The Fostering Algebraic Thinking Toolkit is a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. Underlying the Toolkit is a core belief that good mathematics teaching begins with understanding how mathematics is learned. The focus here is on how students think about mathematics.
The Toolkit features four separate modules containing notes for the facilitator and reproducible blackline masters for the workshop participants. Each module concentrates on a different kind of classroom evidence and, in facilitated sessions, asks teachers to collect student and/or teacher data to share and analyze with colleagues. A module can be covered in four three-hour sessions.
The first module, Introduction and Analyzing Written Student Work gives participants an opportunity to analyze students' written work for evidence of algebraic thinking, and to become comfortable with the language of the algebraic habits of mind, before moving on to one of the other modules. Each of the three remaining modules builds on the work done here.
Asking Questions of Students
Together with the accompanying video, this module offers a change both in the type of student data considered—from written to real time—and in the emphasis of the module—from understanding to fostering student thinking. Of the four modules, this one puts the least emphasis on looking at student thinking and focuses more specifically on the relationship between teacher intentions and teacher questions.