Five Stumbling Blocks to Engineering Education
Jack D. Lubahn
From 1961 to 1972 I taught mainly senior courses in Physical Metallurgy. Having come recently from industry, I thought I knew what a young man needed to know when he graduated from Engineering School and took a job in industry. I succeeded in covering less than half of that material, though some of the students had my courses for as much as nine credit hours during their senior year.
The inadequate coverage may have been caused partly by my reluctance to condone a superficial understanding. I insisted on a substantial degree of mastery, and that took a lot of time. Part of the difficulty may have been my tendency to emphasize my field of specialization; and that can easily have the effect of short-changing other subjects. Certainly one important contributing factor was the large fraction of time (over 50 per cent) that I spent in teaching the prerequisites--such subjects as calculus, heat transfer, and stress analysis.
Now that I have been teaching at the Sophomore and Junior levels for almost three years, and have also had considerable experience in counselling and tutoring Freshmen, I am beginning to see some of the stumbling blocks which might be hindering the students from achieving the level of comprehension that they really need in the basic subjects if their education at Senior level is going to be truly effective. There is no single factor. The problem stems from a combination of many factors. I am sure I haven't had experience with all of them as yet; but five stand out so clearly in my mind right now that it seems worthwhile to put them down in writing, together with some possible remedies.
The first of these stumbling blocks is that the students are spread too thin. They run from one thing to another, trying to keep up with a prescribed schedule; and they never seem to be able to catch up, much less mull over the basic concepts in the leisurely manner that mastery requires.
The basic concepts of mathematics, science, and engineering are not easy (I was in graduate school before I really understood calculus finally), and one has to work with these concepts concentratedly and persistently before the dawn finally comes. When I have tried to do this with more than two or three subjects in any four-month period, I find myself making little progress on anything. Many of today's students are experiencing the same thing.
Part of the student's having to run from one thing to another is his own fault, of course. He isn't spending enough time, isn't spending it effectively enough, or hasn't developed enough capacity for prolonged concentration. But it is not all the student's fault. Part of it is due to his studying too many subjects simultaneously. Perhaps we could profit from the example of Harvard's Engineering School, where the student takes only three subjects, each of which is six credit hours, and which are carefully interrelated so as to apply the concepts from one class in the very next class he attends.
I believe the summer field course I taught in Metallurgy was the most efficient course I ever taught. Its efficiency was due to its concentratednesseight hours a day for two weeks.
But the spread-thin is only partly a result of the arrangement of the courses in the overall curriculum. It is also a result of trying to put too much into any given course. Just when the student is beginning to understand a subject, and could profit enormously by a little more work to nail the matter down firmly in his mind, he must drop everything and run to the next subject on the assignment sheet or he will fall behind.
Trying to put too much into a given course is a very easy mistake to make, as I discovered from my own experience. Two years ago in Strength Lab we did eleven experiments on eleven subjects as widely different as test machine characteristics, impact loading, strain gage circuit analysis, plastic bending, curvature analysis, and the heat transfer characteristics of a thermal-stress apparatus.
The students were confused by the wide range of topics, particularly for a course carrying only one credit hour, and many of them failed to grasp the basic concepts. They are much better able to cope with the subject matter now that I have reduced the number of major topics to six.
The second stumbling block is what I call the "blind plug-and-crank syndrome." This is the propensity of students to plug numbers into memorized formulas, or to crank out memorized procedures, without really understanding where those formulas or procedures came from, how to apply them correctly, and most importantly, when they can and when they cannot be used. I have seen a remarkable number of cases of misremember and misapplied formulas and procedures (example: v = v0t + 1/2 at2).
A large part of the blind plug-and-crank syndrome is due to the propensity of authors of textbooks to try to reduce everything down to a formula or a procedure. I suppose these well-meaning people think they are doing the student a favor by presenting him with a gourmet smorgasbord of knowledge, and all he has to do is to enjoy the eating of it (i.e. memorizing it). My experience with such attempts at saving the student from having to think for himself is that they do a great deal more harm than good. The procedure doesn't really work, since only thinking about the problem will solve it, but the mere fact that the procedure has been set down by the author makes it seem to the student that he doesn't have to think. So he doesn't.
Another problem arising from the textbooks that are currently available is that most of the exercise problems are plug-and-crank problems. This leaves the student with the impression that plugging and cranking is all there is to science and engineering. The scarcity of thought problems can be rectified by supplemental problems, of course, but this takes a lot more of the instructor's time and raises the questions of validity in the student's mind. I have noticed a considerable student resistance to thought problems. They would rather be given a procedure that they can follow without thinking. The "blind plug-and-crank syndrome" is probably the most difficult of the five problems I am discussing here, but my experience proves it is not insoluble.
Failure to wean the students away from the blind plug-and-crank syndrome is not only bad for their education; it is very hard on their morale as well. Every week or so I have a student in my office who is in a state of almost total despair about his education. He can see no end to the number of formulas and procedures he must learn, and in his despair he assumes there will be countless thousands of them, thus making it impossible for him ever to become an engineer. His despair is brightened by a glimmer of hope when I explain to him that engineering is not a collection of formulas and procedures, but rather a set of laws, concepts, and principles and that he has learned more than half of these already! (Hooke's law, Ohm's law, Newton's laws of motion, the gas law, the heat flow laws, etc.) His relief at hearing this news is only slightly tarnished by my adding that he hasn't really mastered any of them as yet, and that it will take a few years of practice; he can see that there is an end in sight, to the fundamentals at least.
The third stumbling block is insufficient drill. We don't have enough drill even on formulas, such as A = pr2, (d/dq)(sin q) = cos q, and P = sA, but what is much more important is that we do not have enough drill on the fundamental concepts. As an example, consider the concept of neglecting higher-order terms. This is a concept which the student will have had to apply in a variety of widely different situations before he can appreciate the breadth and power of it, thereby causing it to become a valuable tool in his engineering tool kit. The mere fact that he has seen the binomial expansion and a few series expansions in the Math Department does not make the tool truly accessible to him; he must use it again and again in various situations. It isn't enough to have explained the concept clearly to the student; he has to use it himself in a sufficient number of situations that he will fully grasp the concept. For this education process to be completely effective, it may be necessary that the student be exposed to the concept repeatedly in different courses. That the amount of repetition is inadequate seems to be indicated by the typical excuse of students in my senior courses who couldn't handle physical situations involving non-uniformity: "I think I learned calculus when I was a freshman, but 1 haven't used it since."
It is very easy for a professor to become so preoccupied with the range of topics he is trying to cover, that he fails to provide an adequate variety of situations to which the student must apply a given concept. A few semesters ago in Strength Lab we had an impact experiment which seemed to me to be a good illustration of the use of the First Law of Thermodynamics to deal with such quantities as kinetic energy, elastically stored energy, plastic work, and frictional work. But the students failed to grasp the concept, because they had applied it to only one situation. They could apply it to that situation (with the numbers changed), but they couldn't apply it to any other situation because they hadn't had enough practice in applying it to a variety of different situations. Their grasp of the concept is much better now that we apply it to several elementary and radically different situations instead of one complex situation.
To spend more time on more drill might seem to be only worsening the problem of having more material to cover than time permits. The dilemma is resolved, however, as soon as we recognize that a student cannot master, in four years, all the material he might need for his professional career. We will have to be selective in what we attempt to teach him; and in particular we will have to be quite clear as to what constitutes the core of math, science and engineering that is the irreducible minimum of the fundamental concepts. To provide enough time for mastery of the core of basic concepts, we will have to make a careful assessment of all peripheral material. Any weeding-out process will be painful to those who see their pet subject relegated to second place, who fear for the narrow perspective of our graduates, who perceive the specter of an inadequate foundation of theory, etc. The pain of the weeding-out will be tolerable only insofar as one recognizes the absolute necessity of providing enough time for mastery of the core of fundamental concepts, for without that foundation the student will be unable to specialize or to broaden himself anyway.
The fourth stumbling block is the tendency of sincere and well-meaning professors to get carried away by their specialty. In my own case, I am afraid I have never quite forgiven my alma mater for making me so much a specialist in such fields as assaying, water purification, and properties of oils that I never grasped the basic concepts of calculus, thermodynamics, etc. until many years later. We see the same tendencies today, with equally bad results. We are attempting to turn out specialists in metallography, specialists in truss design, specialists in integration methods, specialists in computer technology, specialists in deriving phase diagrams from thermodynamic data, etc.
I know the tendency, for I have the same tendency myself. When I teach plasticity, it is my intention to use metalworking operations only to provide a few illustrative examples, but the tendency is to try to turn the students into specialists in metalworking operations.
There is nothing wrong with being a specialist, of course. We need people who have studied a specialized field in such depth that they know everything that is known about it. But the place for this kind of training is hardly the under-graduate program. The tendency toward specialization must be strictly curtailed, or there won't be enough time for mastery of the core concepts.
The fifth and last stumbling block is ineffective student motivation. In my own case I am always excited about the prospect of studying a new subject, particularly when I know it will help me to be a more effective engineer or teacher, and I wish the students shared my excitement. Instead, I see a range of attitudes that includes apathy and even hostility. Why? How much of it is inherent in the family and public school background of the student? To what extent can the student's attitude be influenced by the school he attends?
I have the impression that, with the exception of a few dubious students, the entering freshmen are enthusiastic about the prospect of getting into a creative, challenging, exciting, and rewarding profession like engineering. Apparently somebody did a good selling job on him, or he wouldn't have come here. I believe we need to continue to do a selling job. We must tell him again and again, with every course he takes, "You will find this course exciting and challenging and will have lots of opportunities to use what you have learned," rather than telling him, "You have to take this course because it is a required course, and if you fail you will have to repeat it."
But telling him he really needs the course is going to have a very hollow ring to it if the seniors tell him they never used it in any other course and the graduates tell him they never used it in their professional career. The student will become demoralized if he asks his professor what the course is for, and his professor says he doesn't know, or refers him to some other department. The careful choice of a core curriculum, whose value is obvious to both current and past students is the only kind of salesmanship that is going to be truly effective in providing continuing motivation on the part of the students. The more they apply their knowledge to real-life situations, or see it being applied by the graduates, or by their professors in their consulting practice, the more serious will be their study. I feel strongly that good salesmanship can greatly reduce both the number of students who drop courses, and the number that drop out of school.
Taken collectively, these five contributory causes of poor preparation for senior courses might seem to constitute an imposing list, if not an insurmountable problem. Actually, however, not a single one of the problems is insurmountable. The spread-thin problem can be considerably improved by meticulous attention to detail in core curriculum and syllabus, with honest reappraisal of all material that doesn't contribute directly to the mastery of the basic concepts, no matter how enlightening or interesting or broadening it might seem to a particular professor. The plug-and-crank syndrome can be counteracted by selecting mainly thought problems rather than plug-and-crank problems, from the book, and then making up more thought problems if the book doesn't have enough. Providing opportunity for more drill is again a matter of curriculum and syllabus; more time for drill will become available automatically as peripheral material is weeded out. This is particularly true of specialty material. If the method of handling a particular situation is merely an example in the use of the basic concept, rather than an end in itself, it will occupy a much smaller portion of the semester' s work. We must have professors who are dedicated to the overall education of the student, rather than wanting to push their own specialty; and if we can't get them we are going to have to get a disinterested agency to monitor the syllabus of over-zealous professors.
Motivation has always been the most difficult of the education problems, but it is not insurmountable either. We must gear our objectives, as a faculty, to the personal objective of the student, namely to become a creative, practical, successful, professional person. Continually challenging the student in the areas of structural and process design will get a lot more work out of him than any amount of fear of failure. I still remember with a good deal of pleasure the enthusiasm of the senior metallurgists about their engineering projects in the electives I taught in that department, and how excited the Met Practice students were about the contest we used to have to see who could make the strongest hemispherical pressure vessel head by starting with raw copper and aluminum. The old-grads still reminisce about the problem of mine-hoist design they had to solve in "the good old days". And, most recently, I remember vividly the pleasure and amazement registered by one of my Strength of Materials students who suddenly discovered that he could really use what he had learned in the course to design joists, roof rafters, studs, and roof boards for an enormous snow load on a hunting cabin he was going to build in the high country.
Yes, these problems are all soluble. I am not discouraged, and I hope you aren't either. Let's look at these problems, not with discouragement, but rather as an exciting challenge in engineering education.