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Teaching Mathematics to
Children
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CHILD-DIRECTED APPROACH TO SOLVING MATH PROBLEMS
By Jim Hetherman
Children's social interaction during classroom discussions of various paths to solving math problems are very important. By listening to their peers many students adapt more flexible and efficient ways to solve math problems. If your own child is good at math, especially understanding word problems, she or he can become an conduit for raising-up the performance of her entire class, providing, however, that your child's teacher is good at using a child-directed approach to solving math problems.
Teachers who are good at using this approach might pose the following:
Mary received $1.00 for losing a tooth. Saturday, her father took her to some local garage sales so she could purchase some things with her earnings. Mary made a series of expenditures using that $1. Each student must determine how much money Mary had left after each purchase.
Materials available to the students include:
- A 10x10 grid with numbers 1-100 filled-in (a.k.a. a hundred chart)
- A coin worksheet depicting 10 pennies, 4 nickels and 7 dimes
Mary's first purchase was a small picture of Elizabeth Ann Seton, the dedicated volunteer in charitable organizations, for 15 cents.
Students had to determine how much money Mary had left after purchasing the picture of Mrs. Seton, and then to share their problem-solving strategy with the class. The sharing of strategies may go like this:
- Some students may say that they crossed-off one dime and one nickel from the coin worksheet, and then counted the money left over.
- Other students may say that they used the numbers grid, starting at the first square after 15, and counted forward all the spaces left.
- Other students may say that they also used the numbers grid, but started with 90 and counted back 5 more space until coming to 85.
- A few others may say that they used the algorithm 100-15 to solve the problem.
As the sharing is going on, the teacher is recording each of the strategies on the board, and pointing out that there are many approaches that get to the same answer.
The teacher goes through this process again after each of Mary's purchases (which the teacher invents). The teacher encourages each student to write-down an algorithm after each purchase, and then solve the problem using any method they chose. After each step and each sharing, many students would begin to move from their more concrete method of coin counting, to subtracting using the number grid, to the more abstract yet efficient method using an algorithm.
Concrete learners like to learn through their physical senses, what they can touch, see, hear, taste and smell. They like to deal with things that exist in the physical world. Abstract learners prefer the world of ideas and feelings. They use reason and intuition to deal with ideas, concepts, and feelings.
If your own child tends to be more of an abstract learner, then encourage your child to share. The better your child is at sharing her or his approach to solving math problems, the better person your child becomes, and the better at math and problem solving your child's peers become as well.
And don't forget to encourage your child's teacher to use a child-directed approach to solving math problems.
Reference:
Wiener, C. & Smith, C. (2004). Making sense out of
cents. Teaching Children Mathematics, November 2004, NCTM.
Jim Hetherman is a member of the National Council of Teachers of Mathematics. You may send comments about this article to Jim@Burbank.com. Please include the phrase BURBANK MATH in the subject of your email.
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The Picture Communication Symbols ©1981 - 2008 by Mayer-Johnson LLC All Rights Reserved Worldwide. Used with permission.
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