Transcript

How Not to

Kill Thinking

Gerald Aungst

AMLE Conference

Austin, TX

October 12, 2016

Principles of the

MODERN

Math Classroom5|

#5cmath #AMLE2016

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 Myths About Math

5 PrinciplesConjecture

Communication

Collaboration

Chaos

Celebration

Conjecture

Communication

Collaboration

Chaos

Celebration

Communication Chaos

socrative.com

Room code GAUNGST

Principle 1: Conjecture

You Won’t Believe

What This Guy Thinks

About Math…

#2 Will

Absolutely

DROP YOUR

JAW!!!

We are wired to wonder

Things Humans

Still Do Better

Than Computers

Things Humans

Still Do Better

Than Computers

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?

Principle 2: Communication

—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

Principle 3: Collaboration

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

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

Problem-Finding Box

Principle 4: Chaos

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:http://volta.ohiorc.org/for/math/stella/

Principle 5: Celebration

—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.

Catch Me If You Can

I Guarantee It!Certainty

RatingName

1 I have a good start

2 I’m confident

3 I guarantee it!

? I’m not ready yet

The Truth About Math

Action Planning

• 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

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.


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