Why do so many people find maths difficult?

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cpj1987

aKarma

I think the biggest problem with maths is that a lot of people only think of it as a load of methods, rather than something much more. The tendency nowadays is to teach maths as a set of methods and short cuts, which focuses on passing the exams. The result of this is people tend to feel maths is just a case of regurgitating facts/method (much like science at lower levels) and so feel it is beyond boring. The other effect of this is that a teacher can go through and explain how do a new topic, and the majority of the class will then not be able to answer a single question because the situations don't exactly match the explanation. The focus on purely exams means that the majority are left without the skills to work things out for themselves and never have any change of gaining some kind of comprehension of higher ideas behind the subject.

When I was talking to a friend (who has a quite high a at AS maths), he mentioned he was doing 'the topic where you have an equation with a squiggle next to it and apply some method to it and you get another random formula' and that it was boring as hell because he would never use it. This was referring to integration and I think highlights the way a worrying large number of high school maths students may well think despite the fact integration has a important applications in pretty much everything. The teachers should be pressured more to try and impress some kind of understanding of what's actually going on, rather than drill the facts. There's absolutely no point with a population that can pass a-level/gcse/whatever maths without any understanding why.

Worded much better than I've clearly been able to. +rep on the way.

Reply 61

Maniachris

I think alot of school students fail to see the point in maths, and therefore are unwilling to put practice into it.
I'm doing my A2 in maths now and i've realised how useful it is for physics and for many other things so now that i've put alot more practice into it, I find it alot easier and meaningful.

Reply 62

Veecee

In maths there is no where to hide, if you don't know how to get the answer, you are wrong.

In a subject like english you could get marks and probably a decent grade by blabbing around even if you don't fully understand what you are writing. But in maths you have to know exactly, you can't hide behind a wall or ambigious writing. That might be what scares a few people.

Although I think if you wanted to truly understand and delve into the deep concepts of a subject english it can be just as hard as maths.

Reply 63

Jake22

cpj1987

As I've said a few times, I'm not confusing a subject or body of work with how it's taught in school, but that (the way it's taught in school) IS what makes it boring.

Well, whilst that is true, on the other hand it would be pretty difficult to get to the level on piano where one can play, for example, Chopin etudes without ever practising scales, intervals etc. which is often routine and boring.

One salient difference between mathematics and music education is that throughout the musical education process - the student normally has a clear conception of music from the start and is encouraged to use her skills to play music as soon as possible whereas in maths - you tend to only do the scales, interval practice with no concept of the music you are going to create until much later on.

Reply 64

LakHani_Hasnain

cpj1987

As I've said a few times, I'm not confusing a subject or body of work with how it's taught in school, but that (the way it's taught in school) IS what makes it boring.

I have to agree there. I found maths incredibly boring and dull till the end of my IGCSE's, and struggled with it. Reading loads of wikipedia articles about the "how" and "why" helped a lot though; quite interested in maths now. Most of the students here struggle with maths because (to them) it's dull, boring and pointless. That attitude needs to be fixed :no:

Reply 65

Jake22

Me too. I hated maths lessons at school.

I didn't find maths boring, however, because I didn't really work out what it was until I left school.

Reply 66

xBillyBrownx

It's not hard it's just very boring..

Reply 67

JAgg

Because I'm ******* stupid, you happy now?!

Reply 68

cpj1987

Jake22

Precisely that, yeah. I'm aware that you need to learn the basics before you move on to something more substantial - but unfortunately, by then you've lost what...80%+ of your potential students?
To be honest, though, I don't see how you'd ever STOP it being boring if you believe it has to be done in that way? Unfortunately, you can play someone an intricate piece of music and get them interested instantly, because it's in no way boring at all; but give them a page of in-depth maths at 15 years old, and you lose them instantly.

Reply 69

Mr Dactyl

I've always followed the school of thought which blames culture for difficulties in maths (as above). It is indeed perfectly socially acceptable to be bad at maths, where it might be mildly discreditable to be a poor musician or artist. Moreover, it's probably socially negative to be a good mathematician, at least looking at the ones I know! It does seem to imply (to the wider world) a narrowness and dryness of thought, although this is of course far from the truth.

The difficulties in teaching are almost insoluble. It seems one must have a very firm grasp of the basics before you do anything of meaning in maths. Thus there is no scope for much else than practice, practice and more practice. However it's quite possible for an engaging teacher to spark discussion while teaching a method; things you've 'worked out for yourself' stick in the mind better. So it's hard to blame the content, but maybe the teaching could be better.

One last point, on education. The utility of maths and the maths syllabus is called into question above. And this is understandable, especially if you're the - misguided - type who thinks that education should be completely about equipping people for the real world. My take on this is that it doesn't matter whether or not the maths is useful. In ars gratia artis, ars doesn't just mean art, it means science and skill, too. Education's hard to pin down, it's about opening you to new ways of thinking, and broadening you as a person. Maths, like Latin, should be part of that, useful or otherwise.

Reply 70

Jake22

cpj1987

Precisely that, yeah. I'm aware that you need to learn the basics before you move on to something more substantial

Whilst that may be valid - that was not the point I was making. I was discussing the pedagogy of drilling technique.

In fact, in mathematics, one often studies things in precisely the opposite way to logical ordering - you study a very, very specific example of something before even defining the basic object of study.

cpj1987

To be honest, though, I don't see how you'd ever STOP it being boring if you believe it has to be done in that way?

By teaching it in the manner suggested by the musical analogy I posted. e.g. Keep mathematics in mind as the end goal, do bits of drilling technique but motivate this with theory and examples of mathematics, problem solving etc.

cpj1987

Unfortunately, you can play someone an intricate piece of music and get them interested instantly, because it's in no way boring at all; but give them a page of in-depth maths at 15 years old, and you lose them instantly.

To be fair, there are pieces of art music that often require some prior musical training to fully appreciate (e.g. a Boulez Sonata) but the fact is there is more that could be done then what is currently happening in schools. Perhaps it would even be worth separating basic numeracy and mathematics to some extent.

Reply 71

Mr Dactyl

Jake22

Perhaps it would even be worth separating basic numeracy and mathematics to some extent.

I for one would definitely buy that. Chuck all the sums and money and whatever into numeracy, and leave the good stuff in maths.

Reply 72

xenodocheionology

I am actually fascinated by maths! The whole logic of it astounds me, and I honestly think it's amazing how creative it is. The rules that have been made had to actually be DISCOVERED by someone, and with so many sequences and everything the fact that it's actually been discovered is totally cool.

Saying that, I cannot for the life of me understand it. It's not that I find it difficult because once I've been told the rules I can understand, just when I look at the numbers and symbols all written down together my brain just stops. I can't even process it. I think it's also because I find the whole following the rules constantly and consistently to be extremely mind numbingly boring to the point where I just stop thinking about it all..

I have a love/hate relationship with maths :frown:

I wish I could do it but I just can't.

Reply 73

Student2806

People hate it because they don't understand it.
I was like that until Year 9 and then I had this teacher who made it easy to understand, and suddenly I actually started enjoying it. From being crap at it in year 7, I ended up doing it at A Level and got a B :smile:

Now I don't do it anymore, I'm sad to say I miss it.

Reply 74

Arrogant Git

cpj1987

Ah, but not all interesting maths is hard. Doing things like proving simple results (like Pythagoras's theorem or the quadratic formula) would make maths seem less like a random bunch of formula.

Maths is taught, at the moment, in such a staggeringly bad way, it's understandable that some people struggle/get bored. I spent 5 or 6 years bored out of my mind in maths lessons. It took until sixth form to actually realise that there was something more to it. I remember a teacher teaching me trigonometry by drawing on the board which keys we needed to press on our calculator.

I suspect the emphasis should be placed on abstraction earlier in maths. The comment most heard in maths lessons must be "when are we ever going to use this" and it would be helpful if maths were dealt with abstractly rather than trying to portray it as something that has a use. No-one says in English lessons what the use in writing short stories or criticising poems is, do they?

That said, the prevailing attitude in society that states that maths is hard, scary and deeply boring is quite annoying. I'm fed up of having to lie to people about my degree course. Just because people ignorant about something, doesn't mean it's necessarily rubbish. Other things, like art and music attract just as many geeks and autists as maths, but they don't have nearly as bad a reputation.

Reply 75

Jake22

Arrogant Git

That said, the prevailing attitude in society that states that maths is hard, scary and deeply boring is quite annoying. I'm fed up of having to lie to people about my degree course. Just because people ignorant about something, doesn't mean it's necessarily rubbish. Other things, like art and music attract just as many geeks and autists as maths, but they don't have nearly as bad a reputation.

QFT.

I am sick of being at a party or some occasion where I meet new people and I tell them that I am a university student studying mathematics and they say 'Oh, I hate maths, its so boring' etc.

How rude and ignorant... to dismiss somebody's hobby or interest as being worthless/boring etc. especially when they don't know anything about it. I sometimes wish people would keep their uninformed biases to themselves.

Reply 76

cpj1987

Arrogant Git

I agree with the 'when are we ever going to use this' thing completely. It was exactly my reaction to a VERY dull teacher in Year 11.
As I might've made obvious in the past, I was 'lazy' in regards to formal education before university - disillusioned, unhappy with the system, and unable to see the point. Some aspects of maths, for me, were the epitome of this uselessness; and so, where I might've paid SOME attention in other lessons, I really, really switched off in maths.
Eventually, the teacher made a comment on it when I was paying very little attention one lesson, to which I responded 'When am I ever going to measure the angle of a ladder against a wall before I climb it, or spend time working out the speed and direction of someone who's fallen into a river to see where they might end up?'. The typical textbook cases tried to be relevant by putting in these 'real-life' situations, but the result was the complete opposite, and nothing wound me up more than being told by a teacher to learn something because 'it will be useful in this scenario', when it really wouldn't. I think that's something many people pick up on - if they told you what it really WOULD be useful for, instead of trying to make it into a story, it might be received better.

Reply 77

Melancholy

Kolya

If that is true then one would expect a collection of students getting an A grade, a collection of students getting an F grade, and not much in between. Obviously that does not occur, so I would suggest that perhaps pidgeonholing oneself into the "good" or "bad" category is more of a psychological action, rather than any reflection of one's actual performance in mathematics.

That's not necessarily true though. You can argue that case, but it would need to be supported because it does not, in itself, demonstrate your point. A grade is merely a reflection of what percentile (or other division) you got into. Consider that to get an A* grade at GCSE you need to get, say, 85% to get an A*, and then 65% to get a B and then 58% to get a C (I'm aware that GCSE Maths has a fairly difficult exam structure to analyse since they are, in themselves, distributed between higher, intermediate and other tiers). But can you see my point? Just because grades are dispersed fairly evenly (indeed, the exam boards may even forceably manipulate percentage boundaries to make the case) does not mean that ability is dispersed fairly evenly. You seem to be analysing the end result which itself aims to take a look at the varied abilities of young people, and then give them evenly distributed marks by looking at past papers, the current papers and whatever other method they like. If the idea that an A* was always 90%, an A was always 80%... et cetera, actually existed, then your point would make sense.

Even at AS/A-Level, from personal experience in Economics, it's possible to drop a full 5 marks in a paper out of 45 marks and still receive 90 out of 90 UMS points because of the nature of the paper and the low requirement for an A (something like 33/45 for an A, 29/45 for a B, 26/45 for a C; which to me seems ridiculous). It's possible to have major gaps between percentages (like for A* and A compared to C and D) whilst keeping the grade distribution smooth.

Reply 78

Kolya

One problem (that I've only come to appreciate recently) is that you cannot escape doing the serious work by just proving simple results, or doing "fun" maths. The proficiency needs to be there, otherwise everything else that comes later falls apart.

The way the subject is structured, and its nature, means that there is a heavy amount of content that you simply must know, and must be able to do. I hate to say it, but I think that puts some people off. I was able to take a philosophy university module and get a decent mark on it having attended 6 lectures, read a couple of books, and not written any essays since my History AS. To study a comparable module in maths would have required me to take the Maths A-level, attended 50+ hours of lectures, and done a similar amount of problems on my own.

You can't dip into it, and you can't cheat other people about how much you know, and you have to put in the "hard grafting". Unless students realize that,
or it is made clear, then I don't think any amount of fun or enjoyable proofs are going to help, "Arrogant Git".

That doesn't mean it's any less interesting, just different. So really, to summarize, the harder you work at maths, the easier and more interesting it becomes.

It sounds cruel, but, in most cases, if someone finds maths difficult then they just aren't working hard enough.

(Note: It doesn't mean they are lazy - they may have other reasons for not working (like unreasonable expectations, social pressure, etc...) - but if they worked harder it would be more enjoyable and easier. I recognize some people actually simply cannot do it, but most people who claim they are in that group aren't. GCSE and A-level results show a spectrum of performance, not clump of people who are "good", and a clump of people who are "bad". Where someone appears on that spectrum is almost certainly closely correlated to how hard they work.)

Reply 79

Arrogant Git

cpj1987

I agree with the 'when are we ever going to use this' thing completely. It was exactly my reaction to a VERY dull teacher in Year 11.
As I might've made obvious in the past, I was 'lazy' in regards to formal education before university - disillusioned, unhappy with the system, and unable to see the point. Some aspects of maths, for me, were the epitome of this uselessness; and so, where I might've paid SOME attention in other lessons, I really, really switched off in maths.
Eventually, the teacher made a comment on it when I was paying very little attention one lesson, to which I responded 'When am I ever going to measure the angle of a ladder against a wall before I climb it, or spend time working out the speed and direction of someone who's fallen into a river to see where they might end up?'. The typical textbook cases tried to be relevant by putting in these 'real-life' situations, but the result was the complete opposite, and nothing wound me up more than being told by a teacher to learn something because 'it will be useful in this scenario', when it really wouldn't. I think that's something many people pick up on -
if they told you what it really WOULD be useful for, instead of trying to make it into a story, it might be received better.

The problem with that is that most things you learn in maths at school are useful for everything. Take solving quadratics. I can't think of a single mathematical method that relies solely on solving quadratics (there probably are some) but solving quadratics is such an essential tool for a mathematician (or physicist or chemist or engineer or anyone who ever needs any maths ever) that it should be automatic. It's like a music student saying "what's the point of C sharp and refusing to learn it because of that. You can't play many tunes on just C sharp (possibly some Phillip Glass, but not much else) but you'd be completely stuck if you wanted to play a tune without it.

I think that this is a fault of maths teaching which promotes the "when will I ever use this?" question. Perhaps we should also teach the stories behind maths- while teaching Pythagoras's theorem, for example, we show it's true and then teach the stories about the theorem, who developed it and why. I think you need to engage people in the philosophy of maths before you try and teach them the dry theorems and formulae.