Building Math in the classroom - Teaching Through Problem-Solving - Day 9 Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

Japanese technical terms in teaching Neriage: Using students’ variety of solution methods to Build Math in the classroom After An Agenda for Action Recommendations for School Mathematics for the 1980s (NCTM,1980) Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

a problem Key question(s) Student’s response Student’s response Students will learn something new from the process of problem solving and the whole class discussion Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

Short sketch of teaching through problem solving Purpose of the problem solving (goal of the lesson) what the students need to learn in the lesson [according to the standards and/or curriculum]; what the students have learned previously; what is the major focus of this lesson [by comparing (a) and (b), the objective/goal of this lesson should be clearly stated] 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 you would facilitate discussion. Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi