Today I identified a funny teacher in me. My younger brother Thileepan had been preparing for his semester exam. He found it difficult to go through the so-called Fourier Series. He approached me to help him out. I started going through the stuffs that I had learned/studied exactly 6 years back in my bachelor. I could see the difference in grasping now and then clearly. Though I dived into computer science , I still could pick up the differentiation and the long 'S' , integration.
After gone through the stuffs, I asked him to sit and clearly decided not to preach the same in the book. The way the lesson started was really due to the impact of the Tamil Historical Novel - Mannan Magal[1]. Just by day before yesterday I finished reading the novel. The hero, Karikalan, brave and wise warrior of Chozha Emperor stayed in my heart.
"Thileep now you are in trouble that you should attack the Fourier Series in 2 days you have got. What you need is strong weapon(s), conditions suitable for attacking and finally a strategy to attack". He answered 'No' for the questions I have shot: " Periodic functions?, Continuous functions? , functions?". Now I realized why he complained his mathematics teacher ;-)
I casually listened all his "Nos" which I thought really make him comfort. Then without explaining what is function, cts., function , etc. straightaway jumped into battle field. "Dear brother here is your weapon: Euler's Formula , this is perfect and sufficient conditions to attack : Dirichlet's conditions and finally apply this strategy : Bernoulli's formula" . He then ensured that he understood the main idea.
What was remaining? Fundamental stuffs and tricks and tips. Started helping him to understand functions , continuous, discontinuous, periodic functions with diagrams. I tricked him with a test : " When y = mx + c , where m is the only constant then y = f ( ? )". He did answered correctly " f ( x, c ) since y changes w.r.t x and c as well ". Then discussed left , right limits to explain discontinuous functions. Then the importance of intervals and period. Then after explained about why on earth we need Fourier series asked him to start solving simple problems.
As I expected Integration and Trigonometry attacked him back. So now problem by problem he is asked to learn the tricks for integrating and for using trigonometry formulas. I saw him happy ! Me too happy !
But still lot to go through and also there are people who will only understand when we teach bottom to top. Nature of the problem also influence a lot. Teaching is not that easy truly. It is student's responsibility to understand his very own philosophy of understanding. Then how teacher teach will not bother him a much.
- Peramanathan Sathyamoorthy
[1]. Mannan Magal
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