## What is eliciting and interpreting student thinking?

Teachers pose questions or tasks that provoke or allow students to share their thinking about specific academic content in order to evaluate student understanding, guide instructional decisions, and surface ideas that will benefit other students. To do this effectively, a teacher draws out a student’s thinking through carefully-chosen questions and tasks and considers and checks alternative interpretations of the student’s ideas and methods.

## What is challenging about learning this practice in mathematics?

Novices may begin teacher preparation with strongly held beliefs about what it means to teach and learn mathematics based on their own experiences as learners of math. When they understand doing math as primarily about getting correct answers and teaching math as conveying procedures for arriving at correct answers, novices may have strong inclinations to evaluate and remediate student thinking. As a result novices may miss opportunities to identify and build upon students’ existing knowledge and understanding, neglect innovative and mathematically rich student strategies, and fail to recognize the logic underlying students’ misconceptions or errors. Ultimately, these inclinations can interfere with novices’ capacities to be responsive to individual students and their particular instructional needs. By working deliberately on eliciting and interpreting individual students’ thinking, novices can develop first the skills and eventually the dispositions to listen attentively to and probe student ideas and reasoning to develop robust understandings of what students know and can do for use in instruction. Moreover, the practice is central to teaching math in a way that honors students’ contributions and positions students as sense-makers capable of doing meaningful mathematical work.

## How can eliciting and interpreting in mathematics advance justice?

When a teacher elicits students’ thinking with an orientation to fully appreciate the meaning each student is making of a mathematical problem or concept, the teacher communicates openness to multiple perspectives and ways of knowing. This is especially critical in mathematics, a content domain where what counts as competence is often narrowly defined. When this practice is routinely done well, students have repeated opportunities to formulate, revise, and refine mathematical arguments and as a result to come to see themselves as people who are capable of reasoning and making sense of mathematics using what they know to build new understandings. In addition when all students are treated respectfully, when they are truly listened to, when their ideas are valued and understood as resources in instruction, and when these norms extend to how students treat one another, then a teacher’s work to elicit and interpret student thinking can serve as the foundation for engendering what Jo Boaler (2008) has termed relational equity. Like Boaler, we believe that when students experience equitable relations in mathematics classrooms, “the respect they learn to form for each other will impact the opportunities they extend to others in their lives in and beyond school” (p. 167).