As a teacher I am often asked this question: When it comes to learning (and teaching for that matter), should more focus be placed on theory or application? In other words, which approach is more fruitful: Considering specific applications (‘problems’ in technical jargon) as vehicles to understand the fundamentals or developing theory for the express purpose of handling applications?
A word of clarification is in order: this is by no means a this-or-that question. Of course, both the fundamentals and their applications are important in any subject area. The issue is about where to place each category in the overall scheme of learning. More than giving importance to one at the cost of another, it is a question of the best way to approach learning itself.
In every semester one comes across students who claim that they are very good at theory but for some unknown reason they cannot handle applications. On the other end of the spectrum are those that I like to refer to as ‘problem-specialists’. These are students that are very adept at solving problems (as long as they do not deviate too much from set patterns). Their difficulty is that they are stumped as soon as the question deviates from the template that they are used to. To this category belong a large proportion of students who perform exceptionally well in their SSC/HSSC exams, pass university entrance tests with flying colours, but suddenly start having trouble the moment they are required to do any out-of-the-box or abstract thinking in the university.
The fact of the matter is that theory and problems, principles and applications are two sides of the same coin. If somebody does not know how to apply abstract theory to concrete problems, then it can be safely concluded that he does not know the theory, no matter what he likes to tell himself. Abstract thinking has its own joys but real life presents one with concrete problems. In the technical domain, theory for the sake of theory is quite useless, unless it can be applied successfully to those problems. The ultimate test of understanding of fundamentals is how one handles applications.
This much is quite obvious. What is less obvious (judging from the vast numbers who err in this regard) is how to go about learning any subject. Many try to learn theory from applications, which is a big mistake. You could solve hundreds of problems and start believing that you have figured out the underlying principles but suddenly come across a problem that completely exposes your lack of understanding. It is undeniably true that the proof of the pudding is in the eating, but one tries to figure out the details of the recipe from the taste of the pudding at one’s peril.
The problem (as far as most of our students are concerned) is that where applications are considered interesting and worth one’s efforts, theory is thought of as boring and lifeless. Having taught undergraduate and graduate students for more than a decade now, I know for a fact how horrified our typical student is of the very thought of grappling with theory. He would much rather solve innumerable problems as a ‘shortcut’ to understanding the fundamentals. It is incumbent upon us teachers to show him that he can not only have a much clearer concept of the fundamentals if he reverses his approach but that he only requires to put in a fraction of the effort that way.Â
Theory is abstract and therefore typically requires a bridge before it can be applied to concrete situations. But it remains supreme, for it remains relevant at all times. Applications are no-doubt important, but they keep changing, some even getting obsolete with time. But the fundamentals remain relevant. Therefore, it is a waste of time and effort to try and figure out the fundamentals using the many problems found in textbooks. It is the applications that must be understood in light of the principles and not the other way around.
If one is to avoid discontinuities and inconsistencies in one’s picture of the world, one must cultivate the habit of thinking in terms of fundamentals. Theory, if clearly understood, will help one deal with any number of applications. Trying to figure out the fundamentals from specific instances, on the other hand, will never let one construct a consistent and coherent mental picture of the world.
Some readers may be wondering what I am talking about when the fundamentals themselves have been formulated (or confirmed) by observation and characterization of concrete instances. While I agree completely, I would still recommend focusing more on the fundamentals. Unless you happen to be a Newton or a Faraday; in which case you have a valid excuse to focus more on specific instances to try and come up with your own laws.
The problem (as far as most of our students are concerned) is that where applications are considered interesting and worth one’s efforts, theory is thought of as boring and lifeless. Having taught undergraduate and graduate students for more than a decade now, I know for a fact how horrified our typical student is of the very thought of grappling with theory. He would much rather solve innumerable problems as a ‘shortcut’ to understanding the fundamentals. It is incumbent upon us teachers to show him that he can not only have a much clearer concept of the fundamentals if he reverses his approach but that he only requires to put in a fraction of the effort that way.
