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 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

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. 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 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

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

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