Exploring What It Means To Do Mathematics

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Exploring What It Means To Do Mathematics

• Mathematics Methods Dr. Dawn
  Parker

2
Contrasting Perceptions of School Mathematics

• Traditional View
• Rules to memorize
• Arithmetic computations
• (listen, copy, memorize, drill)
• Science of Pattern and Order
• Logical order
• Things that have patterns

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Verbs of Doing Mathematics

• Explore
• Investigate
• Conjecture
• Solve
• Justify
• Represent
• Formulate
• Discover
• Construct
• Verify
• Explain
• Predict
• Develop
• Describe
• Use

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Mathematics Makes Sense

• Students must experience that math makes sense
• Students must believe that they are capable of
  making sense of math
• Teachers must stop teaching by telling and start
  letting students make sense of the mathematics
  they are learning
• Teachers must believe in their studentsAll OF
  THEM!

5
Four Consecutive Numbers

• Some people say that to add four consecutive
  numbers, you add the first and the last numbers
  and multiply by 2. What can you find out about
  that?
• _______
• Example
• 4, 5, 6, and 7 are four consecutive numbers. The
  sum is 22. Also, 4 7 11 and 11 x 2 22.

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Acrobats, Grandmas, and Ivan

• The problem is to use the information given to
  figure out who will win the third round of
  tug-of-war.
• Round 1 On one side are four acrobats, each of
  equal strength. On the other side are five
  neighborhood grandmas, each of equal strength.
  The result is dead even.
• Round 2 On one side is Ivan, a dog. Ivan is
  pitted against two of the grandmas and one
  acrobat. Again, it is a draw.
• Round 3 Ivan and three of the grandmas are on
  one side, and the four acrobats are on the other.
• Who will win the third round?

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Trapezoids

• A trapezoid is a four-sided figure with one pair
  of opposite sides parallel. Draw a trapezoid
  that has an area of 36.

8
Pizzas Small, Medium, or Large?

• Pizzas are often sold in small, medium, and large
  sizesusually measured by the diameter of the
  circular pizza. Of course, the prices are
  different for the three sizes. Do you think a
  large pizza is usually the best buy?
• The Sole DItalia Pizzeria sells small, medium,
  and large pizzas. The small pizza is 9 inches in
  diameter, the medium pizza is 12 inches in
  diameter, and the large pizza is 15 inches in
  diameter. For a plain cheese small pizza, Sole
  DItalia charges 6.00 for a medium pizza, it
  charges 9.00 for a large pizza, it charges
  12.00. Are these fair prices?
• ______________________________
• Which measures should be most closely related to
  the prices chargedcircumference, area, radius,
  or diameter? Why?
• Use your results to write a report on the
  fairness of Sole DItalias pizza prices.