This is my YouTube short of the day - based on my frustration that schools teach maths that is irrelevant to 99.8% of the population and ignore budgeting and tax:
The transcript is:
Do we really need to learn trigonometry at school?
It's a question I've been asking since I was about 17 when I was asked to calculate the surface area of a slice through a cone.
Why did I need to know how to do it then?
No idea.
Have I ever used it since?
Never.
Was I taught about anything useful, like how to calculate VAT?
No.
Did I ever get taught about how to calculate my tax affairs?
No.
Was I ever taught how to do lots of other really useful things in life, like a percentage markup on a product which I was going to sell?
No.
I was taught useless trigonometry.
Are we being taught the right maths in schools?
Ask your politicians at this election because I bet most of you have got a story similar to mine.
You didn't learn what you needed to know. You did learn what you didn't need to know.
Maths is failing us if it teaches us nonsense that we're never going to use.
Make it an election issue.
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I assume you are being facetious and provocative. Trig has many practical applications – even setting out the location for a humble garden shed needs basic trig.
We need to include trig and some of the other things you mention. Alternatively, just hire a tax expert as one would hire a builder.
Come on, I gave never once when doing diy used a single element of my trigonometry.
I used a tape measure.
And I looked by eye to make sure things are square.
That’s it.
Beyond that, what does the average builder use?
I am very serious.
Everyone will have their own list of “essential maths for life”… mine would include basic trig (3,4,5 triangles to get my raised beds square) but the point you make is correct.
We need “maths for life” for all and “maths for university” for those that want to.
You get it
The average builder does not need more than a tape and a level. The architect or designer will generally give diagonal measurements to check for alignment and square on a reasonably level site. Anything more complex, then he will get a setting out engineer. Quantity Surveyors need a bit of trig to calculate various measures of materials.
What’s missing is an holistic view of numbers. A sense of proportion and scale should be taught instead of abstract geometry and then maybe people will understand why increasing inequality is detrimental to most people’s health and wellbeing. People are easily hoodwinked when a rich person tells them the how much tax they pay as they are overwhelmed by the absolute value and fail to ask what proportion of their income that represents to compare it with others.
The super rich have large passive incomes which in a month might amount to a lifetime’s earnings of the average person.
Teaching perspective and proportion is critical to understanding climate change and tipping points. Just think of a roller coaster.
Thus, when it comes to voting the population might have a better idea when making their choice.
Let me offer you a basic point that illustrates your argument
Most (the vast majority) people think £100 million is more than £1 billion.
Actually it’s only 10% of it
These terms are in the media all the time
When people understand them then thinks about a little more maths
Trig tries to teach reasoning. I have ennovated circa 5 houses & I make furniture (as a “hobby”) . Indeed I don’t use trig.
But I do use some trig on a regular basis (area of a triangle 1/2 the base x the height) plus the relationship between the lines of a right angle triangle. etc.
Key point: it forces logical thinking.
& I never liked trig – but…no trig – no engineering.
But why does it need to be taught in preference to much more useful skills to thsoe who will literally never use it?
And why so early?
Why can’t such specialisation for a tiny minority begin at 16+?
No one has persuaded me of that as yet.
This is an interesting debate.
It is true that there is a lot of obscure stuff taught at school including trigonometry (and algebra). However, you have partly fallen into the fallacy that the Labour Party of the 70’s and Conservative Party of the 80’s fell into with thinking that Education is predominantly about teaching the people only “useful stuff” for when they become workers so that they can help the economy. It is a dangerous concept and paradoxically ties in with the grade inflation of the last 30 years. There is a pressure to show that schooling is teaching people valuable, desirable things!
Politicians and some employers pat themselves on the back and reassure the public that they are giving young people the necessary skills for life. Of course, these life skills are very important but so is being able to use logic, develop analysis and learning how to think – both inside and outside the box. I am not a blind advocate of ‘education for education’s sake’ as that is folly. Schooling should be realistic and have a practical application, but some of it really ought to be stretching human brains as much as is reasonable to tease out the natural geniuses in whichever field e.g. music, art, physics, design, who are more likely to be the innovators and inventers of the future. Additionally, thinking abstractly and creatively are also useful ‘alternative’ skills which some people eschew. Different people have varied tastes and preferences. For what it’s worth, my father-in-law still uses some trigonometry when he does carpentry and DIY jobs round the home. Trigonometry and algebra do help with developing logical thinking as well as being important in Engineering. Teachers do need to enthuse their pupils/students and give them that enjoyment and thirst for knowledge. That is an incredibly hard skill to learn and is very difficult if the teacher does not love that particular subject.
As for the point about learning Medicine, Law etc. after age 16. I seriously worry about the understanding of these complex professions… They are difficult occupations to get into, not because of artificial gatekeeping and class snobbery but mainly due to the layer upon layer of understanding that enables an experienced practitioner to work through complex problems and deal with the unusual or unexpected situation. The basic sciences understanding required to practice Medicine safely is seriously underestimated, even by some medics. It sometimes looks fairly ‘easy’ on television, and when one attends one’s GP Surgery! I can assure you that doctoring is anything but straightforward. As a practicing senior doctor and trainer of younger doctors, I am often appalled by the limited recall of basic science in some doctors. One of the chief problems in modern Medical practice is uncertainty and defensive practice – the ‘what if?’. Due to fear of litigation and a limited understanding of the underlying biological processes and epidemiology of diseases, we all resort to over investigation of relatively ‘normal’ symptoms. Like wider society we have all become risk averse, ad absurdum. Some clinicians then struggle to pick up what is definitely odd or serious as they investigate virtually everything therefore do not differentiate enough. This has huge costs for society at large and for individuals who become worried and anxious waiting for tests, or who may undergo the wrong investigations and therefore receive incorrect or suboptimal treatments. Healthcare expenditure is going up predominantly due to changing population demographics, increasing frailty with multi-morbidity, and costly technological developments. However, some of the costs are increasing due to an over reliance on learned patterns of behaviour, standardised protocols and a reduced emphasis on basic science understanding.
We need both practical skills for the modern financialised World, but we still need the underpinnings of many different subjects to give us a broad appreciation of diverse skills and areas of human endeavour. Some of these topics may feel obscure and irrelevant but they can open up our creativity and understanding of the complexity of this wonderful planet.
The comment on trigonometry came out of conversations my wife and I have had with many people, young and old. Furbthe record, until, forced to retire by ill health, she was a GP, but also (unusually) an MRCP. She has eight medical qualifications.
She would entirely agree with you about the dangers from standardised protocols, etc. She would also agree with you about the lack of understanding of risk leading to dangerous over-investigation. But she would not agree with you that this requires a knowledge of rigid, rule base, profoundly formulaic maths where there is a singular ‘right’ answer. The problem in medicine is that there is a risk in believing there might be a right answer when there is always a sectrum of risk. What would help medics, lawyers, and many others is a much better understanding of probability, the normal distribution, and more. But even then, knowing about standard deviations is not critical. Understanding that there is a risk spectrum that infirmary the heuristics we all use in life does matter. In other words, it is not the ability to learn the calculation per se that matters. The awareness of the concept is more important.
Rote learning dies nit deliver that. Actually, most gives a totally false impression of most of maths, and the uncertainty it can manage.
This is what I am finding pretty deeply frustrating about this discussion.
I think there are more important things to teach:
1. Critical thinking, some logic
2. Key history: colonialism
3. Basic politics and economics
Please excuse me Richard if I say that, IMO, this is one of your worst posts ever.
I think it one of my most appropriate
It is not that UK schools teach trigonometry that bothers me, it is the other areas of mathematics Richard mentions that UK schools DO NOT teach that bothers me.
Trigonometry has its place in education but so does calculation of one’s tax affairs. Leaving either out is a failure of the the educational curriculum.
Quite so
And one is a universal need and the other is not
Richard,
Let’s not gear the education system with the skills needed to do book-keeping! Normally the example people criticise is quadratic equations.
For those of us who do use maths (mathematicians, scientists, engineers, etc), the mathematics taught in schools is the bare minimum. It is v difficult for the human brain to develop those skills later in life. Internationally, our maths curriculum for under 16s is “thin”.
However: when I was at school we were also taught arithmetic. Basic numeracy. And advanced numeracy. It covered the things you mentioned (percentage markup, discount, tax, cumulative interest).
And, for the record, I also believe some things which people claim to be unnecessary to teach (art, music, literature, languages, sport, humanities, evolution, ethics) are important ….. To expose us to these things, help us see the world, and to aid thinking in different ways. Not just to train us to do one specific task.
Agreed
I left school in 1974 and stopped doing maths in 1972. My arithmetical skills are great but there was a lot about maths that I could not grasp, partly because it was taught without explanation, just ‘facts’. When I went to university in 1984 to study archaeology we were taught 345 triangles in order to lay out a straight grid on site and calculate length if you couldn’t get a tape measure in the right place. Apart from that I don’t think I have ever used what I was taught in ‘O’ Level maths.
That’s it…..
Subjects like trigonometry are the basis of more advanced mathematics. When I started my degree (in the early 1980s) I had the advantage of have a good background in matracies having done SMP maths. I was studying control engineering and mathematical modeling of systems is a major part of this.
While working as an Engineer, at mostly the technician level, an understanding of how systems behave has been helpful. While I would admit not to have used state space forms since graduation, I have occasionally taken a step response recording and understand how this is relevant to the system and showing good performance. My practical experience has also taught me to see the limits of such mathematical models.
For many subjects mathematics is a vital tool although it can become an end in itself. I do remember some control engineering text books could be looked as the writer saying “look at me, I can do complex maths”!. I suspect this is true in other subjects such as economics.
I do agree that basic practical uses of maths does need to be covered, again I remember a schools TV series in the early 1980s ( on the BBC) called Everyday Maths that gave a coverage of basic mathematics in life in an entertaining manner.
In the sixth form we were lucky that as part of the general studies curriculum the deputy head ( a maths teacher by background ) gave a short series on basics of real life money management including aspects like mortgages, life insurance and social benefits. He also showed how for the most part you can’t win by gambling.
You learned that when you were already specialising in maths though….
Richard – its not the maths you should be having a go at – its the real word applications – which I think you are really calling for – tax rates, VAT etc.
All things spatial – geolocation, maps – ‘where am I?’ etc etc – are sort of trig – related.
And as I T suggests – we should be taught how our country works or doesn’t work – , critical thinking, basic economic ideas , colonial history etc..
I completely disagree
I gave never once used anything likevt4i since leaving school
Not a single calculation
So why teach it?
And I can happily use geolocation and mass without knowing it now
As I say, 99.8% are in that situation and we waste school time teaching it
I agree, Richard. I failed my Higher Maths (Scotland’s equivalent to GCSE) in year 5 of my secondary education, but I needed to pass it in order to be eligible for entry to a CA Apprenticeship, so I had to do a 6th year. I got the Higher at the 2nd attempt, did the CA course, had a long career in accountancy and never used any of the advanced maths which took me 2 years to learn. The extra year of pointless study cost me a year’s earnings.
So many have that experience, Ken.
You appear to be are asking for more emphasis on functional mathematics of the sort that a person might use in everyday life. Quite a lot of that is arithmetic, percentages, fractions. Very basic stuff which I am sure your mathematical education prepared you to do. For example, VAT at 20% is add a fifth to the exclusive amount, or a sixth of the inclusive price. The pandemic demonstrates why people need more education on graphs and statistics.
And of course all sorts of jobs need trigonometry, from an engineers or pilots to plumbers, carpenters, electricians and garden designers.
But if you ever need the surface area or volume of a right cone, I suggest you simply look up the formula. (The area is π r^2 + π r l (where l is the slant length, a hypotenuse which you can get from Pythagoras from the radius and height; and volume is a third of a cylinder, π r^2 h/3.)
I’d go much further and suggest some basic education is needed on all sorts of practical aspects of everyday life, from how the political systems works (or doesn’t work) to the basics of home maintenance to nutrition. Essentially we want to form 16 or 18 or 21 year olds who can become functional independent members of society.
Thanks
Quadratic equations!
Why Sir?
In the syllabus.
Ps We were taught the old method of goal difference-which I have forgotten along with Schleswig-Holstein question.
I guess we should stop teaching poetry, music and then move on to history too.
Who needs this rubbish.
It would perhaps be useful if our politicians learned about Laplace transform so that they understood systems control theory and had a better chance of properly controlling our economy.
And Laplace transform does require trigonometry.
I wonder where that could fit into the school curriculum.
They are profoundly valuable to everyone
So us tax and budgeting
My point is a real oneb
Seriously, if you think poetry is profoundly valuable to everyone, why would you deprive people of the beauty of mathematics?
Sorry – but 99.8% of people will never, ever, think mathematics beautiful whereas almost every child gets poetry.
For those who need maths, do it in the sixth form
Until then do arithmetic. Sorry, but I will never agree with you on this.
You are being entirely inconsistent.
Please review previous comments – where you said you agreed with me.
I pointed out:
– (for those who need it beyond school) … Maths curriculum in England is thin.
– maths is difficult to aquire later in life (ie we can’t defer non-trivial exposure to maths till 18-20). I reckon the same applies to music/art.
So why, having agreed, do you encourage comments contrary to that, but supportive if your conjecture?
Richard, i think you are wrong on this. We need a method of exposing students to many things. Maths too … Functional maths for all. But we can’t defer maths skills to 6th form … That’s too late. Ditto music/art etc for those who’ll want and have the talent to go there.
I suspect few get the beauty of maths….. As you are an academic, I’m surprised you seem so happy to question a subject’s validity just because it isn’t needed to perform most tasks in most peoples’ lives. That rules out virtually every subject on the curriculum.
You aren’t transforming to being someone able to calculate the price of things, but not the value? Reflect!
I did not say don’t teach maths. Maybe you did not notice that. If not, however, you clearly did not read what I wrote. Maybe that’s why your comment so widely misses the mark.
I said don’t teach stuff that will not engage children with maths – like the absurd, non-contextualised, alienating teaching of the rules of trigonometry that are treated as important in an attempt to enforce rigidity in thinking and unquestioning acceptance just like square bashing is in the army. If you want to turn children off maths – and the vast majority are – then of course teach maths in such a literally rigid and formulaic way and then wonder why almost no one the benefited.
I am much more interested in education that engages and that does require foundations to be laid.
So teach ratio analysis and why it is vital in the context the child gets, by all means. Real world scenarios – not abstract analysis of triangles – will do very well for that. Then when they have to do trigonometry they’ll find it is just a form of ratio analysis, after all. So it will not be hard to learn later on.
And to compare with music, it’s a crime in my opinion that the vast majority of children leave school unable to read at least the treble clef, or know the difference between a major and minor key and so understand the music that surrounds them in life. Sure that’s hard to teach at 18. So why don’t we teach this form of literacy throughout school life that is relevant to almost all lives instead of trigonometry, which is not? But as we all know, it’s always been treated as a bit irrelevant.
Agree 100%. Along with algebra, quadratic equations and all the rest. Maths was the most miserable lesson in the whole curriculum. Have reached old age without ever needing it.
How money actually works, mortgages, pensions etc would have been much more useful.
Thank you!
If only 0.2% of the population think maths beautiful, it’s a sad indictment of our educational system.
Triginometry, as developed by Euclid in 300 BC, was part of the core of education for 2000 years, not because many want to calculate the area of the slice of a cone but because it’s a key example of logical thinking.
We need to teach both the basic ideas of mathematics (`pure mathematics’) AND how to apply it. For example the distinction between arithmetic and geometric progressions gives us the alternatives of simple and compound interest.
Coming back to that 0.2%, we need better teaching of maths so that fewer pupils get stuck at a low level of understanding – and that I think involves conveying the beauty of mathematics – and we need to connect it better to real life, which I take to be Richard’s fundamental aim here.
The various professional bodies are acutely aware of the need for better mathematical understanding in the population. The election manifesto of my own – the Royal Statistical Society – can be found at
https://rss.org.uk/news-publication/news-publications/2024/general-news/the-rss-launches-its-manifesto-for-the-2024-genera/
But you cannot progress in maths or English unless the basics are known – and awareness of them in bith subjects is staggeringly low. Hence my question
Beauuty requires an ability to see it.
And learning any trigonometry is almost impossible if you cannot do arithmetic well. And most people leave school quite unable to do so.
I disagree with your argument, Richard, that mathematics should be taught later. This is not because mathematics is beautiful (which I agree with Tim Kent it is) but because it is an essential tool for science and engineering, and it is crucial that a child’s interest in it is nurtured early. I do agree, however, that it can be overused, as you, Richard, indicate it has been in economics. I emphasise that mathematics is a tool. It should never be the master. In physics also, there has been a tendency to accept propositions purely on the basis of mathematical representation, often divorced from reality.
This is what I tell my maths students who ask me the same question every year (“when will I ever need to know this):
1. You will never need to know most of the maths you learn in school.
2. But I guarantee that you will need to know some maths some of the time
3. I don’t know what topics that will include, because it will depend on your career: accountant, scientist, healthcare worker, etc.
4. But learning maths will help you solve problems, even if they are not mathematical.
5. And if 130% of students find this joke funny, then I’ve done my job well.
🙂
Might a submerged purpose of state education be to invisibly teach gullibility and unquestioning obedience in order to develop a biddable/controllable future citizenry?
Hi Richard,
In this instance, you are wrong. You were taught how to calculate vat, tax rates and markup, because you were taught percentage. You may have learned later to apply that information in your work, like an engineer may learn to apply trigonometry.
In fact covering a number of maths topics pepares everyone for their chosen careers. Not all will use every topic, though.
Regards
With respect, unless you contextualise why you are teaching such things the vast majority do not recall a thing.
So, I am right and you are wrong.
And if you think applying a percentage is all you need to learn about VAT you are not just wrong but seriously deluded.
This blog OP isn’t really about maths at all but has an underlying question of who calls the shots in, and how the school curriculum is built and established.
Firstly, we need to distinguish between education and schooling. The latter has social and economic purposes, even deliberate conditioning, as well in facilitating the learning and development of us as weans and then adults.
Education has the derivation of ‘leading out’ and we lose that at our peril.
Unfortunately, we have not learned the basics of conserving our planetary home.
That is probably the largest lacuna in schooling.
Secondly, learning as learning does not need an immediate end use, or any personally tailored application.
Education has an intrinsic value to us as humans.
We have a natural inquisitiveness as part of our own humanity, and which has allowed us to reach current technologies in only a few thousand years, (if not how to apply them rationally).
As we don’t know what we don’t know, especially as young people, or even what interests us, then the principle of a broad based education has to be the priority.
The education system then needs constructing to provide for the full range of educational outcomes we need as humans, both for work and play, survival and personal development.
Teaching only “what is useful” is highly reductive and will tend to truncate curriculum options to just what employers want.
Reducing us to homo economicus, or serf workers who consume, is an awfully monochrome view of schooling or education.
I absolutely reject that as the dominant underlying principle, or even priority of schooling.
Of my own 47 year working life, over 50% of it has involved jobs/professions that did not even exist when I was 18. Nor did I know then what might interest, influence or stimulate me as a person.
How could I possibly know at 18 all that would be useful at 35, or 45 ?
How many of us have a life path fully envisioned at 16 or 18 ?.
How many of us know what creative skills and interests we might want to develop during our lives ?
How many of us know where we might travel, and what languages might be helpful ?
How many of us know what practical skills might assist us ?
Thirdly, in these social media discussions, personal experience will strongly affect our judgements as to what is useful, but it provides a spurious logic in deciding how curriculum options are constructed for the whole population. Education cannot be just based on ‘my’ experience.
Nor should the political class decide. We have the 6-7% of the privately educated dominating the political class and I would argue strongly against that clique deciding school curricula, and equally that schooling ought to be fundamentally decided by business, industry or academia, though all will have an input.
We were still taught pedagogy and education philosophy when I did my teacher’s training, and I do not believe anyone who is not familiar with educational principles, learning theory and practice should have any role in deciding the detailed content, and methods of schooling.
Mr Gove’s dismal fact and knowledge based education dogma with fixed examinations as the dominant assessment actually prevents both skills and research based learning, which have to be the priority, when most people have immediate access to personal computing more powerful than NASA’s for the Apollo programme, in their back pockets.
I have yet to see the fundamental aim of schooling as being stated that sixteen year olds ought to be able to say,
“I don’t know this, or how to do this, but I know how to find out, and I have the confidence in my critical skills to evaluate the information, and the resilience to learn new techniques”.
What I am sure of though, is that mathematics, and mathematical skills, will be integral to future school curricula, as they are now.
I wholly agree with the diea of a broad based education
That is precisely why I asked why so much time is wasted on minutiae of almnost no consequence
But I think you get that
As I am sure you get my arguments against reductionism.
I’ve forgotten most of the maths and physics I learned , most people will have too of most subjects they learnt at schools.
What I haven’t forgotten is my times tables, multiplication and division. Also logical thinking that is vital to be able to analyse real life data, set goals , track results and make adjustments. Equations can be looked up. Hard maths can be done with calculators and spreadsheets.
Also reading and writing and spelling.
The quality of that in the young today , most people below 50 is abysmal, unless they specialised.
I have given up trying to explain net of vat and gross to my fellow ‘managers’ after the fifth or more time. Their failure to understand the difference between cashflow and p&l. That the bank balance never tells the full story… and I’m not an accountant, many of them are self employed or employed in major organisations, yet the concept of Gross Profit is hard for them to grasp , the intricacy of bottom line cash GP compared to individual product GP too! You can’t have the same mark up on beers, wines and spirits to achieve the target cash GP…
What else?
Chemistry and geography and languages were/are useful a good basis for further understanding.
Economics turned out to be mostly useless neo-religious ‘belief’ systems and theories- like Religious Education. It did curiously help with constructing arguments and essays, reading and writing and research – more than from the English classes! Which were wasted on learning to write poetry or read Julius Caesar and other classics which on prepubescent and teenage minds are a complete waste. Later I read a lot more and understand better now.
The worst subject though at school level was History.. being based on EuroCentric navel gazing as being the only history that matters.
Tax to me, only makes sense in two ways, local and national. As a means of enhancing local service funding by local councils for their locality; and for wealth equality in a nation, to avoid the socioeconomic geographic disparity, to stop the poor being poverty stricken (we are failing) and to stop the richest getting ever more richer (again failing). The 70 odd Tax Free Zones which are furiously being set up will totally destroy whatever homogeneity remains today.
Much more to agree with than in most comments today
I am reminded of https://www.smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher .
Richard,
I have to say I am with Tim on this one, and Geejay’s first sentence reflects my initial reaction.
I did an economics degree after which I went on to teach maths (frightening to think that was over 50 years ago).
One reason was to try to aid an understanding of proportion in all its forms, especially in relation to everyday situations where I felt there was not enough emphasis. So my classes, and I’m sure many others, would fact check things like 20% extra free adverts and we did a personal finance topic in year 9 over 30 years ago. Yes, people deserve a solid grounding in those basics. But I am saddened by your statement that 99.8% of people will never think maths beautiful although that is probably true given the curriculum and the mechanical way it is expected to be delivered combined with the lack of specialists teaching it.
I was going to write a response to your post about testing along the lines that IT has a lot to answer for because its number crunching abilities seem to have stopped people thinking about the value of the conclusions being drawn from the data they are crunching. However, on the flip side, the power of IT to reveal the patterns and beauty in mathematics and its relevance to the natural world has opened opportunities to inspire students beyond the functional. Surely education should be about expanding horizons and encouraging enquiring minds as well as functionality.
I am all for encouraging enquiring minds
But when 99.8% of the poluation will never enquire about maths – or have reaosn to do so – why spend so uch time it – not elast when most can’t do basic arithemtic and statistics, which are vastly more useful and much more ikely to engage them?
I am genuinely utterly bemused as to why teaching material utterly useless to most people – that only alienates them from what they do need to learn in maths – is such a good idea
What is this desire to deny children the education they really need all about? Can anyone explain?
Teaching maths is so relevant that by Year 13 many 6th formers can’t recall their GCSE stuff from a year before. Neither do they understand any real world economics, politics etc but they do know if they wear the wrong colour belt or forget their tie they get a detention. Matthew Arnold in 1860 prescribed a curriculum of numeracy, literacy and obedience to their betters (those at the ‘great’schools like Eton). Plus ca change?
I always admired people who could do mental arythmatics. It was a skill i never mastered at school. Basically because the teacher was able to show you up as being a dunce or slow whitted. I dont think i ever answered correctly. I used to blush from head to toe.
Now im in my late 60s, i realise i was never given time to grasp and enjoy the logic of maths. Trying to keep the flexibility in how my brain problem solves stuff is a vital life skill that needs to be worked at.
Ive bought a book with several thousand basic sums which I spend 20 minutes a day working through. After a short time ive realised that: adding, subtracting, multiplication and division exposes ever more clearly interelated patterns that reinfforce each other.
Yes I agree, school teaching methods set you up to fail in life.
Bernard raised some valid points. why only a score of 0?
I think it is healthy to have a reasoned discussion but when somebody simply asserts they are right and others are wrong we have moved into different territory. To quote Shoshana Zuboff “Who knows, who decides, and who decides who decide”? Politicians, laypeople, educationists, a mix of those, something else?
One thing is certain, everyone thinks they know better than teachers.
I have taught.
I spent last week at a teaching conference for those teaching undergraduates, in the main, and they’re the ones who have got to university
It was universally agreed that there are massive holes in most new student’s education on very, very basic issues. Most cannot write a sentence, for example. A lot canno do much mental arithmetic. They cannot reliably estimate an answer to get an idea whether the figire they get from their calucaltor might be right, or not.
Almost every employer says so as well
Now tell me, why when a tiny propertion of jobs require trigonometry – and all choidlren know that – are we teaching it and alienating them from maths
And please don’t post an assetion that I do not know what I am talking about in response. Answer the question instead, please.
There is a hell of a difference between teaching in a university and teaching in schools so to claim your teaching in a uni is in any way comparable is ridiculous. Some schools are easy some are extremely challenging. One of my first classes was boys who had to stay on an extra year because the leaving age had been raised to 16 when they expected to leave at 15. Their favourite ploy was animal noises and banging their desk lids. Do you find a lot of that where you teach?
But look, I’m not defending any particular part of the curriculum because you could say about almost any subject 99% won’t use it again whether it’s trig or poetry. (And I taught English – in Scotland). And IT can do so much so why teach tax returns or sums?
I go back to Zuboff – who is to decide? Because it can’t be someone who’s decided a subject is pointless if 99.9% will never use it again. That’s too close to the right wing solution, no more froth, no more subjects that can’t be monetised, no more learning a musical instrument, no more visits to museums and so on. Your argument leads directly to Sunak’s rip off degrees.
We need an informed debate about the purposes of education and its content and also about who are going to make the decisions.
I suspect you know remarkably little about university education based on your comment. Sure they don’t bang the desks, but then those who would don’t turn up. Only around 50% of students do now on many courses, because yet again, most of what is taught is irrelevant, or at least its relevance is never explained and contextualised, which results in the same perception for the student. And if you think not worrying a int that is not relevant, I would be surprised.
As for suggesting I am offering a right wing solution – that’s just insulting, and I take it as such. Wanting young people to learn skills that will prepare them for life – like critical thinking, or the simple ability to communicate well, to manage their affairs, to know when they are being conned by maths as used by politicians and many others – is not right wing. It is about empowerment. Trigonometry is about being told there is an order and then complying with it. That’s deeply right wing. And these days very cheap to mark. That’s also very right wing. What I want is anything but that.
Richard,
I have to say I am with Tim on this one and Geejay’s first sentence describes my initial reaction. Granted education should be better at providing key skills for life and the sound understanding of percentages (and equivalent forms of proportion) is essential to handling modern life and avoiding being hoodwinked. In the school where I taught we included an introduction to personal finance in year 9 maths – and that was 30 years ago.
However surely we are doing youngsters a disservice if education does not extend horizons and encourage enquiry.
I was going to respond to the post on testing by saying that IT has a lot to answer for because the ability to crunch numbers seems to have displaced the ability to assess the value of the results. However, on the flip side, IT enables the beauty of mathematics and its links to phenomena and patterns in the natural world to be discovered much more easily by youngsters, enrich their perceptions and reduce that 99.8% figure of yours. Yes the curriculum needs readdressing but I feel that a purely utilitarian approach would be short changing our youngsters.
To quote a certain Mr Lennon, “You may say I’m a dreamer”.
If a peson can add up on a spreadsheet, that’s useful
Writing a formula to do so is good
Plotting a graph and interpreting it so no politician cons them would be great
But I asked a group of aduts today – all graduates and most with post-graduarte qualifications – had used trigonomery, ever, and they all laughed at the aburdity of the question. Of course they had not.
When so many (I mean massive)basic skills are absent i9n so many young people I still cannot see what is wrong with my qeustion
It is perfectly reasonable that an accountant asked what schoolchildren should learn in maths lessons would say percentages.
But that doesn’t make it unreasonable that a structural engineer asked the same question would say trigonometry, or a rocket scientist would say differential equations, or an epidemiologist would say statistics.
As Ex-Teacher says above, is is part of education that students who are developing their intellectual abilities get introduced to the way mathematics has the tools that can be developed in all those specialities and many more. Just as they should be introduced to the power of the written word to explain, stimulate and bring joy. And many more things.
If schools are stripped of everything not of immediate practical utility, what they do ceases to be education.
Let me provocative here then
Almost all of what is taught in English is also irrelevant. I have read so many undergraduate essays where the students have no idea how to construct a sentence, do not know how to use a comma or full stop, and think you should randomnly capitalise words in sentences. Paragraphs are a mystery to them. They have no clue how to write an argument. And they have apprently got grade A A levels, and can do trigonometry. Writing a sentence seems much more important to me.
I have to agree with you that there are some school subjects that don’t achieve what I think ought to be their aims. As you say English Language should be about being able to express yourself in a clear way that is intelligible to others (i.e. following the conventions of grammar, spelling, punctuation, capitalisation, etc.) whether it is creative writing or presenting an argument in an essay. If students who have done well at GCSE can’t do that there is something wrong. And I could criticise other subjects if it weren’t going off topic.
On the specifics of maths, I am not convinced either that the current secondary curriculum is ideally balanced. Arguably it is biased towards the preferences of university-level mathematicians. But that doesn’t mean it should be dominated by another vested interest (accountants) instead. Ultimately the experts on planning a curriculum for children are experienced teachers, and they should be able to draw on the ideas of multiple stakeholders in society – including accountants but also those structural engineers, rocket scientists and epidemiologists I mentioned as well as many more. But possibly not politicians!
I am not arguing fur accountants
I am arguing for relevance in life
And relevance to inspire learning
Jonathan
“As Ex-Teacher says above, is is part of education that students who are developing their intellectual abilities get introduced to the way mathematics has the tools that can be developed in all those specialities and many more.”
Wouldn’t that be fantastic, if it happened. Instead students are taught eg, this is how you find a sine or a cosine. When I asked why would you need to I was ignored. Perhaps it comes back to the question of how things should be taught – I cannot remember something if I don’t undestand how or why it works or how it could be used. I was told that I didn’t need to know that.
Spot on
Method
Not reason
And in every subject under the sun that is meaningless
A provocative argument. A lot of maths is kind of abstract and notionally “useless”. While I never used trig directly for its intended purpose as an adult, I definitely used maths topics as a basis for other subjects in school. For me physics and craft & design (a combination of woodwork, metalwork, design and planning) all required this, and if I hadn’t already done it I would have had to spend time learning the maths in addition to the new courses material.
A lot of these maths like algebra, trig, complex equation solving was helpful to give me a grounding for ideas like substitution, equations, plotting, which in turn helps me to read graphs and charts better, know how to construct proper formula in a spreadsheet program, and helped me with the basis for computer science when I studied it as an adult. So I still think it’s helpful to cover these, if not as in depth as your extreme example of finding cross sections of blocks.
There’s plenty of other topics which I’ve never used directly, and so are not really “useful”, but which have still helped me form a better understanding of the world around me, and so are valuable for kids to learn. I can still recite how various geographic features form – This is useless information, but it gives me a better appreciation for the natural world around me. I’ve never reacted anything in a test tube since school, but knowing that different categories of chemicals react in different ways impacts me when cooking, and when thinking about serious issues like climate change. The mental models we form as kids when we learn these useless things stay with us and help us, and I do think it’s a lot more difficult to build those as we get older.
One last point I want to raise is I enjoyed learning trig and other maths-y stuff, and I would argue that is the most important thing, as anything that’s boring kids will shut off and not want to learn. Taxes and managing money would have been very boring for me, and I’m not sure I would have wanted to learn it had topics like percentages been presented in that context. You mentioned poetry in a comment above and this kind of creative English I was never able to “learn” and failed to make any progress with because teachers never found a way to engage me. It’s fair to say you want to teach kids economaths, but how do you make it engaging?
For the record, I have done quite a loot of 3D design
I can create a working chassis for a model railway engine fromn scratch
That I know of I have never evcer done a trigonometric caculation to do so
I am still utterly baffled by all the claims made by thosee defending maths
99% of livves are lived withoput trigonemtry, at all
So why are we spending so kuch time teaching it when so much is missed out of the curriculum. And why7 is no one engaging wth that entirely fair question rather than. talking about the ‘beauty’ of maths, which very few get, even if I happen to do so. One of my degree final papers was in stats, after all.
As a mining engineer I do all my calculations on a spread sheet program. This keeps every thing simple and gives me a record when I need my calculations checked. When peoples lives can be on the line I always have my calculations reviewed.
All my designs are done using a CAD (computer aided design) for the same reasons.
This is exactly why Education politics and policy makers should be run by people with experience in the education system. You’ve completely missed many of the reasons for studying Maths (or other subjects).
I have taught a university syllabus that required maths
I can’t see I have missed a thing
Percentages are in the current GCSE syllabus, and both VAT and price markups feature fairly regularly in the exams (including the famous 10% up then 10% down question).
My argument for trigonometry (and algebra) being taught in schools is this: it teaches you data relationships; it teaches you logic; it teaches you care in handling data; it forces you to think about how what is written on the page relates to the real world.
I’m retired now, but I did teach up to A-level Maths. Maths is far, far better taught these days.
Spreadsheets also do that, and using a budgeting example would bring it to life.
And I am not questioning A level maths. Of course it can be taught there.
Maths is a highly hierarchical subject consisting of many conceptual layers each dependent on those below. Basic concepts like the trig taught at gcse cannot be left to age 16+.
If medicine, law and so much else can arrive post 16, so too can trigonometry
Alternatively, make it part of a further maths gcse. But wasting time teaching it to everyone just alienates them from maths.
And for the record, I have never once calculated a sine, cosine or tangent since I was 18, and a, certain I never will.
I am one of the 99% you want to impose this waste of time on when there are so many more important things to do.
I believe even though I am studying maths now I believe I will use most of my skills in the job I wish to specialise in which is carpentry so I think in any job you can apply 90% of the math skills learned like percentage change, interest, even things like how much surface area an item has got so you can work out how to put it in your car. So I disagree with what your saying here.
I bet you won’t
And you’ll work out what goes in your car by eye, or maybe with a tape measure. Even trial and error. You won’t calculate it. Why? Because the other measures are easier and your model of your car will be less accurate than the real thing
Time will tell
I have been arguing for this with my friends for ages. At school I was terrible at math, partly because it took me too long to grasp a new concept and before I had properly understood we had moved on to something else until I was deeply lost!! I’m sure there are many people who can and do use trig. but like a lot of other subjects that we don’t learn until we have more choice as adults I think most people can do without it at ordinary school level when there are so many other practical things that everyone will have to use like basic financial info. Luckily when I went o school in UK back in the 50s-60s you could still graduate without having a Math o or a level. Here in Canada you cannot graduate high school without passing math… I don’t know how many artists, musicians, historians mathophobes etc that has cut out of further education but it must be a lot! Not good. You will be happy to know that a recent article in The Globe and Mail (national newspaper May 31st)states “Ontario will add compulsory financial literacy test to its high school graduation curriculum in 2025” This will cover “skills to create and manage a household budget, save for a home and learn to invest” So while I don’t think I agree with all those priorities, its a start!
Thanks
Oh, so if we’re going to be taught about ‘household budgets’, then I’m sure the ‘macro-economists’ amongst us will be agog with expectations….
It occurs to me that the kind of economic modelling pursued by the likes of Ty Keynes and Steve Keen also requires a knowledge of trig functions.
Beats me why
It is based on double entry
Keen’s economics is based on modelling the economy as a complex thermodynamic system. You are referring to the Godley tables used to represent financial stocks and flows.
I am
That is what Ty uses, as far as I am aware – hence my comment
I was abysmal at math in school, but none of my teachers realized why I scrambled numbers; I was dyslexic/dyscalculic. I struggled with reading and writing in school too, but as an adult I have had articles published. I detested needlework and would rather have learned carpentry, but I became an accomplished Sailmaker. What we learn in school isn’t necessarily the skill we will rely on most as an adult. Although I dropped out of formal education at 17 and started traveling, mostly on boats I have never stopped learning. Back before GPS, I taught myself how to do celestial navigation, a skill that stood me in good stead during 150,000 miles of passage making and 13 crossings of the North and South Atlantic under sail. I never need Trig.
Most of us will go through at least one major career change in our adult life. During my second major career in healthcare I avoided getting bogged down with that dreaded paperwork; I stuck to practical roles and had even less need of specialized math skills. Like many other dyslexics I was more inclined to the visuospatial, excelling at critical thinking and innovation. Now I am focused on designing pieces of kit which start out with just a rough concept drawing and can advance further using design tools online. Thankfully, the simplest design programs do not require advanced math.
I think that we should encourage school children to develop debating skills. I learned to appreciate the art of debating at the Oxford Union. It has helped me to give ‘elevator pitches’ for my inventions and deliver press interviews. You use this important skill in your video presentations. Why do I consider this skill so important? Because it builds self confidence and prepares young people for the inevitable job interview when they will need to present their skills and positive attributes. They will need to communicate well with coworkers and later in their working lives they will need to mentor others. I worry that the addiction to text messages is dumbing down the language and shredding necessary communication skills.
Much to agree with
Critical thinking and critical appraisal are skills you obviously have. Trig never taught that
I have always had mathematical ability and pretty much always maintained an interest in maths, but I agree with you that UK school maths is dire (I had the misfortune of going through secondary school when the SMILE system was in vogue, and that represents the closest I ever came to hating maths),
Thanks
To lighten the tone a bit, are you familiar with Tom Lehrer’s song “New Math”? You might find it amusing, particularly if anyone ever tried to teach you modular arithmetic alongside the trigonometry.
Too strong, too simplistic.
I have always used simple trig thoughout my life. More important than lying percentages!
It should be part of a general education. Physics is the genuine stuff of life.
You, I suspect, are too strongly focussed on economics and taxes, something which mostly passes me by, though I may sometimes suffer the consequences. Practical stuff does not though. Ivory tower stuff is for academic folks, some of whom do not have their feet on the ground. Perhaps you do have one foot on the ground.
No I am not trolling, but you should be more pluralistic.
Politely, this is total nonsense.
It has precisely nothing to do with economics. Your assumptions are irritating. It is about life skills.
Can you tell me this last time you calculated the sine of something and why? I do a great deal of modelling, and model engineering plus CAD, and never have, ever. So why do you, unless it has a specific work function – which ours you in a tiny proportion of the population.
Meanwhile, budgeting, basic cooking and much more is not properly taufht – which would be liberating for many.
And precisely because percentages lie they are much important – and massively misunderstood. For example, very few people realise that rising a number by 20% and then reducing the resulting sum by 20% does not take you back to the starting figure. That’s why people are conned. What’s the cosine of being conned!
But what really gets me about your comment – and many others is its arrogance. So, you can do physics. Well done. The vast majority can’t, don’t and won’t. But they need to communicate. They need to be numerate. They need to know how to budget. They need to know they are not being conned. And you think that not relevant. Why?
“Physics is the genuine stuff of life”
Strictly, physics does not study “the stuff of life”. Physics works because it provides usable predictions about the material world ‘in life’, but it does not study ‘life’ itself (better served by the biological sciences, behavioural sciences, or philosophy – the last would, for example help to avoid careless uses of language or meaning …..).
Or to make the point in simple terms; Mr Wilcox, you can solve the puzzle by applying your remedy to your own argument.
Very good
I was hopeless at maths at grammar school I hated the subject. When it came to deciding which subjects to drop at O Level I chose not to do maths.Later in life I found myself in engineering. I worked in the Production Engineering dept of a medium sized company. In the early 70s computer aided machines were introduced. I was sent on a course learning to manually programme computer aided lathes. This meant using trig and other forms of maths. Amazingly, when I was forced to use them I successfully produced computer programmes sometime pages long. These were then transferred on to black tape for use on the machine. Fortunately ,this only lasted about a year when technology improved and the machines programmed themselves. So even later in life it is possible to learn complex things. The argument about teaching students to think logically is the same excuse used to teach Latin. That’s another waste of time.
You learned because it was relevant
Most children know maths is not relevant to them and are persuaded of the fact by teaching that does not in anyway explain the relevance of it.
I have discussed this with quite a lot of young people. The only reason they think they were required to learn most maths was to pass an exam. The use of it was never explained. Therefore they were utterly uninterested innit. They’re not stupid, in other words.
The Welsh curriculum has two different GCSE subjects – maths and numeracy. Guess this is the 16 year old version of pure and applied. I think the numeracy one probably covers what Richard has in mind.
Numeracy should be compulsory
Maths is a decidedly optional requirement
I am very old. However I regard math problems as recreational mental challenges in the same way we regard the challenges of different kinds of puzzles. I believe (without any evidence) that trying to solve a mathematical problem keeps my old brain active and helps me to retain my marbles.
That’s absolutely fine.
But that has nothing to do with trigonometry in schools. There is much better maths to learn than that.
Nothing I have said is about not teaching maths. It is about teaching maths (and everything else) in a way that engages. Learning the rules of trigonometry is about rote learning intended to deliver compliant automatons.
Richard, I normally agree with you, but on this one I don’t. You are confusing basic mathematical skills and financial literacy. Sadly most people are taught maths very badly and leave school barely understanding tne basics and hating the subject. The point of school maths is firstly to provide the building blocks should you choose to go further with it, and trigonometry is vital for those choosing engineering etc. Secondly to develop core reasoning skills, which again are vital for many scientific disciplines and to be able to evaluate things.
I did A level Maths and you could argue barely used in until I returned to university as a mature student. I’d forgotten all the trigonometry I’d learned for A level but it soon came back and the reasoning skills I’d developed gave me a headstart over the students without maths A level. And yes I did use trigonometry in several parts of my degree.
I admit I’ve always loved maths. But like many things we learn at school, we don’t know what is going to be useful in our future lives and sometimes it is the skills we learn that are more important than the actual knowledge. I have to say I found being forced to study poetry and Shakespeare for more painful and irrelevant than any maths I was taught. And I’ve managed to apply my mathematical skills to finances without any additional training. You could argue for finances for life to be taught at schools but as well not instead of basic maths.
I am not confusing mathematical skill with financial literacy, in the slightest.
Maybe I made a mistake in saying that teaching maths in the context of financial literacy- an applied mathematical skill requiring judgement, the management of uncertainty and an appreciation of risk (the two not being the same thing) was an alternative to the uncontextualised teaching of rigid, formulaic trigonometry that delivers the deeply uncomfortable suggestion that maths suggests there are right and wrong answers, when usually that is not true – almost everything in context is within a range.
I am making the point understanding matters. Most maths teaching fails to impart in students that contextual understanding or any joy fur the subject – which I think exists. So I think it a waste of time.
Of course I agree in building blocks, but trigonometry is little more than ratio analysis and there are vastly better ways to teach that. Trigonometry in comparison very decidedly optional.
What bemuses me is that this is so hard to understand when maths education – including all the dire (enforced) teaching on decontextualised quadratics and trig and so on – continues to be such a dismal failure for the country. Why is everyone here so keen to maintain rule based learning that does not work? I am struggling with that, I admit.
I was fortunate to go to a very progressive comprehensive and follow the SMP modern maths syllabus which was not at all rules based, so can’t comment on this. It seems you are eluding to how maths is taught and the current very rigid curriculum not the actual subject matter?
I have to say I was very concerned about the distinct lack of basic numerate literacy of our senior politicians during COVID. It was very clear that they did not understand the modelling data and forecasts they were presented with which had major impacts on their decision making. Clearly a public school education followed by an Oxford PPE degree did not instill such skills and people died because of this.
Now you are getting my point.
See this morning’s post
With the advent of Computer Aided Design it becomes possible for example to very quickly determine the diagonal of a rectangle very precisely. Presumably AI will have a role in making access to trigonometry functions much easier.
But when I designed on paper I never used trigonometry either
Why? Because I never found a reason to do so
I measured up, and drew what was required.
It’s all about conditioning, school. We learn about being on time, we’re expected to be interested during period one (of time) in, say, maths, or French, or chemistry, or biology, and then in the next period (of time) we’re expected to abandon all thoughts of what went before and suddenly find ourselves engrossed by, say, maths, or French, or chemistry, or biology or whatever we’re directed to be interested in… instead of following any natural inclinations we might have, following our own individual noses, we’re indoctrinated into accepting being ruled by time and direction instead of any natural order like the coming up or going down of the sun… we accept regimentation as somehow being natural when it clearly isn’t… and of course we’re made into useful idiots by learning about such things as the Weimar hyperinflation, presented to us as an inevitable consequence of creating money, one of the reasons we today find it so hard to get money creation realities through to the indoctrinated. I’m all in favour of education, but that isn’t what you get in school. School isn’t there for any good reason. I’d be in favour myself of allowing kids to have their own (tiny) homes from their early teens onwards as realistically by then many are young adults and not children at all, and work for their living. Then provide further education for those who want it when they want it. The current system is petrified of children, scared out of its mind by the thought they might come up with something, if encouraged, which would upset the existing status quo and the gilded lives of those who profit from the suppression of the rest of us. Any benign and unafraid system would be hurling resource after resource at our young, eagerly awaiting what discoveries their fertile unbridled imaginations could come up with. Instead, we have school. Pfffft!
Children arrive in school at 4 as massively creative himan beings
By the time they’re 18 most have lost almst all their creative ability
That’s what school does, because it demands neat answers, not the ability to pose questions
Trig is very useful in animation and game design/development. It underlies most of the SFX and CGI we see in films. In computer graphics it can be argued that everything is a triangle:
https://steemit.com/computer-graphics/@jrkirby/the-fundamentals-of-computer-graphics-i-triangles-and-rendering#:~:text=Everything%20is%20a%20Triangle,-That%20face%3F&text=Why%20not%20squares%20or%20circles,a%20surface%20in%203D%20space.
I’ve taught primary school kids trig to code animation. I do agree that context is key – get them to make something useful or interesting. If they don’t apply it they won’t see much purpose.
Now that is good….
Children who can’t “do” maths learn to hate maths.
Children who hate maths become teachers who hate maths.
Teachers who hate maths teach children to hate maths.
The Cockcroft Report pointed out that there is a seven-year gap between earliest and latest age for acquiring mathematical skills. A child of seven can grasp fractions as a division into parts that her peer at the next desk may not understand until they’re 14. After that, it will descend into rote-learning.
When the government decrees the age at which concepts will be grasped, the teacher hates even more the subject.
Understanding the concepts are far more important than calculating the answer. (I say that with feeling: I passed my O-level by knowing *how* to do calculus, even though all my answers from doing the arithmetic were wrong.)
You decry trig. When you get called for jury service, recuse yourself from any case where the speed of a vehicle has been calculated by measurement of skid marks across the road. Make sure that your fellow jurors fully understand the probabilities involved in DNA tests offered as proof.
At least if one has encountered the concept, one can begin to understand the conversation. It’s even better if your teacher loves their subject. And best of all is where the government stops standard-testing.
I have an A level in maths
I understand trig
I can no dount still do it, if I decide to do so
So why are you being so rude whilst completely missing the opiint I made?
Indeed, why are ypu so accepting of a status quo that denies children so much education they need?
All the discussion here is valuable but misses a vital point: to teach a subject well you need to understand it but in state schools at least there is a dearth of mathematicians who are trained maths teachers. Children are now often being taught maths by any teacher free to take on the extra work. My daughter, trained in secondary art but teaching DT – because this is also a subject with severe teacher shortages – was told by colleagues to keep quiet about her years working in an accounts office lest she find herself with added maths classes. As it is she’s teaching woodwork having never done any before, let alone teach it. She’s also teaching cookery; at least she does that at home!
What a ridiculous state of affairs.
Thanks