Lesson study is a framework for teachers to collaborate on a research lesson. Fortunately we were able to work with students in a geometry class at the Park City Learning Center. From their teacher we determined the topics they would be studying prior to our lesson. The group shared research on how students learn Geometry, and looked at important topics from high school geometry. We narrowed this list to topics which we thought students struggled with, and those we had difficulty teaching. From this list we chose our goal, "What is the connection between similar triangles and right triangle Trigonometry?"
Our morning course, Reflecting on Practice, influenced our choice of an open-ended problem. After exploring a variety of ideas, we selected one that focused on similarity and right triangle Trigonometry as parallel solution methods. Selecting a problem which connected similar triangles to right triangle trigonometry proved to be a challenge. The resulting struggle and animated conversations sometimes led to frustration and fear that we would not be successful in completing our lesson. But in the end, it led us to fully explore the topic and the intricacies of our goal.
Teaching the lesson twice gave us ample opportunity to revise our lesson and focus on the most effective questions to achieve our goal. After teaching the lesson to our colleagues, it became obvious that we needed to revisit how we posed our questions. Particularly important were both the initial prompt and the questions used to lead our class discussion. The changes we made led to dramatic improvement when the lesson was taught to the students.
Our debriefing was greatly enriched by the fresh insight and suggestions of two outside observers. Struggling through the lesson study process enabled us to put together a quality lesson. We plan to further test the lesson with our own students.
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With program support provided by Math for America
This material is based upon work supported by the National Science Foundation under Grant No. 0314808.