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Effective and Ineffective Problem Solvers

Arthur Whimbey spent decades advising students about how to improve their analytic abilities. Two of his books are Intelligence Can be Taught (1975) and Problem Solving and Comprehension (1982). Whimbey found that students who were good problem solvers had an approach completely different from students who were ineffective problem solvers.

What is the difference between good problem solvers and ineffective problem solvers, according to Whimbey?

Active analysis of a problem

Good problem solvers are optimistic about the possibilities for solving a problem through a careful, persistent analysis. They start by breaking the problem into parts starting at a point where they can make some progress, and working from there. They are active in trying different problem solving methods, such as making diagrams, asking themselves questions, and trying to pin down abstractions as concrete examples.

In contrast, poor problem solvers often believe that "you either know it or you don't, and if you don't there's no use trying." They are likely to react to the problem as a whole instead of breaking it down into simpler sub-problems. They are unlikely to try different techniques for understanding the problem or figuring it out.

Accuracy and Double-Checking

Good problem solvers are concerned with accuracy. They check and re-check each step of the problem, if necessary. They reread instructions. They avoid guessing.

In contrast, poor problem solvers tend to be sloppy and inaccurate at critical phases in a problem-solving process. They may misunderstand the way a problem is stated, or the instructions for solving it. They may take a stab at an answer or follow a sudden intuition without checking to see if it is accurate. They lack the slow, step-by-step approach. (Adapted from Whimbey, 1982)

How is Whimbey's advice consistent with the other problem solving techniques?

Whimbey's developed a technique that boosted student test scores. First, he had to get students to slow down, think carefully, and have faith in the value of a systematic approach. He then urged them to break problems into sub-problems and double-check their accuracy at every step.

These recommendations are consistent with Wickelgren's recommendations as well as the constraint-satisfaction approach. Both involve analyzing a problem into parts and working systematically toward a solution.

Whimbey also studied the reading habits of at-risk students. He concluded that poor readers often do not "read" at all, in the sense of systematically reconstructing an author's meanings. They skim. While skimming, they guess at the meaning of what they are reading, using their pre-existing knowledge. Yet they think they are reading. And they remain satisfied with their inaccurate understanding, because typically they do not carry out any systematic self-testing procedures. The inadequacy of their comprehension becomes obvious when they are asked even the simplest questions about what they have read. As Whimbey put it:

What were two characteristics of so-called "low aptitude" students?

Students of low aptitude had a characteristic way of approaching the material. First, they carried out one-shot thinking. Their initial attempt at understanding a problem or a passage was likely to be their last...

Second, the low-aptitude students were more willing to tolerate gaps in their knowledge than high-aptitude students. If they didn't understand something, it did not bother them; they just plunged ahead... (p.47)

The phrase one-shot thinking was originally used by the researchers Bereiter and Engelmann to describe the response styles of disadvantaged preschool children. Such children seemed to think a teacher wanted answers quickly, so they would provide an answer right away, even if it was wrong.

What do some African-American scholars believe?

Some African-American scholars believe this cognitive style is more common in their communities because of the value placed on quick verbal give-and-take among African-American family members and friends. The child picks up the idea that a quick answer is valued and takes this assumption to school, where it may lead to problems. As a rule, intelligence tests (like multiple choice tests in college classrooms) present problems in which the obvious or first guess is not the right answer. A child raised in the "quick answer" tradition may do very poorly on such tests. This does not mean the child is stupid; it means that an adjustment in cognitive style might be necessary to do well in school.

What did Whimbey discover, when he taught students to slow down and test themselves?

Whimbey developed techniques for training students to slow down and test their own answers before making a decision. Almost all students who followed his instructions improved their performance on standardized tests. Whimbey titled his first book Intelligence Can be Taught (1975). He found that students who learned a few simple techniques like pacing themselves and double-checking their cognitive processes ended up scoring substantially higher on so-called intelligence tests.

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