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1:10 – 1:40 pm |
Session 24
– Contributed Reports |
Marquis A |
Student problem solving in the context of volumes of
revolution Anand Bernard and Steven
Jones The
literature on problem solving indicates that focusing on strategies for
specific types of problems may be more beneficial than seeking to determine
grand, general problem solving strategies that work across large domains.
Given this guideline, we seek to understand and map out different strategies
studentsÕ used in the specific context of volumes of revolution problems from
calculus. Our study demonstrates the complex nature of solving volumes of
revolution problems based on the multitude of diverse paths the students in
our study took to achieve the desired Òepistemic formÓ of an integral
expression for a given volume problem. While the large-grained, overarching
strategy for these students did not differ much, the complexity came in how
the student carried out each step in their overall strategy. 14 |
Marquis B |
StudentsÕ conceptions of factorials prior to and within
combinatorial contexts Elise Lockwood and Sarah
Erickson Counting
problems offer rich opportunities for students to engage in mathematical
thinking, but they can be difficult for students to solve. In this paper, we
present a study that examines student thinking about one concept within
counting, factorials, which are a key aspect of many combinatorial ideas. In
an effort to better understand studentsÕ conceptions of factorials, we
conducted interviews with 20 undergraduate students. We present a key
distinction between computational versus combinatorial conceptions, and we
explore three aspects of data that shed light on studentsÕ conceptions (their
initial characterizations, their definitions of 0!, and their responses to
Likert-response questions). We present implications this may have for
mathematics educators both within and separate from combinatorics, and we
discuss possible directions for future research. 32 |
Marquis C |
When should research on proof-oriented mathematical
behavior attend to the role of particular mathematical content? Paul Christian Dawkins and
Shiv Karunakaran Because
proving characterizes much mathematical practice, it continues to be a
prominent focus of mathematics education research. Aspects of proving, such
as definition use, example use, and logic, act as subdomains for this area of
research. To yield such content-general claims, studies often downplay or try
to control for the influence of particular mathematical content (analysis,
algebra, number theory etc.) and studentsÕ mathematical meanings for this
content. In this paper, we consider the possible negative consequences for
mathematics education research of adopting such a domain-general
characterization of proving behavior. We do so by comparing content-general
and content-specific analyses of two proving episodes taken from the prior
research of the two authors respectively. We intend to sensitize the research
community to the role particular mathematical content can and should play in
research on mathematical proving. 48 |