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An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday, March 31, 2016 1:21 PM NCTM 2016 San Fransisco Page 1

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Page 1: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

An exciting, effective, enjoyable, efficient and

engaging way to educate.John Benson

Evanston High, Retired (2010)

Thursday, March 31, 20161:21 PM

NCTM 2016 San Fransisco Page 1

Page 2: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pass through truthThursday, December 10, 201511:29 AM

NCTM 2016 San Fransisco Page 2

Page 3: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

What is the smallest positive integer that uses all of the vowels in the English Alphabet?

Friday, January 10, 20147:47 PM

NCTM 2016 San Fransisco Page 3

Page 4: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Enabling Students to LearnNCTM

San FranciscoFriday April 15, 2016

John BensonEvanston High Retired

1 TitleMonday, December 30, 20139:28 AM

NCTM 2016 San Fransisco Page 4

Page 5: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

6X6 Triangular gridSunday, January 05, 201410:44 AM

NCTM 2016 San Fransisco Page 5

Page 6: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

In mathematics the art of proposing a question must be held of higher value than solving it.Georg Cantor

Monday, January 06, 20143:19 PM

NCTM 2016 San Fransisco Page 6

Page 7: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

What just happened?

Sunday, January 05, 201411:37 AM

NCTM 2016 San Fransisco Page 7

Page 8: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I presented you with a situation.

I asked you for an appropriate question.

Friday, January 10, 20146:18 PM

NCTM 2016 San Fransisco Page 8

Page 9: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I asked you to think about that question.

I did NOT explain how I thought you should do it. We did NOT do an example first. NOT even a hint

NCTM 2016 San Fransisco Page 9

Page 10: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I walked around and observed what you were doing and listened to what you were saying

Occasionally I reported someone's answer

NCTM 2016 San Fransisco Page 10

Page 11: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I walked around, looked and listened until I it was time for us to talk. "The Teachable Moment"

Why did I do this?

I wanted to share an example of what I think a math class should be like.

NCTM 2016 San Fransisco Page 11

Page 12: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

NCTM 2016 San Fransisco Page 12

Page 13: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I believe learning happens while a person is working on a good problem

Sunday, January 05, 20145:43 PM

NCTM 2016 San Fransisco Page 13

Page 14: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Why did I pick THIS problem?

Friday, January 10, 20147:51 PM

NCTM 2016 San Fransisco Page 14

Page 15: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Given trapezoid TRAP, with

Tuesday, December 01, 20155:16 PM

NCTM 2016 San Fransisco Page 15

Page 16: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I taught it. They just didn't learn it

Sunday, January 05, 201410:47 AM

NCTM 2016 San Fransisco Page 16

Page 17: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

How did I come to these conclusions?

Friday, January 17, 201412:37 AM

NCTM 2016 San Fransisco Page 17

Page 18: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

David R Johnson

Every Minute Counts Saturday, April 09, 201612:18 PM

NCTM 2016 San Fransisco Page 18

Page 19: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

David RThursday, June 07, 201211:35 AM

NCTM 2016 San Fransisco Page 19

Page 20: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

5 3 4

OO1Friday, January 10, 201410:21 PM

NCTM 2016 San Fransisco Page 20

Page 21: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

5 3 4

002Friday, January 10, 201410:24 PM

NCTM 2016 San Fransisco Page 21

Page 22: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

5 3 4 2

003Friday, January 10, 201410:26 PM

NCTM 2016 San Fransisco Page 22

Page 23: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

6 0 5 1 4 2 3 3

004Friday, January 10, 201410:28 PM

NCTM 2016 San Fransisco Page 23

Page 24: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

AlgSunday, January 05, 20145:30 PM

NCTM 2016 San Fransisco Page 24

Page 25: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

NCTM 2016 San Fransisco Page 25

Page 26: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

WorksheetSunday, January 05, 20142:51 PM

NCTM 2016 San Fransisco Page 26

Page 27: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

NCTM 2016 San Fransisco Page 27

Page 28: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 7Thursday, June 07, 201211:39 AM

NCTM 2016 San Fransisco Page 28

Page 29: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

One Good Problem

They work on it

Sunday, January 05, 20145:25 PM

NCTM 2016 San Fransisco Page 29

Page 30: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I walk around

NCTM 2016 San Fransisco Page 30

Page 31: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Everyone discusses it

Repeat

NCTM 2016 San Fransisco Page 31

Page 32: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 3Thursday, June 07, 201211:38 AM

NCTM 2016 San Fransisco Page 32

Page 33: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 4Thursday, June 07, 201211:39 AM

NCTM 2016 San Fransisco Page 33

Page 34: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 5Thursday, June 07, 201211:39 AM

NCTM 2016 San Fransisco Page 34

Page 35: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 6 BACKWARDSThursday, June 07, 201211:39 AM

NCTM 2016 San Fransisco Page 35

Page 36: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Teaching this way creates anactive mind set in the mind and habits of students, even without mentioning it.

The assumption is that you will figure it out

Mind SetWednesday, December 02, 201511:13 PM

NCTM 2016 San Fransisco Page 36

Page 37: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 8Thursday, June 07, 201211:39 AM

NCTM 2016 San Fransisco Page 37

Page 38: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pythagorean mugSaturday, April 09, 20169:39 PM

NCTM 2016 San Fransisco Page 38

Page 39: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Good Mathematicians should not have good teachers as they prevent you from learning by yourself. I had noneEdward Kasner

Friday, January 17, 201412:44 PM

NCTM 2016 San Fransisco Page 39

Page 40: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

The person may not even realize what they just learned.

Sunday, January 05, 20145:45 PM

NCTM 2016 San Fransisco Page 40

Page 41: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

It might have been content.It might have been a problem solving strategy.It might have been some relationship that is hard to put into words.

Sunday, January 05, 20145:46 PM

NCTM 2016 San Fransisco Page 41

Page 42: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 9Thursday, June 07, 201211:40 AM

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Page 43: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 10Thursday, June 07, 201211:40 AM

NCTM 2016 San Fransisco Page 43

Page 44: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

"People will forget what you said, people will forget what you did, but people will never forget how you made them feel."

(Maya Angelou, American writer)

Monday, January 06, 20148:46 AM

NCTM 2016 San Fransisco Page 44

Page 45: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I enjoy working with youFriday, January 10, 201410:18 PM

NCTM 2016 San Fransisco Page 45

Page 46: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pro 11Thursday, June 07, 201211:41 AM

NCTM 2016 San Fransisco Page 46

Page 47: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

One does not come to know something unless one loves it. Goethe

Saturday, January 04, 201411:47 AM

NCTM 2016 San Fransisco Page 47

Page 48: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Here are a few specific things I did that made every minute count.

Friday, January 10, 20149:42 PM

NCTM 2016 San Fransisco Page 48

Page 49: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I met students at the door and gave them a good problem to work on.

Friday, January 10, 20149:43 PM

NCTM 2016 San Fransisco Page 49

Page 50: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

MailboxesThursday, June 07, 201211:35 AM

NCTM 2016 San Fransisco Page 50

Page 51: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Assignment sheetsThursday, June 07, 201211:36 AM

NCTM 2016 San Fransisco Page 51

Page 52: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

CalThursday, June 07, 201211:36 AM

NCTM 2016 San Fransisco Page 52

Page 53: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

ansThursday, June 07, 201211:36 AM

NCTM 2016 San Fransisco Page 53

Page 54: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

quizThursday, June 07, 201211:36 AM

NCTM 2016 San Fransisco Page 54

Page 55: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Where in the world  can you find a hexagon?

Monday, May 23, 20111:39 PM

NCTM 2016 San Fransisco Page 55

Page 56: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

stSunday, April 18, 20104:39 PM

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Page 57: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

honeycombSunday, April 18, 20108:34 AM

NCTM 2016 San Fransisco Page 57

Page 58: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Hex tilesSunday, April 18, 20108:33 AM

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Page 59: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Pasted from <http://static.promopeddler.com/prodpics/bigprodimgs/4800000/4801717.jpg>

pencilSunday, April 18, 20108:35 AM

NCTM 2016 San Fransisco Page 59

Page 60: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Hex nutFriday, January 29, 201011:18 PM

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Page 62: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Square nutSunday, April 18, 20108:45 AM

NCTM 2016 San Fransisco Page 62

Page 63: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

p1Monday, October 12, 200910:33 PM

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Page 64: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

p2Saturday, October 17, 20099:56 AM

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Page 65: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Nut Close upSaturday, April 09, 201612:19 PM

NCTM 2016 San Fransisco Page 65

Page 66: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

WrenchSaturday, April 09, 201612:21 PM

NCTM 2016 San Fransisco Page 66

Page 67: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Wrench Close upSaturday, April 09, 201612:19 PM

NCTM 2016 San Fransisco Page 67

Page 68: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Success consists of going from failure to failure without loss of enthusiasm.Winston Churchill

Sunday, January 05, 201410:56 AM

NCTM 2016 San Fransisco Page 68

Page 69: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

I will not let anything get in the way of me and my competitive enthusiasm to win.

Michael Jordan

Sunday, January 05, 201410:58 AM

NCTM 2016 San Fransisco Page 69

Page 70: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Fires can't be made with dead embers, nor can enthusiasm be stirred by spiritless men. Enthusiasm in our daily work lightens effort and turns even labor into pleasant tasks.James A. Baldwin

Sunday, January 05, 201411:08 AM

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SamFriday, January 10, 201410:12 PM

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Saturday, April 09, 201612:19 PM

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systemThursday, January 16, 20149:14 PM

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geometryThursday, January 16, 20149:13 PM

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Puzzles

Friday, January 17, 201412:39 AM

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Page 83: Thursday, March 31, 2016 1:21 An exciting, effective ......An exciting, effective, enjoyable, efficient and engaging way to educate. John Benson Evanston High, Retired (2010) Thursday,

Stories

Friday, January 17, 201412:39 AM

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OPUSFriday, January 17, 201412:04 AM

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Sunday, April 10, 20168:30 PM

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