How to improve at Mathematics?

In summary, the conversation focuses on the topic of improving math skills and problem solving abilities. The individuals suggest practicing exercises, applying concepts to real life situations, and using strategies from books such as "How to solve it" by G. Polya and "Thinking Mathematically" by John Mason. They also recommend trying to solve difficult problems and deriving formulas on your own for a better understanding of math.
  • #1
Sumanyu
10
0
Hello,


I've been lurking around this forum for a short while; reading questions, responses and other intellectual goodies...

So far, I have a positive outlook on this community and I hope I receive insights regarding my trouble in math...

I'm not 'strong' in mathematics.. yes I did receive 100% on a math 10 provincial and my current mark is 100% as well.. however, I don't feel I'm necessarily strong at problem solving or applying learned concepts to real life..

I need some insights as to how to improve at math at a fast rate... I know practice is one of the key elements; but, I don't know how to practice..


Thanks in advance!
 
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  • #2
Hi Sumanyu!

I think the most important part in learning math is doing the exercises (like those found in a textbook).

- An exercise test your knowledge, you soon find out if you should go over definitions and theorems again.

- Applying concepts yourself helps greatly in memorizing them.

- Creativity and assertiveness are challenged with the more difficult exercises.

- Problem solving skills are improved as you learn strategies and tools.
 
  • #3
The short book "How to solve it" by G. Polya would be a good investment. Occasionally come back to it. Summary below already gives a lot.

http://www.math.utah.edu/~pa/math/polya.htmlbook [Broken]
 
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  • #4
Thank you yyat...

I haven't had luck at finding difficult exercises... I can do all questions in the textbook...

The issue is, I'm not good at solving contest questions... Moreover, I'm quite slow at those type of questions...



Thank you epenguin as well..

I've already read the book by G. Polya =)

I try to use the strategies he has listed... so far they've helped me improve; however, I just need access to material for practice or specifically 'how to practice'
 
  • #5
Terry Tao wrote an interesting book on the subject, base around problems for you to solve. You can download the pdf from his site if I recall.
 
  • #6
maze said:
Terry Tao wrote an interesting book on the subject, base around problems for you to solve. You can download the pdf from his site if I recall.

As far as I know you can only view sample chapters, here is the link:
http://terrytao.wordpress.com/books/solving-mathematical-problems/" [Broken]
 
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  • #7
hmm, looks like he took down the full pdf off the site.
 
  • #8
ok. you got lot of advice already. here i will tell you few points which made change in my maths interest.
--> Try to solve the same problem in different ways even though you got correct answer.
--> try to substitute known and simple values in order to solve the equations.
 
  • #9
I recommend Thinking Mathematically by John Mason. It really trains your problem solving skills.
 
  • #10
Try doing problems which are higher level than you actually know how to solve, and then give a serious try to solve them. Learning real math is not about learning to solve every problem but learning to think in the correct ways.

When you do operations you should not think "I do it like this since this is how I have always done it before and it always gave me points", you should think "I do it like this since according to the given axioms it is the truth and the only truth".

Don't learn to derive things by reading the derivations in a book, learn to derive things by deriving them yourself, most formulas are quite easy actually. Sometimes you need a few pointers but you can almost always do 90% of the work yourself and actually deriving things yourself gives you incomparably more understanding of math.

For example start out with the basic operations +- and maybe */, then sit down and derive every theorem and formula you have learned in math without using any book. Add axioms as you see fit and so on. And by deriving I mean that you should do a proof that makes you certain that it is true, not to make certain that you get points on a test. Then when you are done, get a book and validify everything to make sure it was all correct, and understand which thinking process went wrong at the points you errored and then correct that process.

Imo the schools teach math in the wrong way, they try to get as many to pass as possible but they don't care at all about the kids understanding so roughly everybody coming to the higher maths got a really bad foundation to stand on.

Anyway to get good enough to do the really hard things you just need really good understanding of the fundamentals.
 

1. How can I develop a better understanding of mathematical concepts?

To improve at mathematics, it is important to have a strong foundation of basic mathematical concepts. This can be achieved through consistent practice and using different learning methods, such as visual aids, hands-on activities, and working with a tutor or study group.

2. What are some effective study strategies for mathematics?

Some effective study strategies for mathematics include breaking down complex problems into smaller, manageable parts, practicing regularly, and reviewing material frequently. It is also helpful to identify and focus on areas of weakness and seek help when needed.

3. How can I improve my problem-solving skills in mathematics?

To improve problem-solving skills in mathematics, it is important to understand the problem thoroughly, identify the relevant information, and apply the appropriate formulas or methods. It is also beneficial to practice solving various types of problems and to approach them from different angles.

4. What role does practice play in improving at mathematics?

Practice is crucial for improving at mathematics. Regularly practicing mathematical problems helps to reinforce concepts and improve problem-solving skills. It allows for the identification of areas that need improvement and helps to build confidence and speed when solving problems.

5. How can I stay motivated to improve at mathematics?

To stay motivated to improve at mathematics, it is important to set achievable goals and track your progress. It can also be helpful to find real-life applications for mathematical concepts and to celebrate small successes. Additionally, seeking support from peers or a mentor can provide motivation and accountability.

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