Teaching Problem-Solving Skills: Theory or Practice First?

Helen L. Plants and Wallace S. Venable

Engineering Education, March 1970

Which should come first - theory or practice? Or does it matter? These questions are basic to the information management aspects of teaching engineering and all applied sciences. Most teachers in these disciplines agree that laboratories, demonstrations, and hands-on experiences have a place in education but they have different opinions about how these should be incorporated into the curriculum.

This article describes a controlled experiment at West Virginia University which sought to determine whether it is better to present a demonstration before discussion of the theory involved or to present discussion before the demonstration. The results apply to practical questions of course and curriculum design.

The experiment also provides partial answers to far more basic questions of whether or not what a teacher does has any measurable effect on his students and whether' engineers are born or made.

The first question is, "What is the proper sequence for presentation of material having both practical and theoretical aspects?" By concentrating on problem-solving behavior, the investigators were able to show that certain problem-solving abilities were enhanced in the class in which demonstration preceded discussion.

The second question, "Does what happens in the classroom affect what the students learn?" has been answered negatively by several nonengineering investigators; in the recent past (Medley and Mitzel, 1963). But this study indicates that what the teacher does in the classroom matters a great deal. It would appear to show that while no significant difference appeared between the classes in the amount of material learned, a significant difference did appear between them in their ability to apply the material to the solution of novel or open-ended problems.

The third question, "Are engineers born or made?" hinges on the second one. If what the teacher does in the classroom affects his students in the way they look at and solve unusual problems, then the teacher can develop his classroom strategy in such a way as to enhance: the ability of his students to "think like engineers." Since differences were demonstrated between two classes taught in different ways, it can be concluded that the classroom technique of the teacher does affect what students learn and that it is therefore possible to teach intangible engineering skills. It is further concluded that in this course in dynamics, these skills were best taught by presenting demonstrations before theory.

The Experiment

This study involved the control of the content of instruction throughout a complete semester course in dynamics, varying the sequence of the theoretical and practical portions of the course. To assure the equality of presentation of the subject material, the content and homework problems were presented in a set of programmed materials (Plants and Venable, 1968) which completely covered the normal content of a semester course in the subject. The same classroom demonstrations and experiments were conducted in each class. A particular lesson was presented to both classes by the same instructor. In addition, both groups were required to take identical quizzes and examinations at the same time, and both had the same schedule of assignments. The order of presentation of subject matter was the controlled difference between the two groups.

Demonstration-First Group (DF) - The presentation of a demonstration of a concept to the first group was made before the students in the section had completed the coverage of the topic in the programmed units. As a result of the demonstration the students were expected to evolve a general principle from the observations made. The principle deduced was then derived and utilized more mathematically in the following program unit.

Theory-First Group (TF) - The second group attended demonstration sessions following the completion date for the mathematically based program units. The factual presentation was the same as that given the first group but the discussion was directed toward the acceptance of the demonstration as a verification of the mathematics rather than toward the demonstration being the empirical foundation of the principle.

The 60 students registered were divided into two sections by assigning alternate students in alphabetical order to each section. Adjustments in section assignments were then made to balance identifiable subgroups (such as foreign students) in the sections The students were sophomores, with a few juniors in each section. All students had completed statics and the mathematics sequence up to differential equations.

At the first meeting, the class was informed that they would be participating in an experiment in team teaching and that they would be divided into two sections meeting simultaneously and both responsible to two instructors. It was pointed out that this would allow the instructor on a particular lesson to make more extensive preparation of class presentations and that the same would be presented to both sections. The students thus realized that they were the subjects of a study, although they were not aware of its true nature.

Both groups were taught by two teachers. The schedule was so arranged that material taught by Teacher A to one class was taught by Teacher A to the other class. Each had 21 hours of contact with each class to minimize the effect of differences in the teachers.

In the TF section both teachers taught in an expository mode, lecturing and answering questions. In the DF section both teachers taught in an exploratory mode, i.e., the class was conducted on a discussion basis and questions were answered by the instructor only as a last resort (instead an effort was made to help the questioner arrive at his own answer). These differences in teaching modes were the outgrowth of the controlled difference in order of presentation, since the differing sequences required different classroom strategies for effectiveness.


The outcomes were measured by the following kinds of tests.

A. Entering Measurement - At the beginning of the term all students were asked to complete a demographic data form, and they were given a visual-vocabulary test and the Mechanical Comprehension Test by Owens and Bennett.

B. Tests on Course Content - During the term students took 28 post-tests over the programmed material and four one-hour examinations. As these tests covered the information usually included in a course in dynamics, the combined results made up the technical content score.

C. Problem-Recognition Test - This test consists of four problems, each of which can be solved incorrectly by an obvious method. The correct solution in each instance was not evident and in one case required the student to make assumptions about certain anomalies in the problem. Its purpose was to measure the ability of the student to recognize the difference between the real problem and the expected problem and to solve the actual problems successfully.

D. Test of Fluency in Generating Alternatives - This test indicated fluency in generating two sorts of alternatives:

In evaluating tests C and D above, every attempt was rated independently by each of three instructors who were familiar with the course, according to rating scales for the particular tests. The rating scale for the problem-recognition test reflects whether or not the student is able to identify and comprehend the true problem involved and the degree to which he is able to solve it. The rating scale for the creative solutions portion of the test of fluency in generating alternatives reflects both the number of solutions proposed and the grader's opinion of their merit. The rating scale for the algorithmic strategies portion of the teat of fluency in generating alternatives is weighted so that each successive independent algorithm receives a higher score than the preceding solution. Again, some weight is attached to the merit of the attack.


There was a significant difference in the performance of the two sections on two of the three special tests (figures 1 and 2). The group which received demonstrations before theory (DF) scored higher on both the problem-recognition test and the creative solutions portion of the test of fluency in generating alternatives. There was no significant difference in performance on the algorithmic strategies portion of the latter test.

Figure 1. Problem recognition test results (maximum possible score = 60)

Figure 2.Creative solutions test results (maximum possible score = 24)

There was no significant difference in the performance of the two groups on the tests covering the technical content of the course. This was in accordance with the original hypothesis. It is quite possible that the algorithmic strategies test was, in truth, a reflection of the technical content of the course, since all of the strategies depended upon the manipulation of material taught in the course.

A study of the differences in correlations between the various measures illustrates the profound effect of order of presentation on the ability of the students to recognize and solve unexpected problems. In the TF section, the technical content test showed a significant correlation with the visual vocabulary test and the mechanical comprehension test. This would appear to indicate that what the student learned in this section was considerably affected by what he already knew at the beginning of the course. In the DF section, none of these correlations were significant, thus implying that for these students the experience in the classroom overshadowed the prior background.

In addition, the TF section technical content test correlated significantly with the problem-recognition test and algorithmic strategies test, so that these in. a sense were merely reflections of the same skill. In the DF section, there were no significant correlations between these tests, indicating that in this group the problem recognition and strategic skills had developed independently of content learning. Furthermore, for the students in the DF section, there was no significant correlation between prior grade point average and problem recognition, although there was a highly significant correlation between these scores for the TF group. In the DF group the poorer student was as likely to score on problem recognition as was his better classmate. Thus, the DF presentation served as a better training in problem recognition and had a greater effect on that skill than did the students' previous achievement.

Subjective Evaluations

During the course of the semester, a student evaluation was made of each teacher. Although this evaluation was actually a part of another study, the results cast some additional light on the experimental sections, 80 they are mentioned here.

The student evaluation of the teachers showed significant differences between the two sections on two items, both relating to the elder teacher. This instructor was rated more expert by the DF group than by the TF group and a better teacher by the TF group.

In all areas except subject expertise, the students in the TF rated both teachers more highly than did the DF section. The TF section apparently was much more satisfied with the instruction it received than was the DF section. On the basis of the test results, however, the TF section had actually learned less. The DF section rated its instructors lower but tested better.; .

The instructors also had opinions. Both instructors had expected to find the Demonstration-First group the more pleasant to teach. Instead both rapidly came to prefer -the Theory-First group, perhaps because they exerted greater control over it. Both felt that the Theory-First group was more interested and responsive; both were convinced that the Theory-First group was learning more and were repeatedly surprised when test data failed to bear this out.


Several conclusions may be drawn from this study.

The first and most obvious conclusion is that in this course in dynamics, the greater development of engineering skills was produced by an appropriate management of instruction: the presentation of demonstrations before pertinent theory. The DF group was essentially taught to look first at a problem, then at the information necessary to solve it. The TF group was taught to look first at an item of information, then at its possible applications. The training given the DF group apparently gave it the better preparation for applying its knowledge to novel situations.

A second conclusion is that even when the teacher is not responsible for transmitting content information, he has a vital role in a course. In this case, specific gains in student ability could only be attributed to the teacher's efforts because the content was transmitted by programmed instruction.

Third, these findings indicate that problem recognition and creativity in the solution of problems engineering skills of the highest order - are affected by what the teacher does, and that these skills can therefore be taught. In this case, the effect of the order of presentation was so profound that tests measuring past performance and background ceased to be valid predictors of success in the DF class, although they continued reliable in the TF group. In other words, in both groups the students who could have been expected to do well did well, but in the DF group students who would have been expected to do poorly did well also.

A final observation is that what the teacher does affects his own feelings about the class and the feelings of the class about the teacher. Both teachers preferred teaching the Theory-First class, and this class had more positive feelings about both teachers. The more comfortable class was the less competent class - perhaps indicating that the mode of instruction preferred by the student may not be best for him. Furthermore, the instructor's intuitive feelings about the effectiveness of instruction seem to be no more reliable than the students' intuition.

All of these conclusions lead to the inescapable thesis that a great deal of research, development, and design work should be done before the engineering teacher enters his classroom. If what the teacher does makes a difference, it is necessary to positively identify the most effective behavior. If engineering ability can be enhanced, it is necessary to discover the most effective strategies for doing so. If these goals are to be accomplished, efforts to reach them must be based on measurable achievement rather than on intuition. Only if engineering educators recognize these as goals and take the steps necessary to reach them, can the teaching techniques of tomorrow produce better results than those being achieved today.


  1. Medley, D. M. and Mitzel, H. E.; "Measuring Classroom Behavior by Systematic Observation," Handbook of Research on Teaching, Rand McNally, Chicago, 1963, p.249.
  2. Plants, H. L., and Venable, W. S., A Programmed Introduction to Dynamics, West Virginia University Foundation, Morgantown, 1968.