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I realize that my math learning go wrong way.

Wikipedia says math is finding pattern, formulating conjectures, and proving it. but my math learning didn't focus on them.

memorizing formula doesn't mean to improve ability for finding pattern.

actually I tried to find pattern on Rubiks cube and 15 puzzle. but some of elements to make good study are missing.

one of them is achievement. I can't make any achievement since it is too hard for my level. I can't find many patterns and solution except only intuitive ones from Rubiks cube and 15 puzzle.

I don't have many experience on real math but have only curiosity to motivate myself.

the intention of this post is to get some hint where I should start from. I think there must be easy activities. do you have any easy activities suggestion?(easy enough to find pattern and solution so I can feel achievement)

I expect easy activities + motivation => put them in practice => achievement => immersion => next activities

should there be any error or wrong point of view, please let me know. thanks!

this post might looks vague and seems meaningless to answer. I don't wish a painstaking answer. I will be appreciated with just little hint.

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Since you are interested in the Rubik's cube, I'd suggest starting with [group theory](en.wikipedia.org/wiki/Group_(mathematics%29). Also you may be interested in the A* algorithm which can be used to solve the cube and the 15-puzzle. –  Dan Brumleve Dec 15 '12 at 7:26

3 Answers 3

You are right - the only way you can get better at problem solving is by solving problems. But you don't have to dive in to very sophisticated problems right away.

Try searching Amazon or elsewhere for books on math puzzles. Maybe you will be able to find a similar book at a local library. Pick one that you think will best fit your math & language abilities and work your way through some of the exercises.

If any of the problems captures your interest, investigate it more thoroughly. Write down questions as you think of them. Mathematics is as much about discovering questions that deserve answering as it is about actually answering them.

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Check out artofproblemsolving.com - it has a wealth of competition-oriented math problems, and identifying patterns is key to solving a lot of types of problems.

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Math is a huge modeling system. It is a formulation of real life problems and their solution, and organizes the way of thought even when they can't be so readily quantified. Wikipedia is right, it is about finding a pattern in the problem to structure and formulate it in some form. It is mostly the intuition that helps see what is behind the problem and it comes with exercise.

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