Many people have asked me this question "how to do well in Math"?
Well I don't have a straight forward answer, during lesson I try to observe the student's way of handling math question and I try to correct their thinking process towards thinking from first order principles and learn to be more mindful to reduce carelessness.
But take a step backwards, another way is simply to be more consistent in your effort towards the subject. Many articles have been written about this, "Excellence is a habit", "the winner is the guy that's most consistent" etc.
I have my own term for this, and it is "accumulated advantage", akin to compounded investment returns.
The basic idea is this - You must make an effort to improve week on week, no matter how small the improvement is. Build upon the layers and layers of time and effort, don't get overly distracted by other deadlines or commitments - it's all about discipline and time-management. Eventually you will accumulate a critical mass of knowledge and you will get there.
To demonstrate the concept, imagine two students studying over a course of ten weeks:
Both students starts at the same level 1;
Student A makes an effort to improve 3% week on week;
Student B varies his effort every week - some weeks he puts in more, some weeks less, on some weeks he even regress as he ignores the subject totally in preparation for other items, but his total effort across ten weeks will still sum up to 30%.
Across ten weeks, their accumulated score will look as such:
Notice that student A may lag at first, but on week 5 he's ahead and stays ahead all the way till end of week 10 (a term). Now if this narrative is extended across a year, his lead will only extend further.
So which student do you want to be?
This post is for the sake of illustrating the concept of accumulated advantage, I will address biological issues like sleep and time management in a future post.