Learning Mathematical Knowledge for Teaching in and From Simulations

• In Event: Approximating Teaching: Using Simulations as a Platform for Understanding and Improving Instructional Quality

Abstract

Objective and Framework
Practice-based teacher education relies on the selection and development of settings, such as simulations, that support TCs in learning from engagement in the work of teaching. Research is needed about approaches to simulation design. Drawing on learning theory and our own experience with simulations for assessment, we designed and studied three simulation contexts in which TCs elicited and interpreted a simulated student’s thinking. We examined the development of TCs’ mathematical knowledge for teaching (MKT) (Ball, Thames, & Hoover, 2008). All three simulation contexts were built around the same set of student work, featuring two related multiplication approaches.

Context A involves (1) preparing for an interaction with one simulated student (i.e., a teacher educator taking on the role of the student) about a student’s written work; (2) eliciting the student’s thinking to understand the steps she took, why she performed particular steps, and her understanding of the key mathematical ideas involved; and (3) responding to questions about the student’s thinking.

Context B is Context A followed by a structured self-reflection. We incorporated the structured self-reflection based on research (e.g., National Research Council, 2000; Santagata & Taylor, 2018) showing the importance of reflection in professional learning experiences.

Context C is a simulation in which the simulated student provides additional information (likely to extend and contrast with the TC’s ideas) and requests information/representation/explanations. These modifications were made based on ideas suggested in research literature (e.g., providing more opportunities for the TCs to take up the student’s thinking and the mathematical ideas contained in a student’s work (Grossman, Schoenfeld, & Lee, 2005)).

Methods and Data Sources
Forty-five TCs participated. Prior to the simulations, all participants completed assessments of MKT (LMT, 2008) and Mathematical Knowledge of multiplication algorithms. TCs also completed a survey focused on their disposition toward different multiplication approaches. These assessments were used to produce three groups (one for each context) that were balanced for MKT. Then participants engaged in the simulation and surrounding structures. The assessments were then given again to capture information that would allow us to categorize dimensions of a TC’s MKT that could change through engagement in the simulation or activities surrounding the simulation. Data also included video-recorded participation in the simulation, post-simulation interviews, and written responses to reflection questions for the TCs in Context B. These data were coded for elements of MKT demonstrated by the TCs during the simulation and in response to post-simulation questions/reflection.

Results
Analyses revealed that participants in both Context B and C enhanced their MKT. Some of the participants in Context A enhanced their MKT, but the gains were not consistent across the group. The paper highlights the nature and degree of differences/changes in MKT in the three contexts.

Significance
This study links particular simulation features (e.g., structured self-reflection) to the learning of MKT. In a larger sense, focusing on, and systematically studying, design features that could be harnessed to create simulations that foster learning opportunities for TCs could support more substantial and meaningful uses.

Authors

• Meghan M. Shaughnessy, Boston University

• Timothy A. Boerst, University of Michigan