1. 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

2. NCTM’s view of problem solving
Problem solving means engaging in a task for which the solution method is not known in advance.
Problem solving is an integral part of all mathematics learning, and so it should not be an isolated part of the mathematics program.
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

3. The Secret of The Crystal Ball
Chose any two digit number.
Add together both digits.
Subtract the total from your original number.
When you have the final number look it up on the chart and find the relevant symbol.
Concentrate on the symbol and when you have it clearly in your mind.
Click on the crystal ball to see the symbol.
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi

4. Designing a lesson for teaching through problem solving
Curriculum & Textbook
Teaching through problem solving
Students
Problem
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi

5. How would you use this mathematical situation for your students
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

6. Task for each table -Wednesday and Thursday-
Short sketch of teaching through problem solving
Purpose of the problem solving (goal of the lesson)
What mathematics, beside developing problem solving skills, you would teach by using this situation?
Questioning
How would you pose the problem
What question(s) would you ask to your students to learn mathematics?
Beyond show and tell
Anticipate students’ responses to your questions that including misunderstandings to facilitate discussion
Briefly describe how would you facilitate discussion
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007
by Akihiko Takahashi