Good way of learning math

Question

In my secondary school, I have been copying the solutions of the questions I could not solve and I guess this helps you to memorize (not blind memorization, sending the info to long term memory). Do you think that this technique works in university studies or let say self-study? And have you tried that? Or do you think that it depends on the learning style of a person?

Answer 1

Personally, I think understanding why something works in general is much better than learning a solution for a specific question and being to reproduce that answer to a single question. As long as, in the process of copying these answers, you understand why they work, what identities they used, and the like, it'll be a very efficient method. But if you only learn the solution to that exact question, without thinking about more general things, you're not really learning.

Answer 2

One question I often ask myself in these kinds of circumstances is "how would I have thought of doing that?" or something equivalent. Another is "how did I miss that possibility?"

What I am trying to do with these questions is to uncover any mental blocks which are getting in the way of seeing the mathematical possibilities. Alongside technique and knowledge I find that there are ways of thinking which make a big difference.

The questions and answers on this site are a good resource for this too - if you look at some of the questions in familiar areas you will see people tackling them in different ways, and some of the answers will show where that thinking comes from.

But the main thing is to make sure you don't substitute the answers you see for thinking hard about things yourself. It is doing the work which improves the quality of learning.

Answer 3

It is safe to assume that it depends on your learning style. I tried your approach, I think many people kept some sort of informal notes. Now with the web, hyperlinks can help somewhat in the process. I guess to be successful in your study, some of the following could help:

1-Attempt to spend time to learn the basic principles of algebra and numbers. Understand the formulas and know very well how to apply them.

2-Use more than one source when you don't understand. In every subject you will find the complicated (some call it advanced) material and the easy to digest one.

3-Collect points that you find hard to master or where you often trip in a personal reference (looks like you have been doing this).

4-Question everything in moderation. I know a friend who refused to accept a formula and attempted to prove its false for a long time, he almost failed the main course.

5-Draw a line between academic requirements and personal learning adventures.

6-Find someone of the same interests and exchange ideas.

7-Try to look ahead when you are studying for academic success. I mean see what am I going to be learning the next semester?. Which books should I really read? Whom are the professors I should avoid :)

8- Work slowly but accurately and review your work specially in exams.

9- Don't get disappointing if you can't get something. There are many things that are hard to get.

Good luck.