Examining the Task and Knowledge Demands Needed to Teach with Representations

Source: Journal of Mathematics Teacher Education, Volume 17, Issue 1, pp 37–60, February 2014.

In this study, the authors examine the task and knowledge demands for teaching integer operations with representations by analyzing teaching practice.

Teaching integer operations is used as an intensity case, as integer operations are challenging for students, and teachers are often required to employ several representations to teach this topic. Following a practice-based approach while also taking prior literature into consideration, the authors first generate a list of tasks entailed in teaching with representations and then discuss the knowledge demands imposed on teachers to successfully undertake this work. They highlight these tasks and knowledge demands by analyzing and discussing an integer addition and an integer subtraction episode for each of two teachers, Bonita and Karen.

Based on their analysis, the authors organize the generated knowledge components using the Mathematical Knowledge for Teaching framework.
They conclude by drawing implications for teacher educators and curriculum developers.