Mathematics, Department of


First Advisor

Yvonne Lei

Date of this Version



Miller, E. R. (2018). High cognitive demand examples in precalculus: Examining the work and knowledge entailed in enactment (Doctoral dissertation). University of Nebraska, Lincoln, NE.


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Yvonne Lai. Lincoln, Nebraska: May, 2018.

Copyright (c) 2018 Erica R. Miller


Historically, pass rates in undergraduate precalculus courses have been dismally low and the teaching practices and knowledge of university instructors have been understudied. To help improve teaching effectiveness and student outcomes in undergraduate precalculus courses, I have studied the cognitive demand of enacted examples. The purpose of this dissertation is to examine the pedagogical work and mathematical knowledge entailed in the enactment of high cognitive demand examples in a three-part study. To answer my research questions, I conducted classroom observations as well as pre- and post-observation interviews with seven graduate student instructors at a large public R1 university in the Midwest and used grounded theory to analyze my data. In the first component of the dissertation, I examine what high cognitive demand examples look like and identify three roles that instructors take on when enacting high cognitive demand examples: modeling, facilitating, and monitoring. In the second component, I decomposed the work of enacting high cognitive demand examples into five teaching tasks: attending to the mathematical point, making connections, providing clear verbal explanations, articulating cognitive processes, and supporting student understanding. Finally, in the third component, I examined the mathematical knowledge for teaching entailed in enacting examples and found that there are five domains of knowledge that support the maintenance of cognitive demand: knowledge of connections, representations, unpacking, students, and sequencing. These findings suggest ways in which we can help novice instructors enact high cognitive demand examples by focusing on the work and knowledge entailed in maintaining the cognitive demand.

Advisor: Yvonne Lai