Disclaimer: The observations made in the following article are my own personal observations as a student of Mathematics, however they are not exhaustive. The intended readers of this article could be Aspirants / Math's Lovers or Students.
I draw the experience mostly from my own endeavor , where I qualified IIT twice ( AIR 1252 (JEE'05) & AIR 3462 (JEE'04) ) primarily due to mathematics; Olympiad; Secured a single digit All India Rank in Ramanujan Memorial Mathematical Contest (Conducted by Ramanujan Society) . I believe , in my humble capacity, I can make some contribution for the students fraternity , in the subject. [ Disclaimer Ends].
The
nature of subject is bit different from other two subjects that is Physics and
Chemistry. Mathematics at times is bit abstract. Situation becomes more complex when a student tries to extend his/ her , rote method of learning, nurtured by the Indian Schooling system in last 10 years to IIT JEE kind of paper. Following are four common mistakes made by aspirants , with their possible wayouts:
Mistake1: Whenever you see a problem , you approach it by "which formulae can I apply"? This whole notion of "which formulae can I apply?", is the biggest barrier in understanding Mathematics. The possible wayout from this menace is to understand the derivations involved in the process, by going to its core. By doing so, a student not only gets a better insight on the subject , but would be in more comfortable situation in IIT paper, where examiners come up with new problem by tweaking here and there in derivation stage itself.
Mistake2: Suppose you open a book of mathematics (say Hall & Knight , Loney or Maron) and you read it like a novel. During this, you feel that-"yes this makes sense, this is obvious" , etc, and you find that you have understood the concepts, which is exactly not the case!
In Maths & Physics, problem solving is the key and only when you start solving the problems based on the concept which you just read, then only you will be forced to think about the concept and its application. In this process , you are bound to make mistakes and then you have to read the theory again or consult your teacher (if you have one). For those aspirants , who undergo the organized training or caching for these exam, the theory part is mostly done by the instructor. Still ,if you have time, I would suggest , to read theory from the text books.
Mistake 3: Say you solve a problem and somehow you reached to its answer ( this phenomenon is more pronounced , in case of objective exams), but you are not very sure about each and every step involved in it, eg- why am I opening the modulus? Why am I keeping these limits on integration?, etc. There could be many such ambiguous steps in the solution but once you get the answer, you feel very happy and you move on! This is the biggest trap. Answer is just a means to an end, not an end in itself...the end is the proper understanding of the topic.
Ask yourself, Did you understand every step involved and the logic behind it? If no, then take 15 minutes extra to do brainstorming on the problem again and try to understand the steps involved. If required, read the concept / theory again or consult the teacher.
Mistake 4: "Not Reinforcing or Repeating"
What I mean by this, is, lets say you get a really tough problem and you spent say half an hour and finally you managed to solve it, with reasonably good approach. At that juncture, in your mind, its like a thin / half baked brick wall, which would collapse with little gentle push. But you require a strong and sturdy wall. Meaning for a tough problem, even if you get the answer, don't stop there.
Solve the same problem again, I repeat, same problem again, after couple of days and believe me on this, mostly likely , you will make a mistake again, but this time your understanding will be much better and deeper ( like a 2ft thick sturdy wall!) . In a nutshell, you have to reinforce yourself by solving same thing again.
I hope this helps.