Rote Learning Vis-à-vis Physical Comprehension

During my tenure in Northern Nigeria, I taught in the Civil Engineering Department, Ahmadu Bello University, Zaria for eleven years. I taught hydraulics and fluid mechanics to the under-graduate students. One day, while I was in my office, a friend of mine came to visit me. Like I, he was a civil engineer, and worked in the Irrigation Division of Ministry of Agriculture in one of the States of North Nigeria. After the usual pleasantries, he started quizzing me about my teaching responsibilities and day-to-day experience with the students. Then he became serious and asked me if I understood the true meaning of the differential dy/dx. He was a good student in his college days. He said he could understand up to delta y/delta x, delta y= an infinitesimal interval of ordinate, delta x= an infinitesimal interval of
abscissa). but taking delta x to the limit of zero to compute dy/dx still confounded him. I knew that without understanding the true meaning of the differential term dy/dx, one could do all the calculus that one needed to do, getting correct answers all the time if no mistakes were made in the mechanical procedures, without physically understanding much.

We then talked about calculating the average velocity of a moving body, which was the ratio of distance traveled and the interval of time taken to traverse that distance, expressed symbolically by delta x/ delta t. From there, we moved gradually toward computing the instantaneous velocity by reducing the time interval to progressively smaller values. We comprehended that the process of progressively reducing the time value was effectively going toward the limiting value, dx/dt, when delta t actually becomes zero. Then the computed velocity becomes the instantaneous velocity; the ratio of delta x and delta t becomes the instantaneous value, i.e., dx/dt.

That also clarified the concept of average gradient of a curve between two neighboring points and its point value when the two points tend to coincide with each other. I am sure that my teacher had tried to explain the above procedure, although not quite in so much detail as best as he could do, and then later on everything became mechanical. The rote learning is indeed mechanical in the sense that you learn the various steps mechanically without understanding what each step actually means.

To many students, and the traditional teachers also, science is rather a boring subject because physical perception of the scientific material is not usually truly understood. It is up to a teacher to make science an interesting pursuit by explaining it with the help of examples from real-life experience.

Much of science that is taught in colleges and universities is a bundle of facts and a jumble of computations using calculus. Many students are usually weak in calculus because the bugbear of dy/dx stares in their faces all the time. And science which depends so much on calculus becomes insipid at best. The students take science courses for the reason that they are required in relatively lucrative scientific, engineering and technological jobs.

An extreme example of rote learning was that of a friend and colleague of mine at Engineering College, Lahore (in 1950s). He usually did well in examinations. He used to memorize everything including the applied mathematics also by rote. Let me give a bit of explanation here how the examinations were conducted in my days. In applied mathematics, our professor taught us how to solve various differential equations. He buttressed his teaching with a number (up to about 200) of numerical problems. These problems were typical and truly significant illustrating the practical side of engineering application. His notes and numerical problems did not change from year to year. He would select some 7 or 8 questions from those examples and set them in the examination question paper. The upshot was that anybody who had gained mastery of those numerical examples would pass the examination with flying colors. This friend of mine had memorized all those examples and their solutions by heart.

When the question papers were distributed in our final examination, he immediately stood up and drew the attention of one of the invigilators. He told him, “Sir, this question is wrong.” The invigilator asked him, “What do you mean and how do you know that this is wrong? You couldn’t possibly have attempted to solve it yet.” He said, “Sir, I know it.” The invigilator was nonplussed and rather brisk with him and told him to sit down.

True enough; after about 10 minutes, our professor walked in and announced a correction in one of the questions. It was the same question that my friend had pointed out to the invigilator. I don’t know if he had much of a conception of any thing that he had read but he secured a marginal first class in the final examination and that was quite impressive.

After coming to the U.S., I taught part-time a graduate course in engineering hydraulics at Wayne State University, Detroit, for several years. This was not a core course but was a supporting course for the students who majored in environmental engineering. There used to be some 10 to 15 students in my class. I lectured twice a week and each lecture was 2-hour long. I gave 5 minutes break at the end of the first hour. One day, during the break, a student approached me and started talking to me. He told me he had taken a similar course at the University of Michigan, Ann Arbor. I asked him why then he was repeating it; wasn’t that waste of his time and money? He said, “No, sir. The things I am learning in your class are quite new and they help me to understand what I had learned at Ann Arbor.”

I said, “What do you mean?”

He said, “You are explaining theory with real-life examples and that makes understanding the theory very easy. I think, I am getting the worth of my money and time in your class.”

It was quite flattering. However, this kind of feedback is important because the teacher feels reassured that he is doing the right things.

My full-time job was with the Detroit Water & Sewerage Department which has five very large water treatment plants in its water supply system that serves an area of nearly 3,000 square mile. It has the largest single unit wastewater treatment plant in the world. I used to construct numerical examples from the existing Detroit water supply system and the wastewater system with actual numbers taken from the existing data. For example, if I wanted the students to use their knowledge to compute the hydraulics of a sewer, I would select an existing sewer from the system, give them the appropriate numbers for the length of the sewer, its gradient, etc. and ask them to do the computations. For the hydraulics of closed pipe and pipe networks, I would select a segment of the actual network and ask them to do the required computations. For problems on centrifugal pumps, I would choose an existing pump from numerous pump stations of the Detroit system and give them the pump characteristics and ask them to work out the required computations. In this way, the students felt quite interested and involved thinking they were doing some real-life work and if in their practical life they were required to do similar work, they would know how to do it. Correlating lectures with real-life experience is very relevant and helps the students to develop interest in their learning.

The same kind of approach can be used in teaching any other subject. I had easy access to the real-life data which I would use in constructing practical problems. If such information is not readily available to other teachers, they should strive to contact the sources from where they can get it.

I was inspired to write this article by an interview of Professor Eric Mazur, Gordon McKay Professor of Applied Physics at Harvard, which was published in The New York Times (Using the ‘Beauties of Physics’ to Conquer Science Illiteracy, July 17, 2007). The interview was conducted by Claudia Dreyfus. Professor Mazur commented, “It’s important to mentally engage students in what you’re teaching. We’re way too focused on facts and rote memorization and not on learning the process of doing science.”

To a question: “Where were you educated?” Professor Mazur responded, “At the University of Leiden. In my first year, we started out as 72 physics majors. By the second year, we were winnowed to 11. Only those who could maintain themselves in rote memorization were able to continue.

I was one. But throughout my college years, I often thought of quitting, becoming an artist or a photographer instead. The lectures were deadening, frustrating. Only later, in graduate school; when I got into a laboratory did I see the creative part of science. It’s beautiful to design an experiment.” It’s equally beautiful to construct a working theory from the empirical information.