does maths ability have a shelf life?

[Moscow Mule]

Problem with learning and understanding is that teaching is usually done with the aim of getting the kids past the exams, not to give them a thorough understanding of the subject.

And that (in a nutshell) is what is wrong with the education system.

[sasguru]

when you understand something you can fill in some of the gaps in your learning and accelerate further learning.

Take calculus and newton laws of force and motion. I was taught them completely seperately and we were expected to simply learn the equations for acceleration, velocity and distance etc... Newtons laws would be examined in the Applied/Mechanical mathematics paper, calculus in the pure, 2 different exams, 2 different teachers.
However, if you understand mathematics, you can see clearly how newtons equations are all built up using calculus, this saves you the bother of having to memorise them for the exam as you can simply derive them as required.

Problem with learning and understanding is that teaching is usually done with the aim of getting the kids past the exams, not to give them a thorough understanding of the subject.

Agreed. I don't get the distinction between learning and understanding. You can't learn something you don't understand.

[Diver]

Agreed. I don't get the distinction between learning and understanding. You can't learn something you don't understand.

Erhum! I would point the honourable gentlemen towards some of the people running this great country of ours!

[sasguru]

Erhum! I would point the honourable gentlemen towards some of the people running this great country of ours!

Eh? What does learning and understanding have to do with pigs at the trough.

[Ivor Bigun]

when you understand something you can fill in some of the gaps in your learning and accelerate further learning.

Take calculus and newton laws of force and motion. I was taught them completely seperately and we were expected to simply learn the equations for acceleration, velocity and distance etc... Newtons laws would be examined in the Applied/Mechanical mathematics paper, calculus in the pure, 2 different exams, 2 different teachers.
However, if you understand mathematics, you can see clearly how newtons equations are all built up using calculus, this saves you the bother of having to memorise them for the exam as you can simply derive them as required.

Problem with learning and understanding is that teaching is usually done with the aim of getting the kids past the exams, not to give them a thorough understanding of the subject.

It took unril I was 11 years old to work out how to pass Maths exams.
It was something like this:
- Memorise the "actions" of how to solve the problems.
- Practise so that you can solve it quickly
- Do enough examples so that it covers every question you might be asked (theres a limited range)

Using this brute force technique, it was easy for our teacher to get us all through with great grades. (I got at A at A level).

I would never claim to "understand" math. its was just rote memory and pattern matching.

IMO, There is no secret knowledge. Just using math "tools" doesn't make anyone a genius or clever.
The genius part is a person's ability to "link" all the stuff together to come up with a new tool.

I just think the OP just needs to remember and practise

[sasguru]

It took unril I was 11 years old to work out how to pass Maths exams.
It was something like this:
- Memorise the "actions" of how to solve the problems.
- Practise so that you can solve it quickly
- Do enough examples so that it covers every question you might be asked (theres a limited range)

Using this brute force technique, it was easy for our teacher to get us all through with great grades. (I got at A at A level).

I would never claim to "understand" math. its was just rote memory and pattern matching.

IMO, There is no secret knowledge. Just using math "tools" doesn't make anyone a genius or clever.
The genius part is a person's ability to "link" all the stuff together to come up with a new tool.

I just think the OP just needs to remember and practise

Well very few people can come with a new tool or new knowledge, but that doesn't mean they don't understand, to some extent, the existing body of work. And while I agree rote memory isn't the way to go, what you call "pattern matching" and I would call call "linkage" is the key to understanding.
Going back to one of the OPs about the effect of age, one benefit is that I don't need to pass exams anymore, so I'm re-discovering doing something for the sheer reward of it - when I have the time.

[Charles Foster Kane]

I pretty much managed to sail through secondary school, sixth form and University (still managing to have fun) by analysing trends in past papers, available from the library.

In the case of University essays etc. my friends and I used to meet on the hand-in day and collaborate, taking concepts from each others work, bumping up each others grades.

[Moscow Mule]

Agreed. I don't get the distinction between learning and understanding. You can't learn something you don't understand.

Yes you can.

I learned the proofs for Maxwell's equations (how to write them down at least) as they were part of the syllabus.

I didn't understand how they related to the E & M component of an E-M wave.

You might say that that isn't learning the whole thing, but I guess it depends on where you set your boundaries.

[Ivor Bigun]

Well very few people can come with a new tool or new knowledge, but that doesn't mean they don't understand, to some extent, the existing body of work. And while I agree rote memory isn't the way to go, what you call "pattern matching" and I would call call "linkage" is the key to understanding.
Going back to one of the OPs about the effect of age, one benefit is that I don't need to pass exams anymore, so I'm re-discovering doing something for the sheer reward of it - when I have the time.

Yep, I can understand what you mean with the "puzzle solving" nature of maths. Its also a unique "true world". I particularly like it when a Maths model points out the unexpected when applied to the real world or "proof" that something exists before it is discovered.

[BrilloPad]

i got an A in maths A-level 15 years ago but didnt touch it since

now i've come back to it and im trying to pick up fairly hard maths in work and im really really struggling to grasp it conceptually

am i out of practice, is "maths thinking" something i can get back into, or have 15 years of living well put it out of reach?

Amateur. I got A in A-level, 1 in special, A is Further Maths, 1 in Further Maths special. Got an upper second in my degree - I was very upset.