Why is mathematics so difficult

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NorahLee
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#1
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#1
At some point I thought I had dyscalculia but no it’s just a tough subject and who else feels this way
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randompanda_
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ahahahah I feel the same way, Maths is my least favourite subject
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Kallisto
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Most teachers aren't capable of explaining the calculations, the steps and the logic behind it. The main reason why so many students struggle with this subject.
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Son of the Sea
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As a chain rule, I’d say there’s no formula to make maths easier, it’s hard cos of how difficult it is to integrate all the complexity.
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NorahLee
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(Original post by randompanda_)
ahahahah I feel the same way, Maths is my least favourite subject
Me too I don’t like it at all and it’s becoming a problem
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NorahLee
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(Original post by Kallisto)
Most teachers aren't capable of explaining the calculations, the steps and the logic behind it. The main reason why so many students struggle with this subject.
You’re absolutely right
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Muttley79
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(Original post by Kallisto)
Most teachers aren't capable of explaining the calculations, the steps and the logic behind it. The main reason why so many students struggle with this subject.
That's a pretty sweeping statement - evidence?
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NorahLee
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(Original post by Son of the Sea)
As a chain rule, I’d say there’s no formula to make maths easier, it’s hard cos of how difficult it is to integrate all the complexity.
💯💯
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Eigenvectorxyz
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(Original post by NorahLee)
At some point I thought I had dyscalculia but no it’s just a tough subject and who else feels this way
It's only hard for people who don't put enough effort in to memorise some formulas and do practice questions. I don't understand what's so hard about it.
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Andra01
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I don't think it's hard. I feel we tend to overthink.
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Kallisto
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(Original post by Muttley79)
That's a pretty sweeping statement - evidence?
Just by my own:

teachers who...

- ...just write some formulas on the blackboard without to explain the meanings.
- ...don't tell the students for what the lessons are useful in real life.
- ...don't care if you grasp it and aren't helpful to explain it in understandable words after that.
- ... use the terms to explain without to go in detail.
- ...have no idea or interest in to make lessons funny and have a habit per so to explain the things boringly.


Despite these things, mathematics was one of my favorite subjects, ironically. Just because I am good at it to teach mathematics myself by thinking about it. That does not change the fact that the most teacers in mathematics were horrible.
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_gcx
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This is mostly a ramble.

I don't think it is taught properly. I do a maths degree now and I struggled with maths early in school because the way it was taught was so "trick-based" (it's the best way I can describe it - like "tricks" to long division and such) I didn't really understand what was actually going on. I went into secondary school not being able to add fractions, I remember getting a whole homework set wrong in primary school. (I find it weird how all we do in 8 years of primary school and the first year or so of secondary school maths is arithmetic and linear equations, but I suppose it's a stretch to ask any more) After faffing around with "FOIL" for a while I realised expanding brackets boils down to recognising (a + b)(c + d) = a(c + d) + b(c + d). This was not made clear at all in class, and discovering all this myself was a massive "penny drop" moment. I still don't know how to long divide because I haven't had to.

The teaching pre-university persists like this. It's all very calculation-based, and deep understanding in any topic is not developed. The definitions of the integral and derivative are sketched, but you don't actually know what lim means, and the notation used for Riemann sums was so shockingly appalling it's a wonder they bothered. Then first year maths students are thrust into a course where understanding becomes key and calculations are consequent from that understanding. Many find this a shock and some students never fully recover, and end up transferring to a different subject or dropping out. Many more probably leave a maths degree with it not being what they wanted. People see "proof" as a discrete topic rather than something that basically defines maths, and the exam-centric maths teaching is definitely at least partially to blame for this. Of course, any sufficiently interested student can fill the gap with STEP and extra reading, but I don't think they should have to.

I think A-level further maths should cover the rudiments of set theory, (Russell's paradox, arguing that two sets are equal, that sort of thing) very basic real analysis, (showing sequences converge, maybe the definition of the continuous limit) and mathematical writing, prioritised over topics in numerical methods or vector geometry. Of course you would need people to teach this, and I would question my old school's teachers' ability to, so this is just my fantasy. I think at the very minimum complex numbers and matrices should have been in A2 maths.

Can't say what the solution is. Maths is without question the broadest/most diverse science and in the grand scheme of things what's taught in A-level is "basic" (every working mathematician will be confident with most of the pure content and relevant applied content) and GCSE "sub-basic". (forming the minimum for what a scientifically literate person should know, realistically though it'll be somewhere between GCSE and A-level at the minimum) Does people struggling with these mean that maths is an intrinsically hard subject or that the teaching is just poor? Not sure.
Last edited by _gcx; 1 week ago
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NorahLee
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(Original post by Eigenvectorxyz)
It's only hard for people who don't put enough effort in to memorise some formulas and do practice questions. I don't understand what's so hard about it.
No matter how hard I try it’s still so difficult, I know very little about it
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Kallisto
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Another problems I see with a better understanding for that subject is:

There is not enough time to go with the lessons into detail with all the students in the class. The schedule is too tight for concrete explanations.
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Rufus The Red
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I'd echo the sentiment that it's largely down to teaching quality.
That as well as the common perception that maths is hard which normalises the attitude that one doesn't need to bother trying if you're not a 'maths person' (not that the OP makes me thinks so in this instance).
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Sinnoh
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(Original post by _gcx)
the notation used for Riemann sums was so shockingly appalling it's a wonder they bothered.
ah yes, all integrals equal 0
A-level maths and further maths as it is feels more like a useful toolkit for other subjects than its own thing.

(Original post by Rufus The Red)
I'd echo the sentiment that it's largely down to teaching quality.
That as well as the common perception that maths is hard which normalises the attitude that one doesn't need to bother trying if you're not a 'maths person' (not that the OP makes me thinks so in this instance).
One thing I do notice is that with maths there are some people who are extremely good at it in a way that you don't have with, say, biology. I think that's what leads to the concept of "being a maths person"
(There is an International Biology Olympiad, but it's nothing like the maths one)
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Rufus The Red
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(Original post by Sinnoh)
One thing I do notice is that with maths there are some people who are extremely good at it in a way that you don't have with, say, biology. I think that's what leads to the concept of "being a maths person"
(There is an International Biology Olympiad, but it's nothing like the maths one)
I suppose a point with maths is that if you get an interest (particularly early on when there aren't the more complicated subjects which require some introduction - like complex numbers) then it's quite easy to work out more about maths and become better at it on your own whereas with something like biology you can't discover how organ systems function with just some time and a pen and paper.
My guess would be that this can lead to an early (even primary school level) competency divide among people which, due to the above, is greater than with other subjects. This disparity could then carry through to the idea of 'maths people' and 'non-maths people'.

Another part relating to the above is mindset, I see (and as I'm in year 11, this may be a perception slightly skewed to that age group) is that some people learn a set of rules and apply them rigidly to solve a problem, but others will find different ways to go about the problem (e.g. squaring 79 can be done competently, but laboriously by grid multiplication or 79*2+1 can be subtracted from 80 squared which is an easier calculation, but requires something closer to lateral thinking).
Being able to work the process out yourself is what I'd guess is the separating factor (at risk of sounding like someone trying to flog an online course with a dubious philosophy) between the top x% and the populace at large.
At GCSE level (and I'd guess A-level too, though this may be an unsubstantiated claim) neither approach will limit someone from getting top scores (especially due to some areas which must be rote learned), but once you're discovering rather than applying, the more lateral thinking based approach is necessitated.

However, I would say that the majority of my post is only really relevant to the the upper fraction of people and the rest of the distinction between being good or bad at maths comes largely from either attitude to the subject or the quality of teaching.
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econ73
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This is nonsense. Mathematics is not hard as long as it's taught in a way that you understand the concepts behind it. One time in an exam I forgot the quadratic formula, but I knew how to derive it, so that's what I did and then I went on about the question.
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Kallisto
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(Original post by econ73)
This is nonsense. Mathematics is not hard as long as it's taught in a way that you understand the concepts behind it. One time in an exam I forgot the quadratic formula, but I knew how to derive it, so that's what I did and then I went on about the question.
That is the sense of mathematics, namely to use a formula by thinking about the derivation and the logic behind. Memorising formulas are use- and helpless without understanding.
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_gcx
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(Original post by Kallisto)
That is the sense of mathematics, namely to use a formula by thinking about the derivation and the logic behind. Memorising formulas are use- and helpless without understanding.
To be honest when it's as simple as just plugging numbers into the formula usually you'd just let computers handle it. You probably wouldn't want to find a 5x5 determinant with a few variables by hand and so on, you'd use Sage or something. It's sometimes important to follow these things through by hand to get an understanding of the underlying machinery but past a level people don't care anymore
Last edited by _gcx; 1 week ago
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