First Advisor

Powers, Robert

Second Advisor

Hauk, Shandy

Document Type

Dissertation

Date Created

8-1-2015

Department

College of Natural and Health Sciences, Mathematical Sciences, Mathematical Sciences Student Work

Abstract

The goals of this dissertation were to examine how novice calculus teachers used questions in their classrooms, how those questions and their use might change after video case-based course coordination, and what evidence of influence on student learning might be seen in undergraduate student achievement. This research focused on one way to elicit student ideas--by asking questions--and how professional development might facilitate asking questions as a way to learn about student thinking in calculus. This dissertation defined question depth (in terms of cognitive demand), question category (comprehension check, content check, elicit thinking, probe thinking), and discourse neighborhood as aspects of questioning in classroom “math talk.” The mixed methods included instructor interviews and teaching logs, observations of course coordination meetings, and observation and video-capture for six hours of calculus class meetings for each of five novice instructors. Deep analysis of four class meetings for each instructor informed the revision of a framework describing the relationships among question depth, question category, and the instructors’ professional development. The teaching-focused development activities for these instructors were during regular course coordination meetings and included the use of four video case activities about college classroom and office hour instruction.

Instructors asked an average of about 50 to 125 questions per class with 62% being low cognitive demand checks for comprehension, “Did you get that?” and 32% having slightly deeper demand for a product “What did you get?” or steps in a process “How did you get that?” The remaining 6% of questions had moderate cognitive demand, eliciting details about decision-making “How did you decide the pieces here for using the chain rule?” No novice instructor in this study asked a question that probed deeply for sense-making or complex justification (e.g., “What in the mathematics here indicates that the chain rule is appropriate?”). On the large scale, all tended to follow the teacher initiated-respond-follow-up (IRF) pattern, focused on evaluating and fixing student responses. These results reflect and extend to the college level the K-12 research literature, which has demonstrated that novice teachers begin with evaluative IRF practices. On the smaller scale, instructors had their own ways of enacting some shared discourse patterns, such as questions like “Do you understand?” and “What is the next step?” The main results of the qualitative work were the detailed profiles of novice instructors and their questioning techniques, documentation that neither final exam nor course grades were sensitive to the small changes in instruction that novices implemented when participating in video case-based professional development, and examination of novice instructor’s experiences of that professional development. The model-building result is a revised framework for novice instructor classroom communication that offers language for noticing and talking about question depths and question categories in examination of teaching practice.

Keywords

calculus, college mathematics instructors, discourse, novice, professional development, question

Extent

254 pages

Local Identifiers

Roach_unco_0161D_10443.pdf

Rights Statement

Copyright is held by the author.

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