Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007

by Akihiko Takahashi

Building Math in the classroom

- Teaching Through Problem-Solving -

Day 2

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007

by Akihiko Takahashi

NCTM’s view of problem solving

1) Problem solving means engaging in a task for which the solution method is not known in advance.

2) Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program.

3) Choosing worthwhile problems and mathematical tasks

– There are many, many problems that are interesting and fun but that may not lead to the development of the mathematical ideas that are important for a class at a particular time.

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007

by Akihiko Takahashi

The Secret of The Crystal Ball

1. Chose any two digit number.

2. Add together both digits.

3. Subtract the total from your original number.

4. When you have the final number look it up on the chart and find the relevant symbol.

5. Concentrate on the symbol and when you have it clearly in your mind.

6. Click on the crystal ball to see the symbol.

http://www.cbs.com/primetime/ghost_whisperer/crystal_ball.shtml

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007

by Akihiko Takahashi

Designing a lesson for teaching through problem

solving

Teaching through problem

solving

Curriculum & Textbook

Students Problem

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007

by Akihiko Takahashi

How would you use this mathematical situation for your

students?- Explore mathematics in this

situation-

Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007

by Akihiko Takahashi

Task for each table-Wednesday and Thursday-• Short sketch of teaching through

problem solvinga) Purpose of the problem solving (goal of the

lesson)• What mathematics, beside developing problem

solving skills, you would teach by using this situation?

b) Questioning• How would you pose the problem• What question(s) would you ask to your

students to learn mathematics?c) Beyond show and tell

• Anticipate students’ responses to your questions that including misunderstandings to facilitate discussion

• Briefly describe how would you facilitate discussion