Mathematics in the Real World? What Are Our

Options?

Johnny W. Lott,

Past President, NCTM

Lots of Words

• Mathematics• Real World• Options

• What do they mean to us?

Mathematics

Problem solvingWhat do you want kids to be able to do?

What will they be expected to do when they leave us?

What Are the Complaints that Students Cannot Do?

• Make Change

• Balance Checkbooks

Let’s Make Change!

• My bill is $13.78.

• I give you $20.23.

• How do you give me change?

Think about what you might do.

• Give me Say– 2 pennies $13.80– 1 dime 13.90– 1 dime 14.00– $1 15.00– $5 20.00– 1 dime 20.10– 1 dime 20.20– 3 pennies 20.23– Would you be upset? Would you have correct change?

What did you want to have happen?

• $20.23

– 13.78

$ 6.45

Did you want $5, $1, 1 quarter, and two dimes?

Do you want me to teach real world math?

• Do you want me to teach making change?

• Do you want me to teach subtraction?

• Are they the same?

How about balancing a checkbook?

• Can I have a checkbook balance and still have errors?

• What if I mis-record a check for $10 less then I wrote it for AND mis-record a deposit for $10 more than I deposited?

Do I really want to talk about math in a contextual setting?

• For very early grades, most math is contextual.

• Counting is almost contextual.

• Children’s books help in this regard.

What are children’s books that help do math?

• Note: Elementary grades teachers are usually the best at using contextual mathematics.

What else might we do?

• Consider arrow diagrams.

• Consider number paths.

• Consider set pictures.

Arrow Diagrams

• Consider a +3 arrow diagram.

+3

Fair trades

• One triangle is worth 2 squares• 3 squares are worth 1 circle.

• What is the value of 6 circles?

• Are 14 squares worth 5 circles?

Pascal’s Triangle

• What patterns can you find?

• Find at least 10 patterns.

Consider the 100s chart.

• How many even numbers?• How many odd numbers?• How many multiples of 3?• How many multiples of 4?

• How many numbers can be reached by skip counting by 7 starting with 27?

Beauty

• Beauty of Mathematics

• Beauty in Mathematics

• Beautiful Mathematics

Beauty of Mathematics

• Structure– How many times have you heard,

• Mathematics is so beautiful. • It’s built like a(n) [insert your own phrase].

• Examples: A hanging chain» A spider web» A pretzel» And?

Basic Division

• What does division look like when you divide by hand?

• What does division look like when you use a calculator?

• Note: The structure is the same!

Beauty in Mathematics

• How many times have you heard,– I think that I shall never see – A number lovely as a three.– A three whose hungry mouth is blessed– Awaiting a 10 to cause unrest.– Remember– Poems are made by fools like me– But only God can make a three.

3

13

Beautiful Mathematics

• A child smiling when a problem is solved.

• A child smiling when a new algorithm is discovered

What Can We Do?That we aren’t already doing?

• How about a Mathematics Beauty Pageant?– Distinguished Judges

• Administrators• Parents• Townspeople

– Contestants• Your kids’ favorite problems

Open it up!

• How brave are you?– Other classes– Other grades– School– Internet

Make it a networking event.

• Put together groups of Alaska teachers.– Pick a problem where kids don’t know the answer.

• At 10:00 AM on some day, have each pair of kids go outside and measure the length of a shadow and the height of the object that made the shadow.

• Pool the data and graph it with SHADOW LENGTH on the horizontal axis and HEIGHT on the vertical axis.

• Do this across the state with different teachers and share the data with all classes.

• What do you find? What is significant?

Make a State’s Largest Math Event

Conclusion

• If you truly want mathematics to be ralistic and a thing of beauty, you have to make it happen by– Being creative while doing math– Being adventurous while teaching basics– Being beautiful in the ways that you teach

math.

Do what you know you should be doing!

• Show your enjoyment.

• Use what works.

• Use cooperative learning when wanted.

• Use technology as an aid to learning.

• Remember: Problem solving is the goal.

jlott@mso.umt.edu