This project investigates the outcomes of a teacher education model designed to foster prospective mathematics teachers' abilities to notice and capitalize on important mathematical moments in instruction. The project engages prospective teachers in research-like analysis of unedited teacher-perspective classroom video early in their teacher education coursework in order to help them learn to identify, assess the mathematical potential of, and respond to important student ideas and insights that arise during instruction.

# Shari Stockero

**Michigan Technological University**

**Michigan Technological University**

Mathematical Opportunities in Student Thinking (MOSTs) are high-leverage instances of student mathematical thinking that emerge in whole-class discussions. The challenge for teachers is to build on these opportunities to help the whole class understand the mathematics underlying these student contributions. To help teachers learn how to build on MOSTs, there is a need for professional development resources and tools that facilitators can use. There is also a need for research about how teachers use what they learn in professional development in their teaching. This project is developing a teacher learning sequence that will support teachers in learning to productively use student thinking that surfaces in-the-moment during their instructionâ€”that is, in learning to build on MOSTs.

**Michigan Technological University**

This project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. The study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks.

**Michigan Technological University**

The core research questions of the project are: (1) What is the nature of high-leverage student thinking that teachers have available to them in their classrooms? (2) How do teachers use student thinking during instruction and what goals, orientations and resources underlie that use? (3) What is the learning trajectory for the teaching practice of productively using student thinking? and (4) What supports can be provided to move teachers along that learning trajectory?