Our Thinking About Professional Development

We contend that appropriate forms of professional development for mathematics teachers should include opportunities to engage with mathematical ideas, to explore their own thinking about mathematical processes, and to also consider the mathematical thinking exhibited by their students. The Structured Exploration approach to professional development, introduced by Grace Kelemanik and her colleagues in 1997*, has proven to be a useful framework for us in our efforts.

The Structured Exploration process allows teachers to see mathematics from different points of view and gain a deeper understanding of geometry.  It is a cyclical process that repeats each time teachers engage with a new mathematics problem. The cycle involves five stages:

• Stage 1:    Doing mathematics. Teachers work together with colleagues to explore and solve mathematics problems they will later use with their students.
• Stage 2:    Reflecting on the mathematics.  Using an explicit conceptual framework (the G-HOMs), teachers discuss the mathematical ideas and their thinking about the problem. 
• Stage 3:    Collecting student work. Teachers use the problems in their own classes and collect student work.
• Stage 4:    Analyzing student work. Teachers bring selected student work back to the study group to analyze and discuss with colleagues.
• Stage 5:    Reflecting on students’ thinking. Once again using the G-HOMs framework, teachers discuss students’ mathematical thinking, as revealed in the student work, and ways to elicit more productive thinking in future classes.

We believe that, over time, this repeated process leads to clearer understanding of geometric thinking.  In the FGT materials, teachers engage with eleven different geometry problems.  Nine of these problems are each used as the medium for working through these five stages (the other two problems will only be used to engage with Stages 1 and 2). By the completion of the FGT experience, teachers will have engaged with problems representing a spectrum of geometric content, and will have reflected on their own thinking as well as the thinking of their students in relation to this content.

*Kelemanik, G., Janssen, S., Miller, B., and Ransick, K. (1997). Structured Exploration: New Perspectives on Mathematics Professional Development. Newton, MA: Education Development Center.