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.

1. How Not to
Kill Thinking
Gerald Aungst
PCTM Conference
Seven Springs, PA
August 4, 2016
Principles of the
MODERN
Math Classroom
5|

2. #5cmath #pctm

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

5. 5 Principles
Conjecture
Communication
Collaboration
Chaos
Celebration

6. Conjecture
Communication
Collaboration
Chaos
Celebration

7. Communication Chaos

8. Principle 1:
Conjecture

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?

13. Principle 2:
Communication

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

17. Principle 3:
Collaboration

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

23. Problem-Finding Box

24. Principle 4:
Chaos

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!

28. Principle 5:
Celebration

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

36. 5of the
MODERN
Mathematics
Classroom
Gerald Aungst
www.geraldaungst.com/5cmath
@geraldaungst
geraldaungst@gmail.com
Principles

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.