Date of Award

8-2014

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Natasha M. Speer

Second Committee Member

Robert Franzosa

Third Committee Member

Eisso Atzema

Abstract

Previous studies have indicated that effective mathematics teaching relies on teachers’ knowledge of both students’ thinking and mathematical content. Very little is known about the kind of knowledge teachers draw on when teaching general ideas related to the derivative in calculus or applied derivative problems. Graduate teaching assistants play important roles in the teaching of calculus however, very little is known about their knowledge for teaching. Using a well-established framework for elementary school teachers’ mathematical knowledge for teaching, mathematics graduate teaching assistants’ (GTA) mathematical knowledge for teaching the derivative and applied derivative problems was examined. Task-based interviews were conducted with eight GTAs, three novice GTAs with no teaching experience and five experienced GTAs with four or more semesters of teaching experience. Interview tasks targeted different domains of knowledge GTAs might access when talking about the concept of the derivative and solving applied derivative problems and while engaged in teaching-related work such as examining student solutions. Findings suggest that the existing framework for teachers’ mathematical knowledge for teaching does describe the kinds of knowledge GTAs draw on when discussing derivative and applied derivative problems, however, there were instances when GTAs drew on their science knowledge for teaching as well. When presenting applied derivative examples, discussing sample student work on the applied derivative problems, it was noticed that GTAs drew on their integrated mathematics and science knowledge for teaching. It was also noticed that the experienced GTAs have more organized and more accessible knowledge for teaching compared to the novice GTAs. Implications for research and for novice college mathematics instructor professional development are also discussed.

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