Humans are problem solvers. We face a problem or a difficulty and immediately someone somewhere decides to do something about it, to surmount the problem. Having said that, it is surprising to see that, hardly any of us completes our formal education with anyone having told us what problems solving actually entails.
Many a times, we look around for the solutions when we could be significantly more adept at finding solutions to problems had someone simply given us an approach to problem solving.
Here is a fourfold path to problem solving! The metaphor of a journey is used in this article. And we will assume a problem in Mathematics or Science (this approach can very certainly be used for any kind of problem).
1. Defining the start point and end point (departure point and destination)
When we start any journey, we need to know where we are to begin and where we want to go. In the context of a problem, the starting point would be the information or data that is given to us in the problem. Remember that, at times, the data may not be in consistent units. Making them consistent is important, much like ensuring that you have connecting flights at every stopover. Similarly, the ending point is what we have been asked to do in the problem, perhaps evaluate some quantity or prove something.
2. Identifying the journey path
Having determined the start and end points, we must answer the question, “How do I undertake this journey?” What concepts link the data to what the problem asks us to find? This is like ensuring we are not planning to cross the Arabian Sea on a bicycle! Nor even with a row boat! Or wing it for water in a desert. We must choose the correct concepts. And the tools should be powerful enough for the task at hand, but not too powerful as to obscure the subtleties of the problem.
3. Going for it
Once it is determined how we will undertake our journey, we can proceed with it. This is most often mathematical manipulation as required by the concepts we have chosen to use. Those who are skilled with mathematical manipulations will find this task easy while others may struggle - much like a frequent flier scarcely feels a flutter while taking off or during turbulence while a first timer might even need the handy paper bag!
4. Reading the signs
If you are travelling to Egypt but disembark to a blizzard would you not have a nagging feeling that the plane was diverted? The same is true of any problem. Having performed the necessary mathematical juggling, it is important to ascertain if the answer makes sense. Is it reasonable? If I end up with negative mass or a probability greater than 1, it should make the warning bells ring. If the answer is reasonable, then in all likelihood the problem has been solved.
Very often students jump to step 3 because step 1 is considered pointless or a bore, while step 2 has little action! However, as Einstein said, “The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill.” If you are able to formulate the problem (steps 1 and 2) and develop good mathematical and experimental skill (step 3) then almost all problems will unravel before you and step 4 will simply involve taking in the breathtaking beauty of … well it’s your journey, isn’t it?
Article provided by
ClearConcepts, an Education Services company focused on providing very high quality training for IIT JEE/ AIEEE entrance exams. ClearConcepts can be reached out in Bangalore on 9901710000. To know more, visit http://www.clear-concepts.in
