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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. 98 |
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. 114 |
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. 16 |