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My Top Eight Teachable Moments. Dan Kennedy Baylor School. “A teachable moment , in education, is the time at which learning a particular topic or idea becomes possible or easiest.”. Moment #1: The Magic Numbers for Retail Wine Pricing. Take the wholesale cost of a case of wine.

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slide1

My Top Eight Teachable Moments

Dan Kennedy Baylor School

slide2

“Ateachable moment, in education, is the time at which learning a particular topic or idea becomes possible or easiest.”

slide3

Moment #1:

The Magic Numbers for Retail Wine Pricing

slide4

Take the wholesale cost of a case of wine.

Add the excise tax ($1.21/gallon today).

Divide by 12 to get the bottle cost.

Add 30% retail markup.

Discount the price 10% (a store policy).

Oh, how he yearned for the ability to accomplish all this bothersome math in a single step!

slide5

Praying I would not make this look too simple, I did a little Algebra I on the back of a paper bag…

(x + 1.21 *2.37755)

÷ 12

* (1 + .30)

* (1 - .10)

= 0.0975 x + 0.28049

So, I told him sagely, all you need to do is multiply your wholesale case cost by 0.0975 and add 0.28049.

I thought the man was going to cry.

slide6

He later mounted the paper bag on the wall of his office:

Price * 0.0975 + 0.28049

I also walked away with a free bottle of champagne…and a new respect for Algebra I!

slide7

Moment #2:

“Magic” Math E-mails from the Clueless

slide8

How many of us have received this e-mail from friends wondering what sorcery is behind this trick?

slide10

Moment #3:

My college French grade from Boom Boom Fortier*

(*Not his real name)

slide11

Grade on first test: 72

Grade on second test: 80

College policy: Exam grade counts 1/3 of semester grade

I figured that I could make a B with an 88 on the exam.

I studied hard and nailed the exam.

I got a C for the semester.

slide12

I went to see Mr. Fortier in his office.

He congratulated me on my many trips to the language lab. “I decided not to count those, though. Not enough people went to the lab.”

slide13

“What about the exam?” I asked.

He looked in his grade book.

“Let’s just say you got a 92 on the final exam.

That still doesn’t get you a B, because the final only counts 1/3 of your grade.”

slide14

Mr. Fortier showed me the math.

There were two tests in the semester, each of which he counted 2/3.

The final counted 1/3.

slide15

Convinced it would make no difference, he grumbled and agreed to try it my way.

Semester test average:

= B

He stared at the numbers for a few moments of apparent confusion before opening his grade book again.

slide16

“Of course, there’s no way of saying for sure that you got a 92 on the exam. Maybe you got an 82.”

I assured him that there was no need to crunch the numbers again. I thanked him for his time and left.

slide17

Moment #4:

Scaling Grades on the TI Calculators

slide18

Something I learned about assessment from the AP program:

It is perfectly OK, perhaps even necessary, to scale grades!

75%

= 5

slide19

At our school, 75% is not a good grade. In fact, 65% is a minimal pass.

  • Is this reasonable? Think about it.
  • The all-time NBA record for field goal percentage in a season is 72.7%.
  • The all-time record batting average for major league baseball is .440 (44%).
  • A salesperson who makes a sale on 75% of first contacts is a genius.
  • So how can we expect 75% success from someone who is just learning?
slide20

99

92

82

71

30

20

75

93

slide21

An Important Disclaimer:

Scaling grades is not about building self-esteem.

Scaling grades is about teaching mathematics.

Assessment should support your efforts to teach your students mathematics.

It should not get in the way.

slide26

I showed this calculator program to my Baylor colleagues during an in-service training on assessment.

The English teachers were excited about its potential for grading papers.

Suddenly our students had a ready market for their old TI-82 calculators!

slide27

Moment #5:

Baylor School’s Graduated GPA

slide28

The Challenge:

Design a sliding scale that our school could use to convert our numerical (percentage) grades to grade-point averages on a 4-point scale.

slide29

The assumptions I made:

  • Our lowest D (65) should get 1.0.
  • An average A (95) should get 4.0.
  • The GPA curve should be steeper at the low end than at the high end

I decided to use a power function of the form

slide31

Baylor continues to use this sliding conversion today, over 25 years later. It continues to provide teachable moments for educating students, faculty, administrators, and, of course, parents!

slide32

Moment #6:

My Year with NUMB3RS

slide33

January 2005: CBS premiered a new show in which an FBI agent and his mathematician brother solved crimes using mathematics.

It was calledNUMB3RS.

slide35

Chuck Biehl (Charter School of Wilmington, DE)

Br. Patrick Carney (Depaul Catholic HS, Wayne, NJ)

Pat Flynn (Turner HS, Kansas City, KS)

David Bressoud (Macalester College, MN)

Ron Lancaster (University of Toronto, ONT)

Dan Kennedy (Baylor School, Chattanooga, TN)

Tom Butts (University of Texas at Dallas, TX)

Jonathan Farley (Stanford University, CA)

Terry Wyberg (University of Minnesota)

Johnny Lott (University of Montana)

Terry Souhrada (University of Montana)

Kathy Erickson (Monument Mountain Regional HS, MA)

Ed Burger (Williams College, MA)

Sue Eddins (Illinois Mathematics & Science Academy)

slide36

Karen Longhart

Lenda Hill

Brett Morrow

Heather Gunsallus

slide39

In the episode “Double Down,” some college students beat a casino at Blackjack by cracking the algorithm used by the automatic shuffler to randomize the cards.

Eventually, of course, there was also a murder.

slide40

Which of the following sequences of black and red cards is most likely to result from a random shuffle?

BRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBRBR

RRRRRRRRRRRRRRRRRRRRRRRRRRBBBBBBBBBBBBBBBBBBBBBBBBBB

BBBRRRBRRRRRRRRRBBBBRRRRRBRBBBBBRRRRBBBBBBBBBRBBBRRR

Answer: All three are equally unlikely! Each has about one chance in 496 trillion of occurring.

slide41

Which of the following lottery tickets is least likely to be a winner?

11 12 13 14 15 16

09 13 22 25 31 43

17 21 33 34 38 41

The odds against each: 7,059,051 to 1.

slide42

The activity Now You See It, Now You Don’t introduced students to a method of randomly coding pictures, called steganography.

slide44

Moment #7:

Twinkle, Twinkle, Little Star

slide45

One of the neatest math articles I ever read was a piece by Martin Gardner in the September 1998 issue of Math Horizons.

He called it “Ten Amazing Mathematical Tricks.”

slide46

Twinkle, Twinkle, little star;

How I wonder what you are,

Up above the world so high,

Like a diamond in the sky;

Twinkle, twinkle, little star;

How I wonder what you are.

slide47

7 7 6 4

3 1 6 4 3 4

2 5 3 5 2 4

4 1 7 2 3 3

7 7 6 4

3 1 6 4 3 4

3

slide48

A few months later I attended an entertaining NCTM session on “Mathematical Magic” at which the speaker showed this trick.

He admitted that he had no idea why it worked but that he would love to know the secret.

After the talk, I shared my discovery. It was another Teachable Moment!

slide49

Moment #8:

Rebecca Flake’s Portfolio Entry

Rebecca Flake

slide50

In my classes, each student hands in a portfolio of items. The students choose the items they want me to see and grade.

The main point of this assessment is that they are not responding to a stimulus from me (as in a test or a quiz).

My primary directive for student portfolio entries is this:

Give me evidence of your learning that I otherwise would not have!

slide51

This was my first year to be a peer tutor, and I enjoyed helping the girls in the dorm a lot. Last night, though, I finally saw the importance of my peer tutoring. My roommate came in at 10:00 extremely upset over her Precalculus test that was the next day. I calmed her down and told her that I would help her if I could. Carrie, who had been in the play, had gotten behind in her work, so she didn’t understand what they were doing. She showed me the problem. I knew the answer, but I wasn’t sure how to explain it to her in a way that was not confusing. I thought about it for a while, and I ended up trying several approaches (with Clara’s help) that I had learned in Calculus, until I finally got through to her. Then I made her work a few problems for me, and she did them perfectly. She understood! I was so happy to be able to help her that I had forgotten I was supposed to be studying for my own Calculus test. She was so happy she understood that she began to cry. She really began to cry. It’s great to be able to use the things you have learned to help other people learn too.

slide52

A happy footnote:

Carrie really did understand.

She scored 93 on the Precalculus test the following day – a personal best for her, and a full 9 points above the class average.

Actress Carrie

slide53

Rebecca had obviously had a wonderful Teachable Moment with Carrie.

Thanks to her portfolio entry, she also had a wonderful Teachable Moment with me!