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How Not to
Kill Thinking
Gerald Aungst
PCTM Conference
Seven Springs, PA
August 4, 2016
Principles of the
MODERN
Math Classroom5|
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?
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?
—Albert Einstein
Theoretical Physicist, Authority on Philosophy of Science
If you can’t explain it simply, you don’t
understand it well enough.
Convince Me
• Stage 1: Convince Yourself
• Stage 2: Convince a Friend
• Stage 2.5: Convince a Mathematical Friend
• Stage 3: Convince an Enemy
Think about the last problem you solved
Share at your table
Discuss the process you used to solve it
Traditional Math Instruction
1. Teacher models an algorithm
2. Practice it as a group
3. Practice it alone
Repeat until perfect
5 Principles Math Instruction
3. Teacher models an algorithm
2. Practice it together
1. Practice it alone
(if necessary…)
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?
Where Good Ideas Come From• The Adjacent Possible
• Liquid Networks
• The Slow Hunch
• Serendipity
• Error
• Exaptation
• Platforms
iWonder…if Citizen’s Bank Park were completely filled with popped popcorn, how long would it take the Phillies to eat it all?
—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.
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!
—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.
I Guarantee It!Certainty
RatingName
1 I have a good start
2 I’m confident
3 I guarantee it!
? I’m not ready yet
• Focus on just one
• Choose your most or least comfortable/confident
• Write down 3 things you already do
Choose a Principle
6 Facets of Classroom CultureFacet Action Time Resources
Physical Space
Curriculum materials
Instructional practices
Assessment practices
Daily routines and procedures
Social/emotional environment
5of the
MODERN
Mathematics
Classroom
Gerald Aungst
www.geraldaungst.com/5cmath
@geraldaungst
Principles
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.