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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. 29 |
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. 25 |
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. 97 |