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Unformatted text preview: Johnny W. Lott,
Past President, NCTM Mathematics in the Real
World? What Are Our
Options? Lots of Words
• Real World
• Options • What do they mean to us? Mathematics
What do you want kids to be able to
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
Would you be upset? Would you have correct change? What did you want to have
Did you want $5, $1, 1 quarter, and two
dimes? Do you want me to teach real
• Do you want me to teach making change?
• Do you want me to teach subtraction?
• Are they the same? How about balancing a
• 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
• 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
– 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
• What does division look like when you use a
• 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.
Poems are made by fools like me
But only God can make a three. Beautiful Mathematics
• A child smiling when a problem is
• 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
• Your kids’ favorite problems Open it up!
• How brave are you?
– Other classes
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
• What do you find? What is
significant? Make a State’s Largest Math
• If you truly want mathematics to be ralistic
and a thing of beauty, you have to make it
– 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
• Show your enjoyment.
Use what works.
Use cooperative learning when wanted.
Use technology as an aid to learning.
Remember: Problem solving is the goal. email@example.com ...
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- Winter '08