Thursday

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.

Paper

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.

Paper

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).

Paper

95