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Promoting Mathematical Understanding through Problem-Solving Strategies

Explore problem-solving techniques in math with interactive activities and discussions. Develop critical thinking skills and deepen conceptual understanding. Enhance learning through engaging math challenges. Presentation by Akihiko Takahashi at Park City Mathematics Institute.

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Promoting Mathematical Understanding through Problem-Solving Strategies

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  1. Building Math in the classroom- Teaching Through Problem-Solving - Day 10 Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

  2. Paper Pool Table a problem Key question(s) Student’s response Student’s response 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

  3. Paper Pool Table • What is the relationship between the dimensions of the Paper Pool Table and the total number of hits? Be sure to count the starting and ending points as a “hit.” (Table 4) Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

  4. Visualizing the relationship between factors and multiples Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

  5. Number of hits = (length + width) ÷GCF(length, width) Finding a pattern from a table may not be sufficient….. An anticipated student’s response from Table 8 Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, July 9-July 20, 2007 by Akihiko Takahashi

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

  7. 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

  8. 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

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