How Not to Kill Thinking (PCTM)
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This document outlines five principles of modern math classrooms: conjecture, communication, collaboration, chaos, and celebration. For each principle, the document provides examples and explanations. It encourages students to generate their own questions and ideas, communicate their mathematical thinking to others, work together to solve problems, engage with open-ended and unsolved problems, and celebrate mistakes and learning. The document aims to move math instruction away from rote memorization and toward deeper understanding through exploration and problem-solving.
![Photo Credits
• 5 Principles icons designed by Jerry Gottesman, http://jginkcreative.com/
• Some images licensed from iStock by Getty Images
• “#hashtagyourlife” by Bark. https://www.flickr.com/photos/barkbud/6350091667/
• “Skagen Traffic Signal” by Erik Ogan. https://www.flickr.com/photos/erikogan/2941019357/
• “Eccentric” by Domiriel. https://www.flickr.com/photos/domiriel/8057852296/
• Bacon, by Toyulaewww44 (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via https://commons.wikimedia.org/wiki/File
%3A500gfpx-Bacon.png
• Untitled photo by NCSSM. https://www.flickr.com/photos/ncssm/8609916515/
• “Waiting for Time to Pass” by Richard Phillip Rücker. https://www.flickr.com/photos/70243696@N00/342753239
• “Question mark made of puzzle pieces” by Horia Varlan. https://www.flickr.com/photos/horiavarlan/4273168957/
• “Computing Sciences outreach program for high school students” by Berkeley Lab. https://www.flickr.com/photos/berkeleylab/4863700123/
• “Popcorn” by Micky Zlimen. https://www.flickr.com/photos/emzee/140977871
• “Question mark” by Jean-Marc Valladier. https://www.flickr.com/photos/segozyme/3105128025/
• “suessian megaphone” by Michael. https://www.flickr.com/photos/theparadigmshifter/470341923/
• McKayla Maroney and Barack Obama, “P111512PS-0111” by The White House. https://www.flickr.com/photos/whitehouse/8191317327/
• “Solitaire” by Roger H. Goun. https://www.flickr.com/photos/sskennel/4669788084/
• “Olivia Birds Drawing Ornaments Kids Can Make a Difference” by Laurie Sullivan. http://www.flickr.com/photos/32561453@N05/15805499565
• “Never a Dull Moment!” by Lyle. https://www.flickr.com/photos/lyle58/2085980030/
• "Cheeseburger" by Renee Comet (photographer) This image was released by the National Cancer Institute, an agency part of the National Institutes
of Health, with the ID 2652
• All other images are original photographs by Gerald Aungst.](https://image.slidesharecdn.com/5principlespctm-160804115718/85/How-Not-to-Kill-Thinking-PCTM-37-320.jpg)
How Not to Kill Thinking (PCTM)
- 1. How Not to Kill Thinking Gerald Aungst PCTM Conference Seven Springs, PA August 4, 2016 Principles of the MODERN Math Classroom 5|
- 3. Help me! • Shorter route with more lights? • Longer route with fewer lights? • When does it make sense to go out of your way to avoid an intersection with a traffic signal?
- 4. 4 Myths About Math
- 9. You Won’t Believe What This Guy Thinks About Math… #2 Will Absolutely DROP YOUR JAW!!!
- 10. We are wired to wonder
- 11. Things Humans Still Do Better Than Computers
- 12. Never End With the Answer • Why do you think so? • How do you know? • Are there any other ways to answer it? • What was hard about solving that problem? • What did you use to help you solve this? How did it help?
- 14. —Albert Einstein Theoretical Physicist, Authority on Philosophy of Science If you can’t explain it simply, you don’t understand it well enough.
- 16. Convince Me • Stage 1: Convince Yourself • Stage 2: Convince a Friend • Stage 2.5: Convince a Mathematical Friend • Stage 3: Convince an Enemy
- 18. Think about the last problem you solved Share at your table Discuss the process you used to solve it
- 19. Traditional Math Instruction 1. Teacher models an algorithm 2. Practice it as a group 3. Practice it alone Repeat until perfect
- 20. 5 Principles Math Instruction 3. Teacher models an algorithm 2. Practice it together 1. Practice it alone (if necessary…)
- 21. Help me! • Shorter route with more lights? • Longer route with fewer lights? • When does it make sense to go out of your way to avoid an intersection with a traffic signal?
- 22. Where Good Ideas Come From • The Adjacent Possible • Liquid Networks • The Slow Hunch • Serendipity • Error • Exaptation • Platforms
- 25. iWonder… if Citizen’s Bank Park were completely filled with popped popcorn, how long would it take the Phillies to eat it all?
- 26. —David Perkins Founding Member of Project Zero, Harvard Graduate School of Education Much of formal education . . . feels like learning the pieces of a picture puzzle that never gets put together, or learning about the puzzle without being able to touch the pieces.
- 27. Non-Routine and Unsolved Problems • Bedtime Math: http://bedtimemath.org • Math Pickle: http://www.mathpickle.com • Three-Act Problems: http://threeacts.mrmeyer.com • Stella’s Stunners: Temporarily gone!
- 29. —Jessica, Age 9 A Very Wise Student Mistakes lead to good places so if you make a mistake take it as a step up the learning ladder.
- 30. Catch Me If You Can
- 31. I Guarantee It! Certainty Rating Name 1 I have a good start 2 I’m confident 3 I guarantee it! ? I’m not ready yet
- 32. The Truth About Math
- 33. Action Planning
- 34. • Focus on just one • Choose your most or least comfortable/confident • Write down 3 things you already do Choose a Principle
- 35. 6 Facets of Classroom Culture Facet Action Time Resources Physical Space Curriculum materials Instructional practices Assessment practices Daily routines and procedures Social/emotional environment
- 37. Photo Credits • 5 Principles icons designed by Jerry Gottesman, http://jginkcreative.com/ • Some images licensed from iStock by Getty Images • “#hashtagyourlife” by Bark. https://www.flickr.com/photos/barkbud/6350091667/ • “Skagen Traffic Signal” by Erik Ogan. https://www.flickr.com/photos/erikogan/2941019357/ • “Eccentric” by Domiriel. https://www.flickr.com/photos/domiriel/8057852296/ • Bacon, by Toyulaewww44 (Own work) [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0)], via https://commons.wikimedia.org/wiki/File %3A500gfpx-Bacon.png • Untitled photo by NCSSM. https://www.flickr.com/photos/ncssm/8609916515/ • “Waiting for Time to Pass” by Richard Phillip Rücker. https://www.flickr.com/photos/70243696@N00/342753239 • “Question mark made of puzzle pieces” by Horia Varlan. https://www.flickr.com/photos/horiavarlan/4273168957/ • “Computing Sciences outreach program for high school students” by Berkeley Lab. https://www.flickr.com/photos/berkeleylab/4863700123/ • “Popcorn” by Micky Zlimen. https://www.flickr.com/photos/emzee/140977871 • “Question mark” by Jean-Marc Valladier. https://www.flickr.com/photos/segozyme/3105128025/ • “suessian megaphone” by Michael. https://www.flickr.com/photos/theparadigmshifter/470341923/ • McKayla Maroney and Barack Obama, “P111512PS-0111” by The White House. https://www.flickr.com/photos/whitehouse/8191317327/ • “Solitaire” by Roger H. Goun. https://www.flickr.com/photos/sskennel/4669788084/ • “Olivia Birds Drawing Ornaments Kids Can Make a Difference” by Laurie Sullivan. http://www.flickr.com/photos/32561453@N05/15805499565 • “Never a Dull Moment!” by Lyle. https://www.flickr.com/photos/lyle58/2085980030/ • "Cheeseburger" by Renee Comet (photographer) This image was released by the National Cancer Institute, an agency part of the National Institutes of Health, with the ID 2652 • All other images are original photographs by Gerald Aungst.