In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development of teachers' pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4-14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study provides a new research instrument for measuring teachers' growth in pedagogical content knowledge.
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