Suppose you have already been taught the theory
on certain topic or you have studied that from some sources. Now you are
practicing to solve some problems. Imagine two scenarios. In the first one, you
are taught a method to solve problems and few problems are practiced. You learn
a method. Another method is taught to solve another type of problem and thus
you learn another method. This way you solve many problems, and you also learn
many methods of solving them. Now, if a question is given to you, you may try
identifying a suitable method from all the methods that you have learnt to solve
such questions and then apply that method to solve that. This is quite a common
way of doing bad in Mathematics as one can select an unsuitable method to solve
a question.
In the second scenario, you get a problem
and you yourself try to solve this. If you are able to solve this in one or two
attempts, you learn something. But if you are not able to solve this so easily
and keep trying that yourself in various ways, you learn many aspects of
theories related with that problem. And as you get involved more and more in
such problems, you keep adding new dimensions to your thinking and analyzing
capabilities, you learn new approaches and also develop a very important
capability of finding innovative and elegant solutions to problems on your own.
It is a kind of organic learning, and it provides significant edge over the
other approaches.
Self-preparation is the key because it
allows your thinking process to get strengthened in natural way. It develops a
capability in you to devise your own method by utilizing your concepts. No
doubt that assistance is needed at some of the occasions. Also, some of the
experts at various places have developed exceptional expertise in their field,
and it is wise to take benefits from their expertise. Interacting with other
students with similar aim is also needed. These facilities you get at some of
the coaching centers. But they are not complete substitute of self-preparation.
It is a must to have your own control over the preparation. You are an
individual different than others in many aspects. You should take inputs from
experts, you can join regular or crash courses for coaching, but despite all
these, you should have your own plan and the assistance you take should be on
the basis of your evaluation of your needs. You must have time to do
self-preparation, pursue your plan and take control of your preparation.
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