Why students have mastered or understood the basics of arithmetic such as whole number addition, subtraction, multiplication, or division and yet many of them cannot do word problems well? Our observation is most of commercially available basics worksheets do not pave the way for children to working on word problems. Most worksheets guide children in doing computations in linear and left-right format, they do not involve multi-concept, multi-step, reversing thinking or bottom-up calculation. The connection of working on computational worksheets and word problems is very little. Children seem to enter into a strange world when asked to work on multi-step word problems or use backward strategy because children were not trained in this way by working on computation worksheets in the first place. There is something wrong with our traditional worksheets and we are interested in improving on this problem.
Take a look at the following "chicken and rabbit" word problem.
There are 10 rabbits and chickens altogether and 22 legs in total. How many chickens and rabbits are there?
One way to solve this problem is student can use 10 circles to represent 10 heads and then draw legs to figure out, but what happens when the number of animals gets larger? By not providing a systematic method, children constantly rely on "acting out" or "trial and error" methods, this might be one of the problems children get frustrated by not being able to solve word problems in a more systematic way. For example, children learn how to use variables to solve algebraic word problems and yet, they were not taught on using a systematic method to solve word problems when they were in elementary school. By providing some generalized tools such as line segment, symbols, table, tree diagram, reversing thinking, bottom-up computation, children can use them to solve word problems.
Back to the word problem mentioned earlier, this type of problems can be solved by using system of equations, which is taught at grade 11 in Canada. So without using algebra, how can an elementary student solve this type of "chicken and rabbit" problems? The answer is to provide them a set of tools, which teach children to use as a systematic method so that they can apply them to the word problems.
By providing a set of tools to elementary students, elementary students can solve some difficult problems, which sometimes they see these word problems again when they are in secondary schools.
Most of time, arithmetic computation is operating from left to right in linear fashion, but often in doing fractions, the bottom-up approach is much easier to solve problems. For example, 3 divided by 1/2 is easier to be thought as the reverse of 1/2 and then multiplied by 3. It is the purpose of this article that we feel educators should provide children a set of word problems tools to be used as a systematic way of solving difficult word problems.
More details on how to use these tools, visit www.mathandchess.com.
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