The Four Step in Teaching Engineering
Dan Wolaver

To teach engineering effectively, a teacher must be able to:

  1. Develop an intuitive grasp of concepts and discover solutions to problems by playing around.

  2. Be aware of the steps taken in the discovery—what background knowledge, analogies, and similar problems were used.

  3. Devise a way to lead the student to a similar discovery through questions and exercises, leaving as much as possible to the student.

  4. Assess what the student lacked—why he needed so much help. Be good at listening and getting inside the student's mind.

The process is iterative, going back to step 3, or possibly to step 1, until the student needs little help.

We start with the premise that step 1 is the skill we want the students to gain so they can solve problems as engineers and continue to learn on their own. There are other levels of knowledge to be covered, of course, such as nomenclature, equations, properties of components, and tools for analysis. But these are all lower levels of knowledge on Bloom's taxonomy of cognition. They are alive and well in every engineering course. The problem is that the study of nomenclature, equations, properties, and tools are covered almost to the exclusion of intuition, design, and discovery. And if a course begins with equations and algorithms, they tend to provide crutches that substitute for discovery and intuition. Most teachers will acknowledge that it's process rather than content that is important. Then why not teach the process of discovery and design? Because implementing the four steps above is more difficult than conveying nomenclature, equations, properties, and tools. So we chose to deal here with the part of teaching that needs the most improvement and is the most important in developing effective engineers. George Polya has provided examples of discovery in solving mathematical problems in his books "Mathematics and Plausible Reasoning (Volume I) and (Volume II)."

A teacher that is good at step 1—that can get inside new ideas and use them creatively to solve problems—would also make a good engineer. But to be a good teacher, he must go beyond problem solving and be able to instilling this skill in students. So (with apologies to G. B. Shaw) we can say that those who can, do, and those that know how they can, teach. Being aware of how we solve problems is not easy. The process is fuzzy and moves rapidly, with tenuous connections and alternative attempts. It's difficult to be aware of all the concepts we're using, and, if we are aware, do we know how we know them? So step 2 takes practice to do it well.

Step 3 has long been recognized as a tool in teaching. Socrates' name has been given to the method of teaching by using questions to lead the student. In recent times, George Polya has perhaps best advocated the use of questions in prodding students to discover solutions for themselves (see his book "How to Solve It"). Another way to promote discovery is to devise experiences for the students—homework, labs, and projects. Almost every course in engineering includes these elements, but the challenge is to design and order them so as to lead to a discovery experience—one in which the students uncover a surprise and gain insight. The exercises should neither give too much away nor leave the student stymied. Again, the best balance is achieved if the experience is tailored to each student, but this would require much time from the teacher.

How well have the first three steps worked? What needs revising to do a better job of imparting intuition and skills in discovery? Some of the evaluation in step 4 can take place in grading the homework and exams (if the teacher does the grading rather than teaching assistants). But the mistakes usually don't reveal the underlying misconceptions. To get to the root of the students' problems, it is essential to have discussions in which the teacher does more listening than talking. Because the student doesn't want to expose his ignorance, the teacher must put the student at ease and provide an atmosphere for honest exchange. When the student himself is not aware of what's troubling him, the teacher must probe with questions and use his imagination to guess the problem.

The evaluation is usually disappointing, so the teacher attempts to do a better job by revising his questions in step 3 or by gaining new insight himself in step 1. Perhaps he must prepare the student through some preliminary discoveries to provide background. With iteration, things improve, but always short of satisfactory results because time is short with the students. The aim is to do as well as possible in the time available, and this involves choices. Teaching intuition and discovery usually takes a disproportionate amount of time, so the teaching of nomenclature, equations, properties, and tools must be slighted to make room for discovery. But the current balance is so little on the side of discovery that it surely can't be the proper balance. With practice, the teacher becomes more proficient at the four steps, and the balance will naturally change toward teaching the skills engineers need most.