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Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning

Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning. Breedeen Pickford-Murray The Bay School of San Francisco.

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Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning

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  1. Further Beyond Sudoku:Using Logic Puzzles to Develop Mathematical Reasoning Breedeen Pickford-Murray The Bay School of San Francisco

  2. A proof, that is, a mathematical argument, is [like] a work of fiction, a poem. Its goal is to satisfy. A beautiful proof should explain, and it should explain clearly, deeply, and elegantly… -Paul Lockhart

  3. Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning. CCSS Mathematical Practices

  4. How Do You Know What to Do? How Do You Record Your Thinking? How Do You Convince Your Peers?

  5. New Ideas • Engaging Format • Intuitive Yet Not Obvious Puzzles

  6. Unsolved Solved Yajilin What is the goal of this puzzle? What are the rules? http://www.nikoli.com/en/puzzles/yajilin/

  7. How Do You Know What to Do? Make sense of problems and persevere in solving them. Look for and make use of structure.

  8. Unsolved Solved Yajilin http://www.nikoli.com/en/puzzles/yajilin/

  9. Unsolved Solved Slitherlink What is the goal of this puzzle? What are the rules? http://www.nikoli.com/en/puzzles/slitherlink/

  10. How Do You Record Your Thinking? Reason abstractly and quantitatively. Look for and express regularity in repeated reasoning.

  11. Unsolved Solved Slitherlink http://www.nikoli.com/en/puzzles/slitherlink/

  12. Five NCTM participants ran a race. • Sadie came two places behind Christopher, but did not come in last. • Justin lost to Ashli, but beat Shauna. • Christopher did not come in first, Sadie did not come in last. • What place did each person come in? • Explain how you solved this puzzle, and prove that your answer is the only one that will work, using the statements above to support your argument. Classic Logic Puzzle

  13. How Do You Convince Your Peers? Construct viable arguments and critique the reasoning of others.

  14. Five NCTM participants ran a race. • Sadie came two places behind Christopher, but did not come in last. • Justin lost to Ashli, but beat Shauna. • Christopher did not come in first, Sadie did not come in last. • What place did each person come in? • Explain how you solved this puzzle, and prove that your answer is the only one that will work, using the statements above to support your argument. Classic Logic Puzzle

  15. How Do You Know What to Do? How Do You Record Your Thinking? How Do You Convince Your Peers?

  16. The Life-Cycle of Mathematics—Avery Pickford Indirect reasoning Induction Two-column Parity Visual Axiomatic Be skeptical Respectfully challenge Reflect Hunt for counter-examples Estimate Bound Contextualize Collect data Pattern-sniff Record results How Do You Convince Your Peers? How Do You Record Your Thinking? How Do You Know What to Do? Wild Guess Educated Guess Conjecture Proof Theorem

  17. Mathematical reasoning isn’t simple. • Start with something intuitive and engaging—but not obvious! • Push students to explain their thinking—at all levels. • Help students develop ways to record and organize their thinking. • Build formal written structures separately from introducing new mathematical content. Q.E.D.

  18. Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth. -Benjamin Peirce

  19. BreedeenPickford-Murray The Bay School of San Francisco breedeen.murray@gmail.com @btwnthenumbers The Space Between The Numbers betweenthenumbers.wordpress.com

  20. Rate this presentation on the conference app! www.nctm.org/confapp Download available presentation handouts from the Online Planner! www.nctm.org/planner Join the conversation! Tweet us using the hashtag #NCTMNOLA

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