Lois B. Greenfield
The engineer has earned his reputation as a problem solver. Where does he learn this skill? Surely if one were to look in on most engineering classrooms in this country, one would find both students and teachers concerned with the solution of problems. In what ways do engineering educators teach problem-solving skills to their students? Do they, in fact, make special efforts to teach such skills?
First, I would like to emphasize the difference between the product of problem solving, i.e. the answer or solution to a problem, and the process of problem solving, or the method of attack on a problem. The answer or solution to a problem is readily observed, and can be quantified. The engineering student's homework solutions can be graded, and marked right or wrong. Emphasis is placed on accuracy of the answer, but the method of solution may be equally important. In the "real world" a variety of answers may satisfy the problem conditions-- indeed, two engineers may look at a problem and develop two completely different solutions to what they have seen and identified as two completely different problems.
Although it is possible to infer the process or method of attack used in solving a problem from the product or answer, the conclusion may be misleading. For example, if an engineering student gets the wrong answer to a problem on a test, can we determine the reason for the error? Do we know whether the student has used the wrong formula, made an error in arithmetic, neglected an important bit of data, lacked knowledge of necessary facts, or completely misinterpreted the nature of the problem he was asked to solve? The reason for error may be none of these; or the student may have been so upset by the examination and all that hinged on his performance, that he was unable to demonstrate what he knew.
The instructor may try to infer the process of problem solution from the product obtained by means of statistical techniques. It is possible to determine which questions on the test are most difficult, as well as the order of difficulty. Particularly in objective kinds of tests, it is possible to determine the number of students who get a problem wrong if it is presented in one fashion, and the number who get it wrong when it is presented differently. It is possible to ascertain the wrong answer most frequently given to a particular problem. From such data, the instructor can attempt to figure out why a particular question is difficult, or why he thinks it would be difficult for him if he didn't know how to solve it. The instructor cannot, however, be sure that he is not going beyond the implications of his data. He cannot know with certainty why one answer was preferred above another, where the student might have gone astray in his reasoning, whether the student misinterpreted the question he was being asked, or