Explaining Concepts through Empirical Examples

 

Explaining Concepts through Empirical Examples

Conceptual learning is the buzz word in educationist circles. Yet, ask any of them to explain the concept of conceptual learning, their eyes bug out.

Now, I do not know what conceptual learning is. Yet, I would venture to offer some empirical examples, and how to connect them to concepts is a task I leave to you. I hope that some of my readers would eventually figure out how to teach concepts.

I was in perhaps the eighth or ninth standard in high school, when we were fed the myth of Archimedes jumping out of his bath tub and running naked on the streets when he figured out what came to be called Archimedes Principle. It was still a myth, though forgotten, in my first year of engineering studies; but in a regular show of one-upmanship amongst us hostel-mates, the truth dawned.

If a block of ice, floating in water in a beaker, melts, will the water level go up, down, or stay unchanged? I worked out the answer to the problem taking some typical numbers etc. It turned out the water level would not change. I reworked the equations and the result, to my surprise, ended up being the Archimedes Principle!

In soil mechanics, there is the concept of specific gravity in saturated condition and also in submerged condition. These two are relatable through, you guessed it, Archimedes Principle! With this explanation I stunned a young member of the faculty and almost stunned a very senior member (and she did not acknowledge it, as you may understand why). This was truly a  conceptual explanation of the equation used by foundation engineers.

In the post-graduate course Design of Metal Structures, an open umbrella came to my rescue about teaching the phenomenon of shear lag. One day I was looking at the open umbrella in the balcony, left there for the water on the fabric to drain out or dry off, I noticed the edge of the fabric was curved inwards. Then my mind jumped to tents and how the fabric at the edges tended to create an arc. Though I could derive the mathematical equations to be applied to the phenomenon clearly (if the students understand the concept of taking limits in calculus), that evening I knew how to explain the concept through a practical example (this part of this post is a repeat in this space). Here, an image helped explain the concept.

If you have heard about breakwater enabling a ship to be steady at a wharf or a jetty in a port and also about diffraction in physics lab, you could understand the following near-parallel. When light goes through two tiny apertures spaced slightly apart, you get wavelets that interfere with each other and on a screen you get bands of brightness and darkness.

The navigation channel in a port is between the ends of the two wings of the breakwater (this “opening” to the port could be as far away as a couple of miles or more from the shore). The sea waves pass through the navigation opening and the waves from the two tips of the breakwater interfere between and among themselves and are severely attenuated. What you get is not a set of bands of high and low waves, but completely attenuated waves, and the anchored ships at the wharfs/jetties are still.

The two phenomena, with light (in the double slit experiment) and sea waves in the port could be taken as somewhat parallel, conceptually, as both involve waves interacting with one another.

In a sophomore course in structural analysis I taught, I claimed and showed that a beam can be thought of as a truss and vice versa. The idea is conceptual, of course, and my demonstration was empirical.

This was taught to me by a German structural engineer whom I consider my Godfather in the subject. Truss or a beam, names do not matter. What matters is how the forces “travel” in the structure and whether we have provided for these to be carried. How we assume the structure to behave is of paramount importance. If it is as a truss, provide for compression/tension; if as a beam, provide for bending and shear loads. Trusses are likely to be lighter but require more depth.

As an engineer, one balances what is demanded with how it can be provided. So, at the beginning of a project, check conceptually what the better option is likely to be. Only after that, one should get into the detail.

There is a topic in the course Engineering Mechanics in which the topic Several Connected Bodies (only static) is to be taught. All the books and all the members of faculty everywhere teach this topic through pulleys. I do too, but introduce it through the actions of stunt people in movies! When they jump off a height, their body parts–feet, calf, thigh, pelvic, torso, shoulders and arms, head–do not come to stop at the same time. Instead they come to stop progressively (as listed above). These body parts are indeed several and they are connected! The concept is best described, in my opinion, what the students can experience it, if they dared to jump off the table, for example. This is empiricism at work that explains the concept.

I can cite a dozen more such instances, but I will stop. What I have tried to show and believe that I have done, is that concepts are not in a Platonic realm, accessible only through the mind, but real life and down to earth demonstrations can be made use of to develop concepts. Once this way of thinking matures in a student’s mind, it would only be a short while before she can conceptualize something without recourse to empiricism and possibly in terms of what she may know in an adjacent area.

Raghuram Ekambaram