'Naturally gifted at maths'

[James Nguyen]

Is there such thing?

A person in my school who is one those artsy/english guys told me he wanted to become good enough to do the SMC for Maths, and asked me to teach him some stuff. I'm just wondering if you need to be naturally gifted at maths to become really good, or is that a myth, and someone's smartness is only attributed to the way they were brought up?
He's actually an A* student(at GCSE), but this isn't that big of a deal since they are GCSE's, and the competitions are more of a step up.

So, what I'm asking is:

Even if he is not very good at maths right now, will he be able to become very good with enough work? Could he develop mathematical logic to help him with such questions that require it?

[Charlie Reams]

Interesting question. You're never really going to be able to separate the nature/nurture thing, but I knew a lot of smart people at school who got a long way in maths without trying that hard, and it caught up with them only at degree level. So at SMC level, it seems like it would be hard to close the gap on the people who just seem to find maths easy and intuitive in some way. Depends how good he considers "very good" to be, I suppose. Are we talking getting a Gold medal (is that how it works still?) or Best in School or National Champion?

[Jon Corby]

I think if he gives it 110% effort, he probably can.

[James Nguyen]

Are we talking getting a Gold medal (is that how it works still?) or Best in School or National Champion?

A Gold Medal, maybe a BMO Qualifier. He just turned for some reason, I have no clue why, but I can see he wants to put alot of effort into this.

[Jon O'Neill]

Are we talking getting a Gold medal (is that how it works still?) or Best in School or National Champion?

A Gold Medal, maybe a BMO Qualifier. He just turned for some reason, I have no clue why, but I can see he wants to put alot of effort into this.

I think he if really puts in the hours then with the right tuition he could definitely do it. Problem is, it's going to be a lot of hours, and it's going to be harder now to learn than it was when he was younger (I think?).

I remember hearing something about Vanessa-Mae saying she had in-born musical talent but she worked out that she had done like 5,000 hours of practise as a child. Some guy was claiming anybody would've been that good after 5,000 hours. And that's art!

[Michael Wallace]

Are we talking getting a Gold medal (is that how it works still?) or Best in School or National Champion?

A Gold Medal, maybe a BMO Qualifier. He just turned for some reason, I have no clue why, but I can see he wants to put alot of effort into this.

I think he if really puts in the hours then with the right tuition he could definitely do it. Problem is, it's going to be a lot of hours, and it's going to be harder now to learn than it was when he was younger (I think?).

I remember hearing something about Vanessa-Mae saying she had in-born musical talent but she worked out that she had done like 5,000 hours of practise as a child. Some guy was claiming anybody would've been that good after 5,000 hours. And that's art!

I dunno about that. It's not very hard to get technically good at an instrument, and I'd say the 'musical' bit is a lot harder to teach (it's not very easy to define, but what's arguably more important are the little things that make a Very Good Musician different to a computer playing the same notes).

I think there's a similar thing with maths - you can learn all the tricks and rules and whatever, but it's a lot harder to learn the ability to spot patterns or see through a problem to a nice neat solution. Obviously this is just my own experiences, but I've encountered quite a lot of different mathematicians in my time.

I want to say "everyone can learn to do anything, it's just it will take some people longer than others", but that seems a bit sweeping (and I'm not convinced it's true, although it might be if you allow the fact that everyone has a finite limit to how much time they can spend being taught something).

[Charlie Reams]

I remember hearing something about Vanessa-Mae saying she had in-born musical talent but she worked out that she had done like 5,000 hours of practise as a child. Some guy was claiming anybody would've been that good after 5,000 hours. And that's art!

You might be thinking of Malcolm Gladwell and his book Outliers, and he actually says 10,000 hours (if you're not thinking of that then sorry for being a dick). Based on the only thing I consider myself actually good at (programming), I'd say that's about right. But that's to reach a pretty intense level, getting into the second round of the SMC doesn't need anything like that.

Anyway, you're never going to be able to compete with the people who are naturals and practise for 10,000 hours, so the question is really the extent to which you can compensate for not being a natural by putting in the hours. And although it's totally citation-needed, my intuition is that maths and music are probably two of the subjects where it would be hardest to compensate. But I don't want to discourage this guy: if you want to really work at something then you should go for it, it'll be a good experience in all sorts of ways regardless of the outcome. *wipes tear from eye*

[Ben Hunter]

I remember hearing something about Vanessa-Mae saying she had in-born musical talent but she worked out that she had done like 5,000 hours of practise as a child. Some guy was claiming anybody would've been that good after 5,000 hours. And that's art!

Not everybody would get as far as Vanessa-Mae in 5000 hours. Some people are tone-deaf, others have perfect pitch, and the latter group are going to get a lot further with their practice.

[Michael Wallace]

others have perfect pitch

Bastards, the lot of them

(based solely on having to share musicianship classes over the years with one or two people who had perfect pitch - they were lovely people but it's really annoying when you're doing interval tests or whatever)

[Brian Moore]

And although it's totally citation-needed, my intuition is that maths and music are probably two of the subjects where it would be hardest to compensate.

I wouldn't disagree with that, and I'm pretty sure that there are links between mathematical and musical ability (I suspect in the intuitive grasp of pattern recognition of some sort). In music in particular there is heavy demand on multiple intelligencies (intellectual, emotional, body coordination etc.), which I suspect is more suited to certain brain wiring than others. Just on a really fundamental level you can have musicians who appear to have a completely innate sense of internal pulse, and those who, however much practice they do, don't. They can get better at it, but they just can't groove.

[Brian Moore]

others have perfect pitch

Bastards, the lot of them

(based solely on having to share musicianship classes over the years with one or two people who had perfect pitch - they were lovely people but it's really annoying when you're doing interval tests or whatever)

I wouldn't want perfect pitch - a bloody nightmare if you've got any other tuning system than equal temperament at A=440. To my mind the disadvantages far outweigh the advantages.

[Michael Wallace]

I wouldn't want perfect pitch - a bloody nightmare if you've got any other tuning system than equal temperament at A=440. To my mind the disadvantages far outweigh the advantages.

Must be a great way to pick up the laydeez, though. Maybe.

[Brian Moore]

I wouldn't want perfect pitch - a bloody nightmare if you've got any other tuning system than equal temperament at A=440. To my mind the disadvantages far outweigh the advantages.

Must be a great way to pick up the laydeez, though. Maybe.

I have to compensate by telling them about historical tuning systems and the Pythagorean Comma.

[Innis Carson]

Must be a great way to pick up the laydeez, though. Maybe.

I can confirm that this is not true.

This is bound to sound ignorant, but I've never really understood, how can so many people play music as well as they do without perfect pitch? For example Brian, how can you tell that you're actually pitching the note you're intending to? Or are you just beyond the point of making such mistakes in the first place?

[Gavin Chipper]

Anyway, you're never going to be able to compete with the people who are naturals and practise for 10,000 hours, so the question is really the extent to which you can compensate for not being a natural by putting in the hours. And although it's totally citation-needed, my intuition is that maths and music are probably two of the subjects where it would be hardest to compensate. But I don't want to discourage this guy: if you want to really work at something then you should go for it, it'll be a good experience in all sorts of ways regardless of the outcome. *wipes tear from eye*

Since we're all going on our hunches, I would have guessed that music (playing music) would have been something where practice is pretty much king. But I'd agree with you on maths. Of course with maths and music there's different areas of skill. Someone might be able to write music much better than they can play music or vice versa. And speaking from personal experience, you can be much better in some maths areas than others. So obviously talent can be wasted when you have to be arsed with all of it.

[Gavin Chipper]

Must be a great way to pick up the laydeez, though. Maybe.

I can confirm that this is not true.

This is bound to sound ignorant, but I've never really understood, how can so many people play music as well as they do without perfect pitch? For example Brian, how can you tell that you're actually pitching the note you're intending to? Or are you just beyond the point of making such mistakes in the first place?

You can tell the pitch relative to other notes. It's just that if someone plays a single note out of the blue, you won't necessarily be able to idenify it. Anyway, if you know the piece of music you're playing, and you know which buttons to press/knobs to turn on the particular instrument you're playing, does it even matter if you can hear? (Slight exaggeration maybe but I'm just taking it to the other extreme. Beethoven was deaf though.)

[Brian Moore]

This is bound to sound ignorant, but I've never really understood, how can so many people play music as well as they do without perfect pitch? For example Brian, how can you tell that you're actually pitching the note you're intending to? Or are you just beyond the point of making such mistakes in the first place?

You can tell the pitch relative to other notes. It's just that if someone plays a single note out of the blue, you won't necessarily be able to idenify it. Anyway, if you know the piece of music you're playing, and you know which buttons to press/knobs to turn on the particular instrument you're playing, does it even matter if you can hear?

Right, Gavin, on the relative pitch bit, but yes it does matter, especially on brass instruments as without moving your fingers (or arm in the case of the trombone) you can hit a number of different notes. (On the natural/baroque trumpet it's all done with the lips, so you do very much need to hear what you're going to play.)

'Perfect pitch' is really only a good memory for discrete particular pitches (the equally-tempered scale, as you'll hear on a piano) and being able to name each one. I can't do that, but I can know when a played B flat is out of tune, without reference to anything else. (I've just got that pitch ingrained in my aural memory from 40 years of tuning to it.) But if you ask me to pick a B flat out of thin air, I can't do it that way round.

In any case, the ideal music making is one where the sound you want drives the body to make the right shape to produce that sound. That's what happens when you sing - practising an instrument is all about learning how to produce the aural patterns you hear in your head on the instrument you've chosen to play.

Oh, and how do I play the right notes? - a combination of decent aural skills (I generally can hear what's on the page before I play it) and practice (if I can't hear it, then I work out what it should sound like, then practise it till I can't get it wrong.)

[Phil Reynolds]

I play the right notes

"...but not necessarily in the right order." (E. Morecambe, 1971)

[Charlie Reams]

Seems relevant.

Dozens of studies have found that top performers - whether in maths, music or whatever - learn no faster than those who reach lower levels of attainment - hour after hour, they improve at almost identical rates.

[Jon O'Neill]

Seems relevant.

Dozens of studies have found that top performers - whether in maths, music or whatever - learn no faster than those who reach lower levels of attainment - hour after hour, they improve at almost identical rates.

Must suck for everyone in this thread apart from me to be wrong.

[Jon O'Neill]

You all need to practise being naturally clever more.

[Charlie Reams]

Of course you could ask where the motivation and perseverance to do 10,000 hours of violin practice came from. But it gives a pretty good answer to the original question.

[Gavin Chipper]

Seems relevant.

Dozens of studies have found that top performers - whether in maths, music or whatever - learn no faster than those who reach lower levels of attainment - hour after hour, they improve at almost identical rates.

You'd expect improvement to plateau off anyway, so if a top performer is still managing to improve at the same rate as someone at a lower level, chances are they're more naturally talented! (At the very least, the sentence isn't very clear.)

[Charlie Reams]

Seems relevant.

Dozens of studies have found that top performers - whether in maths, music or whatever - learn no faster than those who reach lower levels of attainment - hour after hour, they improve at almost identical rates.

You'd expect improvement to plateau off anyway, so if a top performer is still managing to improve at the same rate as someone at a lower level, chances are they're more naturally talented! (At the very least, the sentence isn't very clear.)

Your interpretation is weird. Surely it means: if you have two people at the same level, and they do the same amount of practice, they'll have improved by the same amount.

[Gavin Chipper]

Your interpretation is weird. Surely it means: if you have two people at the same level, and they do the same amount of practice, they'll have improved by the same amount.

Yeah maybe, but I think it was a weird sentence. I don't think they made it clear that there are these top performers that they have been following since they weren't top performers and were at the same level as "normal" people.

[Lesley Hines]

It's true that "work hard and you'll do well" is a great message to give to any child, but it's not on to assume all children (and therefore adults) start as equals. It's not taking into account any learning disabilities, behavioural disabilities, physical disabilties etc., or any other stresses that may impair a person's learning. I'd be interested to read the original study, otherwise you're kinda saying "everything being equal, all children will learn at equal rates", which is of course true. It's a shame they describe Dweck as a 'top psychologist" - that means nothing. Manual dexterity (to take the musical example) is also controlled by the amount of noise on the nervous system, for example, rather than simply the amount of practice put in.

To put it into a real-life context I've witnessed, Child A has dyspraxia and dyslexia, and even though he works really hard struggles with reading, is read to a lot (and has been since birth), can recite lots of stuff he's been read but can't piece together phonemes. Child B doesn't struggle and is dramatically advanced for his age, even though he's not given much tuition and Child A has had (im)measurable extra tuition in the classroom. No-one's being told they're cleverer than the other (indeed Child A is very bright indeed and was praised for being bright before he started school), it's just Child A is hampered by circumstances beyond his control and has awesome abilities beyond literacy.

[Charlie Reams]

I'd be interested to read the original study, otherwise you're kinda saying "everything being equal, all children will learn at equal rates", which is of course true.

I don't think anyone would get a publication from such an obvious tautology, even in psychology. Anyway I wrote a long post with a bunch of links and then my browser ate it, so now I'm all angsty, but anyway, here are a few: http://doi.apa.org/psycinfo/1993-40718-001
http://journals.lww.com/academicmedicin ... d.22.aspx/
http://psycnet.apa.org/psycinfo/1996-98355-004
http://psycnet.apa.org/index.cfm?fa=sea ... -40718-001
There are also some dissenting opinions, but since I can't get the full text I don't know how serious they are.

[Lesley Hines]

Cheers; they were interesting. I think it depends on how you define 'talent' - a nice one I've just read is a capacity for achievement or success: that's a different thing to automatic achievement and success that's sometimes implied by the word 'talent'. These studies seem to focus on motivational techniques, rather than comparing the original innate ability which is almost impossible to do anyway. It's a shame these studies aren't available in full (the medical one was particularly interesting) as it's really important to account for the confounding variables. The medical one did mention at the start that the best schools and employers find their cohorts through extensive testing, and I guess some of that testing would be aptitude testing for stuff like simple hard work. I tried to find some animal studies as I thought these would bypass the motivational bits and concentrate on pure intelligence, but I ended up with so much weirdy crap where the authors felt it necessary to insert Biblical quotes I've given up (for now).

As a kid I had to wear built-up shoes to correct, er, something medical my Mum can't remember the name of. Result: I was crap at sport. Couldn't run, although pretty good at climbing, swimming and cycling. That however, I guess, focussed my interests on reading, music, blowing stuff up and taking stuff apart, and other good stuff. Point? No matter how much I was encouraged to practice running (a lot; it's one of the reasons I walk normally now, but still don't run) I'm never going to be a sprinter. My punctuation's pretty cool though

[Ian Volante]

Interesting thread. Right from the beginning of school, I loved maths. As far as I can remember anyway. I'm wondering now whether it's the case that I'd been brought up in a certain way to understand maths, and therefore I found when learning it with other people at age 4 that I was relatively good, and therefore such a positive enhanced my enjoyment.

That said, I appear to be a very quick reader for example. There's often little point people trying to help me on quiz machines as I've often answered the question before they've read it. Again, nature or nurture?

There's a study somewhere [citation needed] that says something about the advantages of exposing very young children to visualised numbers (such as bit dots on a piece of card).

As for music, I don't believe I have perfect pitch (how do you tell?), but a bum note is very obvious to me, even worse are out-of-time beats for example, but then again, weird time ignatures are fascinating. And I find it intensely annoying when pauses between lines in songs are all but ignored by many singers, football crowds being particularly bad for this.

Think I'm rambling now.

[Michael Wallace]

As for music, I don't believe I have perfect pitch (how do you tell?)

Presumably Innis can offer a better explanation, but my experience of people with perfect pitch is that you can play them any note on the piano (for instance) and they can immediately say "A flat" or whatever, the same way you can look at a t-shirt and say "that's red" without having to think. That's how it's been described to me, at any rate.

[Ian Volante]

As for music, I don't believe I have perfect pitch (how do you tell?)

Presumably Innis can offer a better explanation, but my experience of people with perfect pitch is that you can play them any note on the piano (for instance) and they can immediately say "A flat" or whatever, the same way you can look at a t-shirt and say "that's red" without having to think. That's how it's been described to me, at any rate.

I probably don't have it then, I can only do that by reference to, say, middle C.

[Phil Reynolds]

As for music, I don't believe I have perfect pitch (how do you tell?)

Presumably Innis can offer a better explanation, but my experience of people with perfect pitch is that you can play them any note on the piano (for instance) and they can immediately say "A flat" or whatever

Hearing a note in isolation and being able to name it is one way of defining perfect pitch, but in my experience the more common way (or the more useful skill at any rate) is being able to sing a specified note without first hearing it played. In live performances, where a soloist or group are required to sing (or begin to sing) a capella, you'll usually hear a single instrumental note played first to allow them to pitch the opening note of the song - singers with perfect pitch don't need this.

[Jon O'Neill]

As for music, I don't believe I have perfect pitch (how do you tell?)

Presumably Innis can offer a better explanation, but my experience of people with perfect pitch is that you can play them any note on the piano (for instance) and they can immediately say "A flat" or whatever

Hearing a note in isolation and being able to name it is one way of defining perfect pitch, but in my experience the more common way (or the more useful skill at any rate) is being able to sing a specified note without first hearing it played. In live performances, where a soloist or group are required to sing (or begin to sing) a capella, you'll usually hear a single instrumental note played first to allow them to pitch the opening note of the song - singers with perfect pitch don't need this.

Hm.. doesn't this also test how good a singer you are though?

[Phil Reynolds]

Hearing a note in isolation and being able to name it is one way of defining perfect pitch, but in my experience the more common way (or the more useful skill at any rate) is being able to sing a specified note without first hearing it played. In live performances, where a soloist or group are required to sing (or begin to sing) a capella, you'll usually hear a single instrumental note played first to allow them to pitch the opening note of the song - singers with perfect pitch don't need this.

Hm.. doesn't this also test how good a singer you are though?

You're right. I suppose my experience of hearing perfect pitch talked about and defined is mostly limited to the performing arts context, when it's generally applied to people who, it's assumed, can sing. The Wikipedia article on perfect (aka absolute) pitch gives a more rigorous definition and is worth reading.

[Lesley Hines]

As for music, I don't believe I have perfect pitch (how do you tell?)

Presumably Innis can offer a better explanation, but my experience of people with perfect pitch is that you can play them any note on the piano (for instance) and they can immediately say "A flat" or whatever

Hearing a note in isolation and being able to name it is one way of defining perfect pitch, but in my experience the more common way (or the more useful skill at any rate) is being able to sing a specified note without first hearing it played. In live performances, where a soloist or group are required to sing (or begin to sing) a capella, you'll usually hear a single instrumental note played first to allow them to pitch the opening note of the song - singers with perfect pitch don't need this.

My husband can tune a guitar correctly (as in, it's then in tune with my piano) without a reference note and didn't pick up an instrument 'til he was 20 (git ). I offer no explanation for this: his whole family's flummoxed by his musical ability.

[Soph K]

I think you could kind of be Naturally Gifted At Maths, because some people (eg a couple of boys in my class) don't really concentrate, hardly ever do homework and don't do an awful lot of revision but still get good marks in tests, are still in the top set and normally find the work fairly easy. I don't really see how that could happen excluding that they could be Naturally Gifted At Maths...

[Gavin Chipper]

Another thig about being "naturally talented" at something is that sometimes people assume if one person starts off better than another one, he has more natural talent and the other one can only overtake him by putting more work in. But the other person might have more ability to improve even if his starting level is lower (so will overtake even if they put the same hours in), so it could be argued that he is actually more naturally talented.

Also, when people go on about working hard to become good, it's also about what work you do and how you go about it. If you're shit at a subject at school and people just say "work harder", what do you do? If you're not good enough to actually do the homework or whatever because you don't understand it, it's up to the teachers to get you going.

[Soph K]

Another thig about being "naturally talented" at something is that sometimes people assume if one person starts off better than another one, he has more natural talent and the other one can only overtake him by putting more work in. But the other person might have more ability to improve even if his starting level is lower (so will overtake even if they put the same hours in), so it could be argued that he is actually more naturally talented.

Also, when people go on about working hard to become good, it's also about what work you do and how you go about it. If you're shit at a subject at school and people just say "work harder", what do you do? If you're not good enough to actually do the homework or whatever because you don't understand it, it's up to the teachers to get you going.

good point there

[Adam Gillard]

With about 2 weeks of obsessive practice, I managed to get my Spoilage Numbers Attack average score up from about 30 to about 80, and my PB from 40-odd to 123. I was surprised that I could improve so much at what seemed an impossibly difficult numbers game in the first instance, but having been frustrated at regularly getting within 10 of the target but not being able to figure out exactly what to declare within 30 seconds, I managed to develop techniques whereby I could do mental arithmetic quicker (e.g. instead of figuring out exactly what 897*6 is, I'd just know it's 18 less than 5400 (900*6) and in the extra second or so saved I'd realise that I could add 124 to get to the target of 5506). I also realised that when adding 4 big numbers it's easier to work on the tens and units separately and then add the result to the sum of the hundreds (e.g. 912 + 846 + 467 + 337 = 162 + 2400 = 2562). A handful of little time-saving tricks like this basically mean that when I find a way of getting within 10 of the target within 30 seconds, I can now accurately declare something about 85% of the time. (This is support for the "practice makes perfect"-style theory).

[Gavin Chipper]

With about 2 weeks of obsessive practice, I managed to get my Spoilage Numbers Attack average score up from about 30 to about 80, and my PB from 40-odd to 123. I was surprised that I could improve so much at what seemed an impossibly difficult numbers game in the first instance, but having been frustrated at regularly getting within 10 of the target but not being able to figure out exactly what to declare within 30 seconds, I managed to develop techniques whereby I could do mental arithmetic quicker (e.g. instead of figuring out exactly what 897*6 is, I'd just know it's 18 less than 5400 (900*6) and in the extra second or so saved I'd realise that I could add 124 to get to the target of 5506). I also realised that when adding 4 big numbers it's easier to work on the tens and units separately and then add the result to the sum of the hundreds (e.g. 912 + 846 + 467 + 337 = 162 + 2400 = 2562). A handful of little time-saving tricks like this basically mean that when I find a way of getting within 10 of the target within 30 seconds, I can now accurately declare something about 85% of the time. (This is support for the "practice makes perfect"-style theory).

My highest score on Spoilage numbers was set on my very first go at it.

[Adam Gillard]

My highest score on Spoilage numbers was set on my very first go at it.

But I've played nearly 10 times as many Spoilage NAs as you in the last 30 days. I understand that it's impossible / impractical / plain crazy to play that many for most people, but maybe a bit more practice will help.

[Mark James]

(This is support for the "practice makes perfect"-style theory).

My Dad likes to say practice makes permanent not perfect. If you practice something the wrong way you'll only become proficient at doing it the wrong way.

[Brian Moore]

My Dad likes to say practice makes permanent not perfect.

Sadly, the depressing thing is, as far as music is concerned, all that technique you've got then needs to be maintained: use it or lose it. The better you are, the more you need to practise. I remember hearing an interview with the principal oboe of the Berlin Philhamonic, who said she needed to practise 2-3 hours per day just to stay as good as she was - and the evidence of how good she was was demonstrated in real time, in front of her peers, her employers, the conductor, and an audience of thousands. That's stress. No wonder so many professional musicians are alcoholics.

Incidentally, for tax/pension purposes, brass players can retire at 50 according to Inland Revenue rules. Not that I imagine many can afford to, as most of the income will have gone into beer rather than the pension fund.

[James Nguyen]

He's already pretty good, getting a gold on an IMC past paper he did yesterday. Next step: SMC.

[Gavin Chipper]

I saw this article and thought of this thread. End the culture of coaching? Can that happen? How about ending the partitioning of children at age 11 into "intelligent" and "not intelligent"? That's a shit idea, right?