the relationship between engaging with anotherŐs reasoning, decentering, elaborating justifications, and refining/enriching conceptions.




Marquis C

Transforming graduate studentsŐ meanings for average rate of change

Stacy Musgrave and Marilyn Carlson

This report offers a brief conceptual analysis of average rate of change (AROC) and shares evidence that even mathematically sophisticated mathematics graduate students struggle to speak fluently about AROC. We offer data from clinical interviews with graduate teaching assistants who participated in at least one semester of a professional development intervention designed to support mathematics graduate students in developing deep and connected meanings of key ideas of precalculus level mathematics as part of a broader intervention to support mathematics graduate students in teaching ideas of precalculus mathematics meaningfully to students. The results revealed that the post-intervention graduate students describe AROC more conceptually than their pre-intervention counterparts, but many still struggle to verbalize a meaning for AROC beyond average speed, a geometric interpretation based on the slope of a secant line, or a computation.