How to Improve on Mathematical Problem-Solving ?

From Yassine Lassoued

Solving problems is a skill that you can improve while solving problems. It is not a matter of quantity... Solving 1000 problems a month does not necessarily make you a good problem solver... However, thinking about how you solved a problem and trying to generalise the approach you used to solve more problems and to improve your problem solving heuristics is the key. There are many tricks and techniques that you need to develop in order to improve your problem solving skills:

- Ability to decompose a problem into sub-problems
- Abstraction
- Visual conceptualisation of mathematical concepts

One of my favourite techniques is scepticism. Sometimes it helps when you are asked to prove a theorem to try to find a counter-example to it. By doing so, and (obviously) failing, you may spot the key property (hypothesis) that is making it impossible for you to find such a counter-example. That is exactly where you should search for an answer...

From Fadil Habibi D

Short answer: Solve more problems!

Long answer:

In general, one cannot improve his problem-solving skill without solving problems. The problems should not be too easy that even he doesn't need to spend longer time that he usually spends for solving casual problems.

In principle, one need tool(s) to solve math problems. The tools may come in form of theorems, algorithms, techniques, Algebraic identities, and many more. The more advanced the problem, the more complicated the tool(s) or combinations of tools needed to solve it. If you really wish to be able to solve more advanced problems, learning those tools are usually mandatory.

From Sudarshan Diwanji

To improve on math problem solving you need to properly understand the problem and also understand the derivation of the formula which is used in the problem.
For example,
You need to find the area the area of a cirlcle.

1. Write down all given things like the lenght of the radius.
2. The formula for finding the area of a circle is =pi x r x r
3. watch some youtube videos and understand how this formula is derived.
4. Lastly, dont solve the problem completely but solve only till the concept of the question is cleared.Dont do calculations until nescessary.

When you are done solving some questions on the same topic , try and solve a HOTS(Higher Order Thinking Skills) question. You will get many of these on the net.