Park City Mathematics Institute
Secondary School Teacher Program

Reflection on Practice Class: Day 7
Akihiko Takahashi

The group leaders reviewed the discussions from the day before with everyone.

Aki showed us a flow chart of problems with multiple solutions which emphasized the need for comparing and discussing the results. This discussion will lead to further ideas, questions, and possible other problems. The role of the teacher is to first pick an appropriate problem and then to facilitate the discussions. If you push students a little farther, you can have more general solutions. We need to provide all the students something new.

The challenging part with the Crooked Transversal problem is for the student to determine which line to draw. Some draw the line between points A and B and use the angle sum property of triangles. Others draw the line parallel through P and use transversal properties.

Aki then introduced us to our goal for the rest of the week: Change a typical textbook problem into an interesting problem with multiple solution methods. He asked us to focus on two things: "anticipating student's responses to design a lesson" and "making the purpose of the using the problem clear."

In our poster we were asked to include four specific items:

  1. typical textbook problem
  2. How do you change it
  3. anticipating students responses
  4. making the purpose of using the problem clear

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.