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Im Noah
Poster

Post Number: 12
 Posted on Tuesday, 20 May, 2014 - 09:27 pm:

Note: this is for A-Level Maths/Further Maths.

I do the following below;

1) read the theory for whichever topic I'm studying given at the start of the textbook

2) proceed to read the solved examples which the textbook provides (usually 3-5 with full solutions)

3) I then proceed onto answering every question within each exercise.

My problem is that I still forget concepts, for instance, let's say a week later (or even a few days later sometimes).

What am I doing wrong? Others keep telling me to 'understand' but can someone expand on this? I do try to understand each concept but it's inevitable that I'll somehow still forget. What does it mean to specifically 'understand' a given concept/problem? If you have any other advice then please post!
JoelFishel
Prolific poster

Post Number: 268
 Posted on Wednesday, 21 May, 2014 - 12:30 am:

I find that understanding a concept is often more than just reading the theory. Reading the theory thoroughly is certainly a good start, but often doing A-level practice problems is not sufficient for gaining a full understanding of the concept. The usual format of an A-level text book will be to give you an example that you then copy with different numbers (more or less) again and again.

Real understanding comes from tackling more difficult problems which requires you to use a concept in more imaginative ways. A problem that you struggle at for hours/days/even weeks, is going to be far more likely to stick in your mind for the long run.

So the solution, is (I suppose) to maybe try tackling harder problems on the given topic. STEP papers are good for this, alongside AEA (I think that's what they were called, can't quite remember). Olympiad is a wonderful mathematical challenge to get you excited about maths but not useful for A level. Ask your own questions as well, that you may try and solve, or ask your teacher (/this forum) about!

Hope this helps.
Superbus
Regular poster

Post Number: 41
 Posted on Wednesday, 21 May, 2014 - 12:54 am:

I agree with Joel; work through STEP papers.

I actually wouldn't recommend working through A level papers at all. Do one or two to get used to the format, beyond that it's useless.
Theo P
Prolific poster

Post Number: 297
 Posted on Wednesday, 21 May, 2014 - 08:46 am:

As has been mentioned above, doing more challenging questions is a great way to secure an understanding. If you can do STEP questions on a topic then you've probably understood it.

You've asked what it means to 'understand' a concept. Obviously, this is open to interpretation, but I would suggest that in some sense it means having an intuitive idea of why something is the case. I wouldn't say that being able to apply an algorithm constitutes understanding of that method. Perhaps if you give a couple of examples of topic that you're learning, we can expand further on what it might mean to 'understand' them.

A couple of comments on what you currently do:
1) Reading the theory. Reading mathematics is very different to reading a novel. You should be trying to convince yourself that everything makes sense, coming up with (counter-)examples, jumping back to see where things fit in, etc. It's a much more active process.

2) Worked examples. You might like to work through these yourself on a piece of paper. Don't just copy them out mindlessly, but try to do them yourself, referring to the textbook when you need guidance. You'll get more out of them this way.

3) Exercises. Make sure that you're not using your notes or the worked examples to do these. Start on a fresh piece of paper and cover up the notes if necessary. You could spread them out over a few days if you're finding that doing them all in one sitting only allows you to remember them for a couple of days - when you do come back to them, don't look at your notes either.

Try explaining what you've learnt to a friend or family member. I find that this is a really good way to make sure I've understand something. Encourage them to ask questions, or say when something isn't clear. It can help to uncover parts that you need to clarify for yourself.

You're not doing anything wrong! It sounds like you're committed to doing well, so keep at it.
samuel bird
New poster

Post Number: 3
 Posted on Wednesday, 21 May, 2014 - 10:47 am:

If you have trouble with STEp, give the solomon papers a go and then move onto STEP because you will want to. Just give a few of these a go and then go on to STEP. If you are fine with STEP, just do that.

Theo P
Prolific poster

Post Number: 298
 Posted on Wednesday, 21 May, 2014 - 01:20 pm:

Also, von Neumann once said that "in mathematics you don't understand things. You just get used to them." Working through lots of examples, be they A Level or STEP, is certainly going down the right path to get used to ideas.
JoelFishel
Prolific poster

Post Number: 270
 Posted on Thursday, 22 May, 2014 - 12:23 am:

Sorry I'd just like to say that although doing the A level past papers may not be totally enriching I don't think they're useless. In fact I'd say that the number of past papers you've done before the exam is proportional to your mark so don't neglect them completely!
Prolific poster

Post Number: 390
 Posted on Thursday, 22 May, 2014 - 12:16 pm:

Joel Fishel wrote:

In fact I'd say that the number of past papers you've done before the exam is proportional to your mark so don't neglect them completely!

I could possibly believe monotonically increasing' but not proportional to' -- if I did twice as many past papers, I would not get circa 200 marks out of 120 in STEP...
JoelFishel
Prolific poster

Post Number: 272
 Posted on Thursday, 22 May, 2014 - 04:01 pm:

I forgot that concept...