Interpreting Student Thinking When a Student Uses an Alternative Algorithm

• In Event: Approaches to Learning About Student Thinking in Practice-Based Teacher Education

Abstract

Objectives & perspectives
To address challenges with field-based assessments, our project has employed teaching simulations to assess preservice teachers’ (PSTs’) engagement in eliciting and interpreting student thinking. We use a sample of student work to spur an interaction between a PST and an individual with knowledge of the “student’s” process, degree of understanding, and interactional style. While not fully representing the context of professional practice, simulations are able to evoke authentic performances in a context that is standardized in strategic ways to enhance learning and/or assessment (Dotger, 2014). In this study, we use teaching simulations to investigate the capabilities that PSTs bring to teacher education related to interpreting student thinking in a context in which a student is using an alternative algorithm.

Methods & data sources
In this teaching simulation, PSTs: (1) prepare for an interaction with a simulated student about one piece of student work; (2) elicit the simulated student’s thinking to learn about her process for solving the problem and her understanding of key mathematical ideas; and (3) respond to questions about their interpretation of the student’s thinking, including predicting the student’s response to a similar task. To ensure consistency, the simulated student has rules for reasoning and responding. We draw on the videos, work samples and scoring tools collected in relation to three cohorts of PSTs’ performances (~35 per cohort) at the beginning of our teacher education program. Each cohort engaged in a teaching simulation in which the sample of student work showed that the student was using an alternative algorithm to solve an addition or subtraction problem (see Table 1). The specific algorithm and the operation (addition or subtraction) varied across the three years. Performances were video recorded. We coded PSTs’ interpretations of the student thinking with a focus on: (1) describing the student’s process, (2) describing the student’s understanding, (3) anticipating the student’s method on a similar problem, and (4) marshalling available evidence to support claims. All of the performances were appraised by two members of the research team.

Results
Table 1 indicates the percentage of PSTs in each teaching simulation who accurately (a) described the student’s process with evidence, (b) applied the student’s process to a similar problem, and (c) described one understanding of the student with evidence. The findings suggest that the PSTs bring some skills relevant to interpreting a student’s process, such as describing it and applying the process to a similar problem. However, there were differences by assessment. We unpack these differences and offer possible explanations in our full paper. For interpreting the student’s understanding, these PSTs demonstrated very limited skills in this initial experience. There were no significant differences in performances based on the algorithm in the teaching simulation.

Significance of the work
Our project uses samples of student work as part of a teaching simulation to learn about the interpreting skills and capabilities of PSTs at the beginning of teacher education. In addition to the empirical findings, we contribute a method for learning about the skills that PSTs bring.

Authors

• Meghan M. Shaughnessy, Boston University

• Timothy A. Boerst, University of Michigan