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So my question simply is "What is the best method to make sure you retain what you have learnt?"

Okay so I've tried learning mathematics up to where I should be at in the past. Every time though I end up stopping for some reason, whether that be health reasons, family reasons etc. sometimes not even for a long time, such as for a couple days/week. Once this happens the information seems to just drop out of my brain no matter and I have to start again.

I am only trying to currently get up to year 12 level for here in South Australia so I will be caught back up and ready to continue my university study and move onto Discrete Mathematics among other things.

Anyway I've tried the practice, practice, practice approach a while back where I spent probably 6+ months like 5 hours a day on Khan Academy.

To add to the problem I am currently an external student so teaching other people for example maybe difficult as I hear teaching is the best way to learn. Finding other people to teach that will listen would be difficult even as an internal student. I probably wouldn't even feel confident enough to teach due to a lack of understanding myself.

Anyway I'm not giving up yet, still looking for a method that might work. Sure you might argue why waste time asking this question, go do problems and practice more but as I said that doesn't seem to work exactly. I don't have this problem with programming for example so I don't know what is wrong. Plus once I'm back studying at university I doubt I will have enough time to dedicate to just doing problems everyday to make sure the information stays fresh in my mind.

So yeah any help is appreciated (hopefully I'm posting in the correct stackexchange site...), also hopefully not too specific to my case or something too, which I just realised might be a problem...

Thanks.

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    $\begingroup$ Learn how to make good summary notes in your own words on every type of problem you are likely to encounter on exams. Use those notes to brush up as required. $\endgroup$ – Dan Christensen Oct 2 '14 at 18:59
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Becareful that you don't just remember STEPS ON HOW to do it, but WHY THE METHOD WORKS. Once things become common sense and then you practise-practise-practise it's hard to forget. Don't be scared to get it wrong if it helps you understand why it works. Not sure what level maths you are doing but try googling virtualb15 and wootube. NSW syllabus but the maths is all the same =)

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In my experience, to really remember math for a long time, two things need to happen.

1) You need to really understand WHY a mathematical statement is true, in as many different ways as possible. Can you think of a visual explanation? Can you think of another method to solve the problem? Your goal should be to interact with the material in as many different ways as possible, with the goal of explaining things to yourself in new ways. Whatever you do, do not gloss over points that you don't understand. If feel stuck and frustrated, you are almost certainly learning. This process will take longer than you think that it should. Stick with it! DO NOT rely on rote memorization. I did that for way too long, and I can tell you from personal experience that it is not sustainable.

2) Review. If you learn something on Monday, come back to it briefly on Wednesday or Thursday. Then look at it again the next week. Look again the week after that. Come back a month later, and then a few months after that. But make sure that you don't just read your notes. Try to retrieve the important points from your brain before you look. Explain the material to your cat before you look. Work a few new problems (that you have cleverly set aside), or try to prove something new before you look. It is the attempted retrieval process that really cements information into your brain. Even if you don't get it all to come out right away, trying helps. Ultimately, you must convince your brain that this is important, high priority information that is worth retaining and repeated retrievals definitely help!

A final word of advice: Do not be afraid to ask for help and do not be afraid to talk to or teach other people because you fear that your "ignorance" will reveal itself. Just go for it! You'll be glad you did.

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