Mathematics in the Real World? What Are Our Options? Johnny W. Lott, Past President, NCTM.
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Transcript of Mathematics in the Real World? What Are Our Options? Johnny W. Lott, Past President, NCTM.
![Page 1: Mathematics in the Real World? What Are Our Options? Johnny W. Lott, Past President, NCTM.](https://reader034.fdocuments.us/reader034/viewer/2022051211/551815b4550346a7318b4619/html5/thumbnails/1.jpg)
Mathematics in the Real World? What Are Our
Options?
Johnny W. Lott,
Past President, NCTM
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Lots of Words
• Mathematics• Real World• Options
• What do they mean to us?
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Mathematics
Problem solvingWhat do you want kids to be able to do?
What will they be expected to do when they leave us?
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What Are the Complaints that Students Cannot Do?
• Make Change
• Balance Checkbooks
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Let’s Make Change!
• My bill is $13.78.
• I give you $20.23.
• How do you give me change?
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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?
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What did you want to have happen?
• $20.23
– 13.78
$ 6.45
Did you want $5, $1, 1 quarter, and two dimes?
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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?
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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?
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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.
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What are children’s books that help do math?
• Note: Elementary grades teachers are usually the best at using contextual mathematics.
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What else might we do?
• Consider arrow diagrams.
• Consider number paths.
• Consider set pictures.
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Arrow Diagrams
• Consider a +3 arrow diagram.
+3
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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?
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Pascal’s Triangle
• What patterns can you find?
• Find at least 10 patterns.
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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?
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Beauty
• Beauty of Mathematics
• Beauty in Mathematics
• Beautiful Mathematics
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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?
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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!
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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
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Beautiful Mathematics
• A child smiling when a problem is solved.
• A child smiling when a new algorithm is discovered
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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
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Open it up!
• How brave are you?– Other classes– Other grades– School– Internet
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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.
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• Do this across the state with different teachers and share the data with all classes.
• What do you find? What is significant?
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Make a State’s Largest Math Event
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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.
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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.