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10:55 – 11:25 am

Session 11 – Contributed Reports

Marquis A

Symbolizing and Brokering in an Inquiry Oriented Linear Algebra Classroom

Michelle Zandieh, Megan Wawro and Chris Rasmussen

The purpose of this paper is to explore the role of symbolizing and brokering in fostering classroom inquiry. We characterize inquiry both as student inquiry into the mathematics and instructorÕs inquiry into the studentsÕ mathematics. Disciplinary practices of mathematics are the ways that mathematicians go about their profession and include practices such as conjecturing, defining, symbolizing, and algorithmatizing. In this paper we present examples of students and their instructor engaging in the practice of symbolizing in four ways. We integrate this analysis with detail regarding how the instructor serves as a broker between the classroom community and the broader mathematical community.



Marquis B

MathematiciansÕ ideas when formulating proof in real analysis

Melissa Troudt

This report presents some findings from a study that investigated the ideas professional mathematicians find useful in developing mathematical proofs in real analysis. This research sought to describe the ideas the mathematicians developed that they deemed useful in moving their arguments toward a final proof, the context surrounding the development of these ideas in terms of DeweyÕs theory of inquiry, and the evolving structure of the personal argument utilizing ToulminÕs argumentation scheme. Three research mathematicians completed tasks in real analysis thinking aloud in interview and at-home settings and their work was captured via video and Livescribe technology. The results of open iterative coding as well as the application of DeweyÕs and ToulminÕs frameworks were three categories of ideas that emerged through the mathematiciansÕ purposeful recognition of problems to be solved and their reflective and evaluative actions to solve them.



Marquis C

Reinventing the multiplication principle

Elise Lockwood and Branwen Schaub

Counting problems offer opportunities for rich mathematical thinking, yet students struggle to solve such problems correctly. In an effort to better understand studentsÕ understanding of a fundamental aspect of combinatorial enumeration, we had two undergraduate students reinvent a statement of the multiplication principle during an eight-session teaching experiment. In this presentation, we report on the studentsÕ progression from a nascent to a sophisticated statement of the multiplication principle, and we highlight two key mathematical issues that emerged for the students through this process. We additionally present potential implications and directions for further research.