I teach in a tertiary school that believes in a pedagogy that Maths should be learnt by Socratic question-and-answer, in other words, by thinking about the meaning behind mathematical patterns.
When I started teaching using this methodology, I was truly fascinated by it. Because it is so revolutionary and refreshing – no more drilling and solving problem sums and applying formulas without knowing how they come about. This learning by questioning method truly rekindled my interest for Maths.
After 5 years of applying this methodology in teaching, I recognize, however, that it does have its limitation. If a student is weak in the fundamentals, for example simple algebraic manipulation, or indices, or trigonometry, he cannot benefit much from the question-and-answer approach. He will simply get lost in the maze of questions. Or he may be able to understand the line of questioning and the logic behind it, but is not able to apply when a question comes up. It renders him a great audience but an ineffective participant.
I am starting to conclude, that if one has to benefit from the question-and-answer based maths, he has to be thoroughly drilled in the fundamentals first. He cannot be spending five minutes to think about how to solve a linear equation, but it must be like a reflex action to him. Like how I jokingly tell my student, that if I wake them up in the middle of the night and ask them to solve an algebraic equation and they can do it, it means they’ve succeeded in mastering the technique.
Drilling in maths has a bad name nowadays because of the tediousness and the unwillingness involved in doing it. But I believe drilling can be peaceful and satisfying and even addictive. You just need encouraging folks to do it together with you – as in study groups, and have timely and occasional guidance from a teacher so that you do not get stuck all the time.
It’s like Karate Kid being asked to hang the coat a thousand times. It was tedious, yes, but without it he cannot move on to learn greater stuff. There is no shortcut. That is the truth of life.
And I am glad that the master – played by Jacky Chan – told Jaden Smith his disciple why he asked him to repeat the drill so many times. A student should always know why he is asked to do certain things and do it willingly.