Practical vs. Theoretical Problems in Research

By KP Mohanan

Practical vs. Theoretical Problems in Research

By KP Mohanan

"The world’s top 50 thinkers 2021: the winner" in Prospect Magazine (1 Sept 2021) opens with the following remark:

In pursuing questions about how our bodies build themselves from a fertilised egg, Palestinian biologist Jacob Hanna is searching out fundamental truths about the human condition—and making discoveries that destabilise our concepts of what we are and how we come to be. Although he is—for now—far from being a household name, his field of enquiry is thus a fitting one in which to find Prospect readers’ surprise pick for the world’s top thinker of 2021." (https://www.prospectmagazine.co.uk/world/the-worlds-top-50-thinkers-2021-the-winner)

The following write up is an attempt to summarise my thoughts on questions and problems in research, prompted by that opening, with the hope that research students and their mentors would find it useful.

Research Topics, Research Questions, and Research Problems  

When asked to submit a research proposal, most novices respond with a broad topic specifying their area of research. Thus, they may say that they are working on ‘prime numbers’, ‘topology’, ‘black holes’, ‘non-Newtonian fluids’, ‘the behaviour of butterflies’, ‘plant cognition’, ‘design thinking’ or ‘freewill’. These are areas in which the student is interested in.

The starting point for a research proposal is not just the area of research, but a problem or a question whose solution or answer the researcher seeks to find out. Quite often, when I ask, “What is the question or problem whose answer or solution you wish to find out through your research?” I tend to get a blank look, because the student has not thought about it, or is not even aware of the importance of engaging with that question.

Given that during their primary, secondary and tertiary education, the only questions and problems that students in mainstream education in India are exposed to are assessment questions/problems, and they have not had the experience of formulating a question/problem whose solution they wanted to find out, the blank look of incomprehension from Master’s and PhD is perfectly understandable.  When an examiner or teacher in a classroom asks an assessment question or sets an assessment problem, (s)he knows the correct answer/solution. The purpose of the question/problem is to find out if the learner already knows the correct answer, or can come up with the correct answer in a very short time (say, two minutes in an MCQ). The time allocated for the student response does not give the student an opportunity to think.

In contrast, a research question/problem is formulated by researchers, not an examiner or teacher. Its purpose is not assessment but shaping their own subsequent process of research. A researcher comes up with a question/problem because (s)he wants to find out something that (s)he does not know. The process resulting from that question may take a few months or years to come up with an answer/solution, not a couple of minutes, or even half an hour. In a similar manner, the purpose of an inquiry question/problem set by a teacher in a classroom is to trigger the process of inquiry and the resultant learning in students, not to assess what the students have already learnt.

When students are used to assessment tasks and are not used to inquiry tasks, the questions that they themselves ask in a classroom would be those for which they expect the teacher to know the correct answer. Mainstream education in India does not include teachers setting inquiry tasks, so it would be unreasonable to expect research students to come up with research questions/problems.

This state of affairs in our system of education, coupled with not thinking for even thirty minutes before responding to an assessment task, whether in a classroom or examination, has a deadly consequence for the growth of our students.  In the long run, the habit of responding to questions/problems without thinking, with no experience of formulating questions/problems to find out something that one doesn’t know, inhibits the human potential for thinking, and creates a population of adult humans (including those in teaching and research) who are incapable of thinking.

Questions vs. Problems  

A research question must be formulated as a yes-no question or a wh-question. The answer to a yes-no question is either a yes or a no. Examples of such questions include:

  • Is there a correlation between the applicants for IITs and IISERs and the socio-economic class of their parents? 
  • Do straight angled triangles exist?
  • Do fruit flies have minds?

In English, a wh-question begins with a wh-word: when, where, which, what, why, ahow, and so on. (In how, the w and the h are inverted and separated by an o.) It has many answers which cannot reduced to be a simple yes or no. Examples include

  • What is consciousness?
  • What makes students hate or dislike mathematics?
  • How do fungi communicate?
  • Why is it that taxa which have compound eyes also have six legs and vice versa?

In contrast to research questions, we state a problem by specifying a state of affairs that we regard as undesirable or less than desirable, and why it is undesirable or something else is more desirable. The solution to a problem is something that removes the undesirable state of affairs or makes it less undesirable or more desirable.

For instance,

  • a leaking tap is a problem because it is undesirable, and the solution to the problem is something that removes the leak.
  • Infant mortality is a problem because we regard it as undesirable, and a solution must offer a decrease in infant mortality, which is desirable.  
  • Societal inequality of opportunities between men and women is an ethical problem because it is ethically undesirable, but biological inequality of height between men and women is not an ethical problem because it has no relevance to ethics.   
  • Knowing why castor oil is an effective cure for lung infection is a problem because ignorance is an undesirable state of affairs. For the same reason, not having a proof for Goldbach’s conjecture, and not having a mathematical formalism for causal logic are problems. 

Practical vs. Theoretical Problems

Intuitively, most of us recognise a distinction between practical problems and theoretical problems. For a bachelor’s student, not having a boyfriend or a girlfriend or getting poor grades in their course work is a practical problem, but not having a proof for Goldbach’s conjecture, or not understanding the shared concept of the arrow symbol ‘’ in propositional calculus, in chemical equations, in formal grammars, and in category theory are not practical problems. What exactly is a ‘practical’ problem—what is called an ‘authentic’ problem in the education literature?

I would like to suggest that the distinction does not lie in the intrinsic nature of the problems, but in the nature of the way in which we see it and respond to it. A problem is perceived by knowers as practical if it is relevant to something that they are preoccupied with, and expect the solution to be advantages to the situation that they are in. Thus, for a house owner who contacts a plumber, a leaking tap is a practical problem. For students, any problem that has the potential to appear as an assessment task is a practical problem. For the employees of an organisation, any problem that is relevant to the kinds of activities whose successful solution has an impact on their career is a practical problem.

And chances are that professional researchers in mathematics would perceive the unsolved problem of not having a proof for Goldbach’s conjecture is a practical problem. As a result, the offer of helping them to develop recalcitrant mathematical problems is appealing to a novice in mathematical research, but not to an undergrad student, or a CEO in a profit making company. Conversely, the offer of help to increase the capacity to solve the problems of reduced profit would be appealing in the commercial world, I have zero interest in that offer.

In research, the practical problems that others face have the potential to develop into theoretical problems. For mathematician Leonard Euler, the seven bridges of Konigsberg was a practical problem because it was set by a king. But in order to solve the problem, Euler constructed what is called graph theory in mathematics, which helped him to solve the practical problem. (see https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg). Pascal and Fermat created probability theory to solve a practical problem of ‘games of chance’ in gambling (see https://www.aps.org/publications/apsnews/200907/physicshistory.cfm). A medical researcher may create a causal theory of cancer to solve the practical problem of curing cancer. And a theoretical linguist working in google may start working on a theory of semantic representations to solve a practical problem in Natural Language Processing, Machine Language Translation, or Machine Learning. 

Unfortunately, our current system of mainstream education does not help researchers to solve practical problems by constructing theories, because the curriculum does not have a provision for courses or parts courses designed to help learners develop the capacity to construct and evaluate theories  (Watch “The Art and Craft of Constructing  and Evaluating Theories” at http://www.thinq.education/articles/17)  The solution to practical problems must await a different system of education, and creating such a system of education is a practical problem.

 

Photos by Pawel Czerwinski on Unsplash.


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