Understanding and advancing graduate teaching assistants’ mathematical knowledge for teaching
This article points out the importance of ensuring that GTA's can provide high quality explanations for foundational mathematical ideas. It provides evidence that even mathematically sophisticated GTA's often provide low-level explanations of the idea of average rate of change. It explains the intervention that resulted in the GTA's giving much more meaningful explanations of average rate of change.
Graduate student teaching assistants (GTAs) usually teach introductory level courses at the undergraduate level. Since GTAs constitute the majority of future mathematics faculty, their image of effective teaching and preparedness to lead instructional improvements will impact future directions in undergraduate mathematics curriculum and instruction. In this paper, we argue for the need to support GTAs in improving their mathematical meanings of foundational ideas and their ability to support productive student thinking. By investigating GTAs’ meanings for average rate of change, a key content area in precalculus and calculus, we found evidence that even mathematically sophisticated GTAs possess impoverished meanings of this key idea. We argue for the need, and highlight one approach, for supporting GTAs to improve their understanding of foundational mathematical ideas and how these ideas are learned.