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6:10 – 6:40 pm |
Session 7 – Contributed
Reports |
Marquis A |
Covariational and parametric reasoning Teo Paoletti and Kevin
Moore Researchers
have argued that students can develop foundational meanings for a variety of
mathematics topics via quantitative and covariational reasoning. We extend
this research by examining two studentsÕ reasoning that we conjectured
created an intellectual need for parametric functions. We first describe our
theoretical background including different conceptions of covariation
researchers have found useful when analyzing studentsÕ activities
constructing and representing relationships between covarying quantities. We
then present two studentsÕ activities during a teaching experiment in which
they constructed and reasoned about covarying quantities and highlight
aspects of the studentsÕ reasoning that we conjecture created an intellectual
need for parametric functions. We conclude with implications the studentsÕ
activities and reasoning have for future research and curriculum design. 20 |
Marquis B |
Re-claiming during proof production David Plaxco In
this research, I set out to elucidate the construct of Re-Claiming - a way in
which studentsÕ conceptual understanding relates to their proof activity.
This construct emerged during a broader research project in which I analyzed
data from individual interviews with three students from a junior-level
Modern Algebra course in order to model the studentsÕ understanding of
inverse and identity, model their proof activity, and explore connections
between the two models. Each stage of analysis consisted of iterative coding,
drawing on grounded theory methodology (Charmaz, 2006; Glaser & Strauss,
1967). In order to model conceptual understanding, I draw on the
form/function framework (Saxe, et al., 1998). I analyze proof activity using
AberdeinÕs (2006a, 2006b) extension of ToulminÕs (1969) model of
argumentation. Reflection across these two analyses contributed to the
development of the construct of Re-Claiming, which I describe and explore in
this article. 125 |
Marquis C |
Limitations of a "chunky" meaning for slope Cameron Byerley,
Hyunkyoung Yoon and Patrick Thompson This
paper will investigate the question ÒWhat mathematical meanings do high
school mathematics teachers hold for slope?Ó It will also investigate to what
extent these meanings build on an image of quotient as a measure of relative
size. The data comes from the administration of the diagnostic instrument
named ÒMeanings for Mathematics Teaching Secondary MathÓ (MMTsm). 95 |