The cognitive demand of mathematical tasks is an important aspect of analyzing the impact of instruction on student learning. The purpose of this study was to examine the instructional examples enacted by graduate student precalculus instructors in order to answer the following questions: What is the cognitive demand of the enacted examples? What does a high cognitive demand example look like when an instructor uses direct instruction? And how are examples drawn from the written curriculum enacted in different ways? Using both random and purposeful sampling of precalculus lessons, I conducted classroom observations as well as pre- and post-observation interviews with the instructors. A modified version of the Task Analysis Guide (Smith & Stein, 1998) was then used to categorize the cognitive demand of the instructional examples. As a result, I found that 25 out of the 93 examples (27%) I observed were enacted at a high level of cognitive demand. I also present vignettes that illustrate how three different instructors chose to enact the same example type at differing levels of cognitive demand.
Miller, Erica R.
"Analyzing the Cognitive Demand of Enacted Examples in Precalculus: A Comparative Case Study of Graduate Student Instructors,"
Journal of Mathematics and Science: Collaborative Explorations: Vol. 16
, Article 18.
Available at: https://scholarscompass.vcu.edu/jmsce_vamsc/vol16/iss1/18