Hindrances to Problem Solving

Engineering stndents should he aware of certain conditions of the mind that can hinder effective problem solving. One such condition is known to psychologists as fixation or mental set. It involves the persistent application of an inappropriate strategy to a problem because of previously acquired knowledge or experience. 

Luchins (5) demonstrated the tendency of people to cling to an inappropriate method of solution because of the fixation effect. In an experiment involving 2009 students, he asked each participant to measure out mentally a desired quantity of liquid using three jars of specified sizes. The set of problems is given in Table 4.6. All but one of the problems (number 8) could be solved in the following way (a) fill Jar B, (b) pour off enough to fill Jar A, and (c) then pour off enough to fill Jar C twice. This method can be stated by the formula B - A 2C. This leaves the desired amount in Jar B. 

Problems 6 and 7 are solvable by the formula but can also be solved by simpler ones A — C and A + C, respectively. The last two problems are similar in structure to the sixth and seventh problems and can also be solved by a simpler method. Problem 8 does not conform to the formula B - A - 2C but can be solved by A - C. 

Luchins found that 64 percent of the experimental group failed to solve problem 8, but only 5 percent of the control group failed that problem. Because problems 1 through 5 all call for the B A 2C solution, 83 percent of the experimental group used it for problems 6 and 7 even though a simpler method existed. Only 0.6 percent of the control group used the more difficult formula. 

Researchers have also found that a student s motivational level can affect his or her ability to solve problems. It is well known that students who are not highly motivated to study for a test are not likely to perform well on it. Curiously, the opposite experience is also possible. Students can be so hypermotivated to prepare for a test that it will interfere with their performance. A number of studies have shown that there is an optimal motivational level for efficient problem solving. That level tends to vary with the complexity of the problem. In general, the simpler the task, the greater the motivation required for optimal performance. 

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