Park City Mathematics Institute
Secondary School Teacher Program

Reflection on Practice Class: Teaching Through Problem Solving
Akihiko Takahashi

Day Two, Week Two - Tuesday, July 10 2007

Aki reviewed what he presented yesterday.

"We need to know what to expect from students."

Aki handed out an 8th grade math lesson plan on "The Secret of the Crystal Ball" which he presented in Las Cruces, NM this spring. He asked us to look at it and to predict what type of math we might expect from students. "If you want your students to discuss mathematics, you need to stop talking. You don't want to control student's thinking. How can we guide students? When I observe beginning teachers teaching and keep track of who says what it is : TTTTSTTTSTTTTTS. Teachers keep saying same thing - slightly different. With experienced teacher it is: TSSSTSSTSSSST. It is not a dialog just between Teacher and student.h Note: "T" stands for the teacher talking, "S" stands for a student talking.

There are lots of different ways to design a lesson for teaching through problem solving.

  1. Curriculum & Textbook --> teaching through problem solving.

  2. Students --> teaching through problem solving.

  3. Problem solving --> teaching through problem solving.

The situation we are going to use is based on folded origami paper. Your task is to explore what type of mathematics you can get from this situation.

The groups worked on this for about 15 minutes. Then Aki brought the class together and gave the participants instructions for Wednesday and Thursday - including instructions for their poster.

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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.