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## The Practices of Eliciting and Interpreting Student Thinking

Our simulation assessments focus on two related high-leverage practices: **eliciting student thinking** and **interpreting student thinking**. Eliciting student thinking is the work teachers do when they ask questions or pose tasks about specific academic content. For example, teachers elicit student thinking to check student understanding, to gather and probe student solution methods, and to support students in providing more detailed explanations. Interpreting student thinking is the work of characterizing what students think based on evidence from what students say and do. Teachers interpret student thinking when they make sense of students’ responses to questions and/or analyze written work. The combination of eliciting and interpreting underpins other teaching practices, such as formative assessment, that have been shown to substantially impact student learning (Wiliam, 2010; Black & Wiliam, 1998).

We ground our simulation assessments in decompositions (Grossman et al., 2009) of teaching practices. In other words, to develop our assessments, we break down the practices of eliciting and interpreting student thinking into finer-grained teaching tasks.

#### Components of eliciting include:

- Initiating the interaction in a way that invites the student to share initial thinking
- Following up on what the student says and does
- Probing key aspects of the focal mathematics
- Establishing a supportive environment for sharing thinking
- Maintaining a focus on eliciting student thinking

#### Components of interpreting include:

- Using evidence to generate and test claims
- Making qualified claims about student thinking
- Actively working to prevent bias or distortion
- Developing or using appropriate criteria to focus or inform judgment

We also use the assessments to gather evidence of mathematical knowledge for teaching (MKT) (Ball, Thames, and Phelps, 2008). Our simulations assess the following aspects of MKT:

- Using mathematical language and representations in accurate and accessible ways
- Appraising the correctness of a solution to a mathematics problem
- Generating a follow-up mathematics problem to confirm the student’s process
- Applying the student’s process to a similar mathematics problem
- Considering the generalizability of a mathematical process

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