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Problem Solving: Tips For TeachersAuthor(s): Diane Thiessen and John A. Van de WalleSource: The Arithmetic Teacher, Vol. 35, No. 8 (April 1988), pp. 58-59Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193392 .
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Problem Solving iwh^^m Tipi For Teacher* M M
1491
1988
58 Arithmetic Teacher
I li i
3 //(Strategy Spotlight N Helping Students
Approach a Problem
What do your students do if they don't know what to do or where to start? Do they wait for someone, namely, the teacher, to tell them what to do? What do you do to help them? Rereading the problem and having them describe the situation in their own words are two strategies that may be helpful but are often not sufficient.
Other helpful ideas include identifying the known, the unknown, extra information, the relationship be- tween the known and unknown, and what constitutes a reasonable result regarding number size and la- bels. These ideas are general strategies. Research indicates that questions or hints tailored specifically to the problem are more helpful to the students than asking them general questions. Examples of explicit questions are given here, in contrast to general questions such as "What is known?" These ques- tions and hints should serve as a model for the type of questioning and thinking that students should eventually do independently when they approach problems.
Example: What are two numbers whose product is 18 and whose difference is 7?
Edited by John A. Van de Walle Virginia Commonwealth University Richmond, VA 23284-0001 Prepared by Diane Thiessen University oj Northern Iowa
Questions: How many numbers are we looking for? What do we know about the numbers? . . . You said the product must be 18. What is meant by prod- uct? . . . Give an example of numbers with a product of 18. ... Jody, what is your response to Jeremy's answer? . . . Could our answer be 3, 5, and 7? ... Why not? Could our answer be 6 and 3? ... Troy, do you agree with that statement? . . . Could our an- swer be 10 and 3? ... Why not?
Note that the preceding teacher questions hold students accountable by asking them explicit ques- tions to check for understanding. Also, throughout the discussion, class members rather than the teacher should be involved in evaluating each re- sponse to determine if it fits the problem and their thinking. Have some explicit questions planned for each problem. These questions are especially neces- sary if you or your students are novices at problem solving.
The goal of problem solving is to help students develop strategies so that they will become indepen- dent problem solvers. Gradually students should be- come independent and devise questions on their own.
Another step toward helping students become independent thinkers would be introducing a problem and having the students generate questions to help them understand the problem. These questions could be listed on the chalkboard and evaluated by the class. The focus should be on understanding the problem, not devising a plan or solving the problem. To emphasize this point, the students could solve the problems later in smaller groups, as part of a home- work assignment, or not solve them at all.
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April 1988 59
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k^^^ ¿f^^R^T a v~^t^mt^^ Susan was cooking for a large group. After feed-
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finjshed Wednesday and had understanding the problem in proportions and per-
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cents, as well as in addition and subtraction. Part- ^ he finished op the whole analysis is a strategy for solving percent prob- '
lems, but it is crucial that students can understand Sarah had 3.2 kilograms of hamburger that she and analyze the situation in these terms. placed into packages of 0.2 kilograms each. How
r, i_, -r .i-i u -j u j . jo-Mznnf ■ i * many * containers did she fill? Problem: r, i_, -r Todd .i-i u had -j
budgeted u j . jo-Mznnf $45.00 for a jacket.
■ i * many *
Did he have enough to buy the one on sale? In a class of preservice elementary school teach- ers all students missed at least one question and
Questions: Describe the series of decisions that some missed all three. Through class discussion the Todd will need to make. ... In percent problems students were introduced to the strategy of substitut-
we've used part-whole strategies. Describe this prob- in9 whole numbers less than 20 for the fractions or
lem in terms of part and whole. ... Why are you con- usin9 more ordinary fractions, such as 1/2. In retest-
sidering $60.00 the whole? . . . What percent is $60.00? in9. al1 but a few students were able to answer simi-
You said 20 percent was the part. Will the coat cost lar questions correctly. The students' lack of under-
$20 00? If 20 percent is the discount, will we sub- standing of fractions resulted in not understanding a
tract 20? ... What would be the whole if we could situation that they could normally solve. These stu-
subtract 20? ... Since our whole is $60.00, will we dents are not untypical. How would your students
subtract more or less than $20.00? . . . Estimate about do? Have tneV been introduced to the strategy of
how much will be subtracted. usin9 simpler numbers to help understanding?
Part of the Tip Board is reserved for techniques that you've found useful in teaching problem solving in your class. Send your ideas to the editor of the section. W
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