Where I grew up, we were taught math the hard way. We HAD to struggle through problems.
No matter how complex or convoluted the problem was, it was almost a given that students would stay up – until they had solved it. ‘Fun’ as part of the learning process was not a concept that teachers in India were familiar with.
While I was not happy with the teaching methods, it did help me in two ways :
- It promoted a deeper understanding of the underlying concepts – some problems could only be solved by re-grasping the basics.
- It helped build ‘tenacity’ in problem-solving. This was a skill that would help me in any and every profession.
Math is a lot like golf in this regard – you can only learn by doing. You can read all you want – but your understanding will only be superficial. The ‘doing’ in math consists of solving as many problems as possible.
Computer Simulations and the Learning Process
I used to think that Physics was the same way. Solve a bunch of problems – and you will gain insight into the underlying physical concepts. It wasn’t until I got into computer programming that I discovered another way to gain insight into physics.
Write a computer simulation – as detailed as you can make it. A computer program requires every step to be meticulously spelt out – leave out one step – and the entire program fails. This helps expose any ‘gaps’ in understanding of a problem.