Saturday

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.

Paper

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.

Paper

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.

Paper

48