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theses

The improvement of mathematics education relies very heavily on the improvement of undergraduate mathematics education for future teachers (National Research Council, 1989). It is important that undergraduate mathematics instruction for prospective teachers demonstrates techniques to be used in their future classrooms (Blair, 2006; Senk, Keller, & Ferrini-Mundy, 2004). Specifically, pre-service teachers should develop an understanding of the mathematical processes of exploration and proof (Senk, Keller, & Ferrini-Mundy, 2004). If problems that encourage mathematical exploration and justification are to be brought into the undergraduate classroom, understanding how students build and justify their solutions will be of importance. The purpose of this research was to (1) investigate how undergraduate students enrolled in a mathematics course solve and justify their solution to a series of combinatorics tasks, (2) analyze the moves employed by the instructor and (3) investigate how their solutions compare to the solutions of other students involved in the same problem-solving tasks. This case study was conducted in a mathematics class at a liberal arts college. The six students in this class were all mathematics majors studying to be teachers. Using videotaped data and students’ written work, a careful analysis of how the students built their solutions and justified their answers to three combinatoric problems was conducted. It was found that the strategies and justifications used by the students in this study were similar to those used by participants in earlier studies. Furthermore, in investigating how the college math students built their solutions to the problems, it was found that the instructor played a critical role in the learning process. Findings from this study verify that mathematical learning can take place in a college mathematics class that fosters mathematical exploration and justification with well-chosen tasks, collaboration with peers, and student-centered instruction. This study also has implications for implementation in other settings by providing examples of students’ solutions to specific tasks as well as examples of how instructors can effectively interact with students in a mathematical classroom that nurtures the mathematical processes of conjecturing, generalizing, and justifying solutions to problems.

ETD_4954

Ed.D.

Includes bibliographical references

by Anna Brophy

doi:10.7282/T3BC3WHM

ETD doctoral

The author owns the copyright to this work.