To create confident problem solvers, we must not kill student thinking. Learn to use the 5 Principles of Conjecture, Communication, Collaboration, Chaos, and Celebration to design a classroom environment that promotes innovation, and allows students to communicate thinking clearly. Small groups will reflect on how this translates into classroom practice. They will also experience specific strategies associated with the 5 Principles and create a plan for redesigning their own school cultures.
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?
14. 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?
20. Think about the
last problem
you solved
Share at your table
Discuss the process you
used to solve it
21. Traditional Math Instruction
1. Teacher models an algorithm
2. Practice it as a group
3. Practice it alone
Repeat until perfect
22. Traditional Math Instruction
1. Teacher models an algorithm
2. Practice it as a group
3. Practice it alone
Repeat until perfect
23. 5 Principles Math Instruction
3. Teacher models an algorithm
2. Practice it together
1. Practice it alone
(if necessary…)
24. 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?
25. Where Good Ideas Come From
• The Adjacent Possible
• Liquid Networks
• The Slow Hunch
• Serendipity
• Error
• Exaptation
• Platforms
28. iWonder…
if Citizen’s Bank Park
were completely filled
with popped popcorn,
how long would it take
the Phillies to eat it all?
29. —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.
40. 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.