Novice College Mathematics Instructor Communication About Cognitive Demand
By: Helena Almassy
Department: Mathematics
Faculty Advisor: Dr. Shandy Hauk
Many incoming mathematics graduate students become novice instructors with little to no experience teaching at the college level. One aspect of preparing to teach is developing skills in supporting students to engage with mathematical tasks. To do so, novice instructors must consider the context of the student learning experience as well as the level of cognitive demand for the mathematical task (e.g., recalling and applying memorized facts, using procedures with and without connection to other knowledge, and most cognitively demanding: doing mathematics in a novel situation). Though research exists on cognitive demand and the preparation of teachers to attend to it for K-12 mathematics, little research has focused on the needs of novice college mathematics instructors. In this thesis, the focus is on graduate students in mathematics who are employed as instructor-of-record for various undergraduate mathematics courses. The nine graduate teaching associates (GTAs) in this study also were the participants in a semester-long workshop about teaching college mathematics. This study addressed the research question: How are novice instructors’ instructional decisions informed and shaped by consideration of cognitive demand? The data collected included GTAs responses to online activities and three consecutive workshop discussions about cognitive demand in various college mathematics classroom examples. Analysis of audio transcripts and text from the corresponding online activities resulted in the identification of three types of GTA attention to cognitive demand: (1) as a component in scaffolding (e.g., raising, maintaining, and lowering cognitive demand), (2) connecting between cognitive demand and other frameworks, and (3) deepening understanding of what is and is not part of cognitive demand. Each of these results has promise as an area for further research and as a focus for refining the professional preparation of GTAs for their first semesters of teaching.