Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning Breedeen...
20
Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning Breedeen Pickford-Murray The Bay School of San Francisco
-
Upload
stella-rice -
Category
Documents
-
view
213 -
download
0
Transcript of Further Beyond Sudoku: Using Logic Puzzles to Develop Mathematical Reasoning Breedeen...
Further Beyond Sudoku:Using Logic Puzzles to Develop Mathematical Reasoning
Breedeen Pickford-Murray
The Bay School of San Francisco
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
CCSS Mathematical Practices
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.
How Do You Know What to Do?
How Do You Convince Your Peers?
How Do You Record Your Thinking?
PuzzlesNew IdeasEngaging Format Intuitive Yet Not Obvious
Yajilin
Unsolved Solved
What is the goal of this puzzle?What are the rules?
http://www.nikoli.com/en/puzzles/yajilin/
How Do You Know What to Do?
Make sense of problems and persevere in solving them.Look for and make use of structure.
Yajilin
Unsolved Solved
http://www.nikoli.com/en/puzzles/yajilin/
Slitherlink
Unsolved Solved
What is the goal of this puzzle?What are the rules?
http://www.nikoli.com/en/puzzles/slitherlink/
How Do You Record Your Thinking?
Reason abstractly and quantitatively.Look for and express regularity in repeated reasoning.
Slitherlink
Unsolved Solved
http://www.nikoli.com/en/puzzles/slitherlink/
Classic Logic Puzzle
Five NCTM participants ran a race.
1. Sadie came two places behind Christopher, but did not come in last.
2. Justin lost to Ashli, but beat Shauna.
3. 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.
How Do You Convince Your Peers?
Construct viable arguments and critique the reasoning of others.
Classic Logic Puzzle
Five NCTM participants ran a race.
1. Sadie came two places behind Christopher, but did not come in last.
2. Justin lost to Ashli, but beat Shauna.
3. 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.
How Do You Know What to Do?
How Do You Convince Your Peers?
How Do You Record Your Thinking?
The Life-Cycle of Mathematics—Avery Pickford
Wild Guess Educated Guess
Conjecture Proof Theorem
EstimateBoundContextualize
Collect dataPattern-sniffRecord results
Indirect reasoningInductionTwo-columnParityVisualAxiomatic
Be skepticalRespectfully challengeReflectHunt for counter-examples
How Do You Know What to
Do?
How Do You Record Your Thinking?
How Do You Convince Your
Peers?
Q.E.D.
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.
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
Breedeen Pickford-Murray
The Bay School of San Francisco
@btwnthenumbers
The Space Between The Numbers
betweenthenumbers.wordpress.com
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
