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This chapter reports on work from a decade-long project to develop and study the use of teaching simulations focused on the teaching practices of eliciting and interpreting student thinking to support preservice teachers' (PSTs') learning. The chapter describes how teaching simulations focused on these practices allow teacher educators to support PSTs in orienting to student sense-making that is at the heart of equitable mathematics instruction. The teaching simulation approach is described. Examples illustrate how the approach is designed and facilitated in ways that make visible PSTs' engagement with three teaching performance areas (eliciting the student's process, using mathematical knowledge and skill, and conveying respect for the student as a mathematical thinker and learner) that are crucial for more equitable mathematics instruction. Connections between each of the performance areas and more equitable eliciting and interpreting of student thinking are described alongside the ways in which teacher educators can provide feedback that supports PSTs' development. 

We describe how a teaching simulation cycle focused on eliciting and interpreting student thinking in elementary mathematics can reveal important aspects of a teacher candidate’s (TC’s) knowledge and skill with eight performance areas relevant to more equitable mathematics teaching. Appraising a TC’s knowledge and skill with respect to these performance areas is intended to support formative feedback that is actionable in subsequent teaching. 

We share the teaching simulation as one approach to providing formative feedback in teacher preparation and consider the ways in which teacher candidates (TCs) take up the feedback in subsequent simulations. We hypothesize that TCs’ uptake depends on the connections between their own resources, the focus of the feedback provided, and the context of subsequent teaching. 

SimulaTE is studying teaching simulations as formative assessments of pre-service teachers’ (PST) practice of eliciting and interpreting students’ mathematical thinking. Preparation and protocols that promote reliability and validity of the simulations as formative assessments will enhance their effectiveness and generalizability. Teacher educators who use the simulations document each PST’s performance to generate feedback for the PST in nine categories, arising from a decomposition of the teaching practice into specific component skills or actions. A series of coordinated validation studies include research to determine if the nine categories are distinguishable through the use of the simulation assessments, and can benefit from attention beyond other experiences PSTs have in their teacher preparation programs 

SimulaTE is studying teaching simulations as formative assessments of pre-service teachers’ (PST) practice of eliciting and interpreting students’ mathematical thinking. Preparation and protocols that promote reliability and validity of the simulations as formative assessments will enhance their effectiveness and generalizability. Teacher educators who use the simulations document each PST’s performance to generate relevant feedback for the PST. As part of a coordinated set of validity studies, six researchers were prepared on the documentation protocol. Consistency of documentation within the group and with the simulation developers’ judgments provided evidence supporting reliability and validity of the documentation protocol.