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January 6, 2023 - 10:51am
What did Rishi Sunak say in the first major policy speech of his premiership this week? I have no idea, because for the last two days the entire Westminster ecosystem has been talking about nothing but his aspirational proposal, buried toward the end of his speech, to make all schoolchildren study maths in some form up to the age of 18.
This triggered a sort of collective PTSD among the entire Westminster lobby, London policy world, and British third sector. If you think I am exaggerating, I can do nothing better than to quote the actor Simon Pegg, who posted this unhinged (and curiously inarticulate, for someone who professes such love for the humanities) rant online:
It is impossible to imagine Mr Pegg bragging about being illiterate in the same manner. But whereas illiteracy is rightly viewed as a scourge that must be tackled, one can freely admit to being innumerate without suffering from any social embarrassment. Little wonder that Britain’s cultural luminaries regularly brag publicly about the fact they cannot solve maths questions set for 12-year-olds.
Curricular policy obviously cannot be made on the basis that one was good or bad at school in one subject or another. None of the great and good who complain bitterly about mathematics would countenance, say, an argument that history education should be pared back simply because many pupils don’t like history.
Of course, they would never countenance it because history — despite the slow-motion collapse of the academic humanities — is high-status among the British elites; and the sciences, despite all the empty talk about promoting STEM, decidedly are not. C.P. Snow famously complained in 1959 that his brilliant academic colleagues were not embarrassed in the least in their ignorance of the most basic scientific concepts, and nothing has changed since then, to judge from this latest kerfuffle.
None of this is inevitable. Even the Victorians, who Snow blamed for privileging the humanities at the expense of the sciences and whose achievements in both fields were at least as great as ours, knew better than to view the two branches of learning as being engaged in a zero-sum competition.
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SubscribeI accept that most adults will not need complicated mathematics in their adult lives. However I would support the idea of ‘practical statistics’ being taught to prepare students for adult life.
Mind you The Powers That Be might not be so willing for the general population to really understand how the presentation of statistics by governments and the media is often deeply flawed or vigorously ‘spun’.
The problem with teaching statistics at present is that students can often learn a formula for working out mean for example with relative ease, but ask them to understand the reasons why a statistic may be misleading, or how a company decides what kind of statistical data to present in marketing, and they struggle.
Teaching more statistics to children, especially those who are going to need to dedicate a lot more energy to learning a formula than the students I met and saw going through the learning process (all with top grades at maths GCSE expecting to go on to STEM at good universities), is not going to help them to take every piece of data presented to them with a critical eye.
The real problem with education at present is not a lack of numerical skills, for the vast majority of people never need the majority of actual maths skills they learn in schools as is, it is a lack of priority on critical thinking across all subject areas.
Those same intelligent young people I saw grasping multivariable calculus with ease spent their breaks talking about how they were going vegan, and expressing a uniform belief that Brexit supporters were racist, not because of a lack of ability, but because they had spent so much time in an environment where conforming to singular interpretations and opinions was heavily rewarded, where regurgitating a formula was seen as more indicative of their cleverness than an ability to think outside of the box.
Indeed. Mathematics was far from my favourite subject – perhaps because it was taught as a set of recipes to learn.
However we did a term of statistics at Uni where the subject was taught as building a numerical model of the world, and how we could (or should avoid) derive useful information about real life from ‘the model’.
Happy days.
I was fortunate to have a similar experience which lead me to the thought that mathematics is poorly taught in the comprehensive system, I realize that this provokes the reaction “what is taught well within the comprehensive system
I was fortunate to have a similar experience which lead me to the thought that mathematics is poorly taught in the comprehensive system, I realize that this provokes the reaction “what is taught well within the comprehensive system
Indeed. Mathematics was far from my favourite subject – perhaps because it was taught as a set of recipes to learn.
However we did a term of statistics at Uni where the subject was taught as building a numerical model of the world, and how we could (or should avoid) derive useful information about real life from ‘the model’.
Happy days.
This argument that mathematics isn’t needed in later life completely misses the point. Mathematics is about abstract thought and anything which practices that helps to expand the intellect and one’s general ability to think. “Solve for x in this equation” is the beginning of abstract thought.
I don’t disagree that this is what maths should be, but the way that it is actually taught means that even most of those who excel focus not on this, but on regurgitating whatever will lead them to a tick rather than a cross next to their answer, hence why I say they can memorise and use a formula, but they don’t understand the real world contexts where it is applicable, the limitations to particular methods, or the alternatives, because they cannot see the process as an abstraction or extrapolate how to use it in other ways.
All of this side of maths is left by the wayside in the rush to tick off topics on an ever more massive list, and the little analytics that is taught tends to come from things tacked on to the latter parts of humanities or doled out in small doses to those who show sufficient natural skill to make it all the way up to university level maths.
Also, I do think it is a mistake to view maths as expanding the intellect, because unfortunately, all that any educational process can do is assist us in making the most of our in-born intellect, it cannot socially engineer the minds of the populace to produce a society full of people with genius level IQs and skillsets to match, thus those of us who are naturally good at maths need to be a little more understanding of those who cannot, and not think that if we spend enough time making them do maths that they will eventually become proficient at it.
I don’t disagree that this is what maths should be, but the way that it is actually taught means that even most of those who excel focus not on this, but on regurgitating whatever will lead them to a tick rather than a cross next to their answer, hence why I say they can memorise and use a formula, but they don’t understand the real world contexts where it is applicable, the limitations to particular methods, or the alternatives, because they cannot see the process as an abstraction or extrapolate how to use it in other ways.
All of this side of maths is left by the wayside in the rush to tick off topics on an ever more massive list, and the little analytics that is taught tends to come from things tacked on to the latter parts of humanities or doled out in small doses to those who show sufficient natural skill to make it all the way up to university level maths.
Also, I do think it is a mistake to view maths as expanding the intellect, because unfortunately, all that any educational process can do is assist us in making the most of our in-born intellect, it cannot socially engineer the minds of the populace to produce a society full of people with genius level IQs and skillsets to match, thus those of us who are naturally good at maths need to be a little more understanding of those who cannot, and not think that if we spend enough time making them do maths that they will eventually become proficient at it.
A bit of “practical statistics” might help a person do a bit of routine data analysis but without solid theory, a person can be led astray. Learning about means and standard deviations presupposes that the underlying distribution is normal. Some things are distributed normally – heights and weights, IQ, measurement error, and so on. But much confusion (and even heartache) can and does arise when a person makes the leap to assume that most – if not all – things are distributed normally.
For instance, incomes are distributed according to a power law. A lot of muddy thinking about income inequality arises because people are for the most part ignorant of this fact.
Other things that are not distributed normally include: “popularity” on dating sites, stock-market log-returns, extreme weather events, earthquake magnitudes, sizes of corporations, and so on.
And to understand these distributions you do need a bit of curve-sketching and even a bit of Calculus.
So, Bravo to Rishi for making the case for more people to learn Mathematics. And for sure, he needs all the Maths he can get to count his £££.
The majority learn to parrot certain definitions for exams, but they to be blunt don’t care what these definitions signify, they don’t care about curve sketching beyond whether they can do it well enough to get a certain number of marks on a test and they certainly don’t care about what standard distribution is. Nobody can force them to care, and nobody can force them to retain this knowledge for their entire lives.
The current suggestion that everyone learns maths until 18, will only put off the point where the majority will stop maintaining their snippets of parrot learning for a couple more years, it won’t ensure they are any more likely to actually understand the underlying concepts, or make them want to understand them, or ensure that they will use these ideas in their daily lives.
The majority learn to parrot certain definitions for exams, but they to be blunt don’t care what these definitions signify, they don’t care about curve sketching beyond whether they can do it well enough to get a certain number of marks on a test and they certainly don’t care about what standard distribution is. Nobody can force them to care, and nobody can force them to retain this knowledge for their entire lives.
The current suggestion that everyone learns maths until 18, will only put off the point where the majority will stop maintaining their snippets of parrot learning for a couple more years, it won’t ensure they are any more likely to actually understand the underlying concepts, or make them want to understand them, or ensure that they will use these ideas in their daily lives.
I agree that a basic knowledge of stats is most important and desirable for everyone. Basic mathematical and statistical illiteracy is not acceptable in countries with a universal secondary education system. It is a total disgrace for so called “educated” graduates some who wear it almost as a badge of honour. But it is not the whole problem.
For example I’m not convinced that even a high level of statistical literacy on all sides of the global warming/ masks/ Covid/ vaccines, God no God, Russia/ Ukraine arguments would make much difference. We also need the ability to examine the basic assumptions underlying the collection of the stats in the first place or any other form of knowledge or belief.
Our assumptions are often unstated and unspoken because they are rarely examined as they are so obviously true – even if they are not! And the collector of the stats has to have some idea of what is important to him/ her.
What percentage of the UK population believe Russia is the aggressor, the 2020 election was not stolen, belief in God is an indication you are not very “bright”. Compare that respectively to people in Russia, the States. I’m pretty sure it would give very different results. What does that tell us? That many people in Russia and Trump supporters in the States are ignorant and mislead?
I seem to remember the well known response to the book “100 authors against Einstein”. “I if I were wrong one would do”.
Disraeli made a good point. So too Darrell Huff and “how to lie with stats”. Spotting sleight of hand, assumptions, inappropriate use of stats to make a point, requires more than the ability to work out standard Deviations, use of Chi Squared, or T tests. Stats on the number of scientists who believe in God does not prove those that do are not “bright”. Uncritical acceptance of the narrative behind the stats whether conveyed by WHO, MHRA, Michael Mann, the current Health Secretary or my NHS Trust – could that be the problem? Or are stats essentially neutral, a tool, which can sometimes be misapplied for the manipulation of the unwary including the statistically well educated?
It may be true that most adults will not need complicated mathematics, but since when was this an argument against learning such skills?
I don’t agree with this education system where studying is forced. However, it is very beneficial.
I am an A-level maths student. I see people doing A-level maths and further maths lacking in basic arithmetic maths skills. They can do calculus, integrate with parts etc. but their knowledge is not practical, nor can they apply it.
Many people also lack financial understanding, perhaps why the £20 billion cost per year. And there is almost zero education about it in school.
I think a good solution would be a new branch of “practical maths” to be added. In A-level maths for my exam board, a calculator is allowed in ALL tests. There is a lot of learning, and little scope for learning how apply it in the real world. (Same with English to some extent, with all the century old poems, but little skill in writing convincing articles/letters etc).
As well as stats, there would be a mental maths component, with non-calculator shortcuts and tricks, a financial/tax component, and a problem solving component. Problem-solving capability cannot be taught, but surely practice can improve it.
The problem with teaching statistics at present is that students can often learn a formula for working out mean for example with relative ease, but ask them to understand the reasons why a statistic may be misleading, or how a company decides what kind of statistical data to present in marketing, and they struggle.
Teaching more statistics to children, especially those who are going to need to dedicate a lot more energy to learning a formula than the students I met and saw going through the learning process (all with top grades at maths GCSE expecting to go on to STEM at good universities), is not going to help them to take every piece of data presented to them with a critical eye.
The real problem with education at present is not a lack of numerical skills, for the vast majority of people never need the majority of actual maths skills they learn in schools as is, it is a lack of priority on critical thinking across all subject areas.
Those same intelligent young people I saw grasping multivariable calculus with ease spent their breaks talking about how they were going vegan, and expressing a uniform belief that Brexit supporters were racist, not because of a lack of ability, but because they had spent so much time in an environment where conforming to singular interpretations and opinions was heavily rewarded, where regurgitating a formula was seen as more indicative of their cleverness than an ability to think outside of the box.
This argument that mathematics isn’t needed in later life completely misses the point. Mathematics is about abstract thought and anything which practices that helps to expand the intellect and one’s general ability to think. “Solve for x in this equation” is the beginning of abstract thought.
A bit of “practical statistics” might help a person do a bit of routine data analysis but without solid theory, a person can be led astray. Learning about means and standard deviations presupposes that the underlying distribution is normal. Some things are distributed normally – heights and weights, IQ, measurement error, and so on. But much confusion (and even heartache) can and does arise when a person makes the leap to assume that most – if not all – things are distributed normally.
For instance, incomes are distributed according to a power law. A lot of muddy thinking about income inequality arises because people are for the most part ignorant of this fact.
Other things that are not distributed normally include: “popularity” on dating sites, stock-market log-returns, extreme weather events, earthquake magnitudes, sizes of corporations, and so on.
And to understand these distributions you do need a bit of curve-sketching and even a bit of Calculus.
So, Bravo to Rishi for making the case for more people to learn Mathematics. And for sure, he needs all the Maths he can get to count his £££.
I agree that a basic knowledge of stats is most important and desirable for everyone. Basic mathematical and statistical illiteracy is not acceptable in countries with a universal secondary education system. It is a total disgrace for so called “educated” graduates some who wear it almost as a badge of honour. But it is not the whole problem.
For example I’m not convinced that even a high level of statistical literacy on all sides of the global warming/ masks/ Covid/ vaccines, God no God, Russia/ Ukraine arguments would make much difference. We also need the ability to examine the basic assumptions underlying the collection of the stats in the first place or any other form of knowledge or belief.
Our assumptions are often unstated and unspoken because they are rarely examined as they are so obviously true – even if they are not! And the collector of the stats has to have some idea of what is important to him/ her.
What percentage of the UK population believe Russia is the aggressor, the 2020 election was not stolen, belief in God is an indication you are not very “bright”. Compare that respectively to people in Russia, the States. I’m pretty sure it would give very different results. What does that tell us? That many people in Russia and Trump supporters in the States are ignorant and mislead?
I seem to remember the well known response to the book “100 authors against Einstein”. “I if I were wrong one would do”.
Disraeli made a good point. So too Darrell Huff and “how to lie with stats”. Spotting sleight of hand, assumptions, inappropriate use of stats to make a point, requires more than the ability to work out standard Deviations, use of Chi Squared, or T tests. Stats on the number of scientists who believe in God does not prove those that do are not “bright”. Uncritical acceptance of the narrative behind the stats whether conveyed by WHO, MHRA, Michael Mann, the current Health Secretary or my NHS Trust – could that be the problem? Or are stats essentially neutral, a tool, which can sometimes be misapplied for the manipulation of the unwary including the statistically well educated?
It may be true that most adults will not need complicated mathematics, but since when was this an argument against learning such skills?
I don’t agree with this education system where studying is forced. However, it is very beneficial.
I am an A-level maths student. I see people doing A-level maths and further maths lacking in basic arithmetic maths skills. They can do calculus, integrate with parts etc. but their knowledge is not practical, nor can they apply it.
Many people also lack financial understanding, perhaps why the £20 billion cost per year. And there is almost zero education about it in school.
I think a good solution would be a new branch of “practical maths” to be added. In A-level maths for my exam board, a calculator is allowed in ALL tests. There is a lot of learning, and little scope for learning how apply it in the real world. (Same with English to some extent, with all the century old poems, but little skill in writing convincing articles/letters etc).
As well as stats, there would be a mental maths component, with non-calculator shortcuts and tricks, a financial/tax component, and a problem solving component. Problem-solving capability cannot be taught, but surely practice can improve it.
I accept that most adults will not need complicated mathematics in their adult lives. However I would support the idea of ‘practical statistics’ being taught to prepare students for adult life.
Mind you The Powers That Be might not be so willing for the general population to really understand how the presentation of statistics by governments and the media is often deeply flawed or vigorously ‘spun’.
Brilliant article, thank you Yuan Yi Zhu and Unherd.
If it was up to me this article would be printed and stapled to Simon Pegg’s face in the hope that the clown might actually absorb some reason and humility. Failing that, at least rolled up and shoved in the other end, where he’s getting his opinions from at present, evidently.
Are you saying he should be Pegged?
(I agree, btw.)
It always seems to me that the purpose of lefty slebs is to get the Conservatives elected. Decades of celebrity endorsements/ tantrums have never hurt the Tories or helped Labour.
Are you saying he should be Pegged?
(I agree, btw.)
It always seems to me that the purpose of lefty slebs is to get the Conservatives elected. Decades of celebrity endorsements/ tantrums have never hurt the Tories or helped Labour.
Brilliant article, thank you Yuan Yi Zhu and Unherd.
If it was up to me this article would be printed and stapled to Simon Pegg’s face in the hope that the clown might actually absorb some reason and humility. Failing that, at least rolled up and shoved in the other end, where he’s getting his opinions from at present, evidently.
It seems to me that there is a fundamental misunderstanding of what and to which age math should be taught in schools. Before anybody accuses me of being anti-STEMM let me say I’m a MD/PhD, a practicing scientist in the area of biophysics and use plenty of math in my work.
The truth is that the only things people need to know in terms of math (and the only thing they need to remember as adults) are the following:
(a) basic numeracy in terms of being able to add, subtract, multiple and divide (i.e. not hav to be reliant on a calculator).
(b) understand the concept of percentages. What does percent mean.
(c) Have a very basic understanding of statistics and statistical significance: i.e. understand the difference between mean, median and mode, know what a standard deviation is, know the difference between two measures that is required for significance (differ by greater than the sum of 2 standard deviations), and know the difference between standard deviation and standard error of the mean, and appreciate that the standard error of the mean only provides information regarding the precision but not accuracy with which a mean is determined (i.e. the difference between the true mean and the measured mean).
Basically that’s it. And the truth is that nobody who doesn’t make regular use of mathematics in their work lives can be expected to retain or remember anything more. It’s just like anatomy in medical school: 2 weeks after the 1st year exam everybody has forgotten all their anatomy except the real basics – then if they want to become surgeons and pass their FRCS exam they have to spend a year relearning their anatomy!
It is also helpful to have some knowledge of practical measurements, precision, tolerances and error bars. So that when someone tells you (I made up the example here) that the UK inflation rate is 9.75% you really understand that the uncertainty on this sort of measurement can easily be +/-10% – in other words that an “increase” from 9.75% in one month to 9.81% the next might easily be a decrease.
The danger in an increasingly digital world is that the inummerate take the super precise numbers we get out of computers and digital devices at face value.
I think what Rishi Sunak is calling for is not really “more maths”, but rather more “practical numeracy”. Something that could usefully be learned in school. But in fact, something I only really learned in the school science, design and technology and university engineering lab work. I’m not convinced this stuff is taught anything like as well as it used to be when we did more manufacturing. The lessons apply equally to everyday economics and finance.
I completely agree with you.
I completely agree with you.
Maybe, but how many people learn all these things in primary school and then forget them again before they enter the world of work? Plenty, I’d wager, and that alone would justify Sunak’s measures.
Remembering is a process that amongst other things requires repetition and relevance. We encounter more data through our experiences than we will ever be able to recall, so our minds tend to select the data that is most relevant to us to prioritise for storage, and depending on that prioritisation, the information will be more or less readily accessible. If that information is not relevant to life, it may well be forgotten.
Very few students fail to enter the world of work at the age of 16, so there is little time between them gaining qualifications in maths, and them entering some kind of workplace, even if it is only part time, which suggests that the problem is that what is being prioritised in the teaching and testing of maths skills is simply not relevant enough for them to maintain the repetition that keeps the skills fresh outside of a full time classroom environment.
That doesn’t mean that we shouldn’t be teaching maths, but it does indicate that something is going wrong with how we are teaching maths and what we are prioritising in that teaching, and that that needs to be the priority, not tacking on even more items for students to learn and then fail to retain long term.
Remembering is a process that amongst other things requires repetition and relevance. We encounter more data through our experiences than we will ever be able to recall, so our minds tend to select the data that is most relevant to us to prioritise for storage, and depending on that prioritisation, the information will be more or less readily accessible. If that information is not relevant to life, it may well be forgotten.
Very few students fail to enter the world of work at the age of 16, so there is little time between them gaining qualifications in maths, and them entering some kind of workplace, even if it is only part time, which suggests that the problem is that what is being prioritised in the teaching and testing of maths skills is simply not relevant enough for them to maintain the repetition that keeps the skills fresh outside of a full time classroom environment.
That doesn’t mean that we shouldn’t be teaching maths, but it does indicate that something is going wrong with how we are teaching maths and what we are prioritising in that teaching, and that that needs to be the priority, not tacking on even more items for students to learn and then fail to retain long term.
So you’re content that the worlds of physics, chemistry, and a lot of modern biology, are forever closed to most people.
I think that’s a silly comment. Most of the world of physics, chemistry and modern biology is already closed to even those with an undergrad degree in a STEM subject. Moreover, to have an appreciation of those various subjects, virtually everything can be explained in non-mathematical terms (other than things like string theory and the like). You would be surprised at how many biologists simply switch off the moment one shows even an equation as simple as 2+2 = 4.
I think that’s a silly comment. Most of the world of physics, chemistry and modern biology is already closed to even those with an undergrad degree in a STEM subject. Moreover, to have an appreciation of those various subjects, virtually everything can be explained in non-mathematical terms (other than things like string theory and the like). You would be surprised at how many biologists simply switch off the moment one shows even an equation as simple as 2+2 = 4.
Sally Clark would have not had her life wrecked had Sir Roy Meadow had a better education in statistics. The problem is often not what we don’t know but what we think we know but actually don’t. A little learning can be a dangerous thing if wrong and delivered with sufficient confidence by a man with a distinguished reputation.
If my memory serves me well, Roy Meadow was an expert witness for the prosecution so I expect his testimony would have remained unchanged. That’s why one needs expert witnesses for the defense to counteract the expert witnesses for the prosecution!
Don’t forget the evidence by the prosecution’s pathologist Alan Williams. He had known that Harry had evidence of a staph infection and not shared that with the defence.Both men biased and perhaps even bitter regarding any mother who claimed it was a cot-death.
The function of an expert witness is not to bolster any particular case put forward by the prosecution but to provide unbiased evidence on the basis of their expert knowledge so it would be rather shocking if Sir Roy Meadow’s evidence would have remained unchanged had he in fact had an adequate education in statistics sufficient to understand the error of the testimony that he gave in that regard. This is particularly so in the light of the guidance given to expert witnesses by Mr Justice Cresswell in the Ikarian Reefer some years before.
Of course as Jules Ritchie comments this is not invariably practiced and as Waney Squier discovered in shaken baby cases Judges and professional bodies can often be biased in their approach to a defence expert witness who becomes too enthusiastic advancing alternative expert theories contradicting orthodox prosecution theories that in fact have rather less scientific underpinning than was claimed.
Don’t forget the evidence by the prosecution’s pathologist Alan Williams. He had known that Harry had evidence of a staph infection and not shared that with the defence.Both men biased and perhaps even bitter regarding any mother who claimed it was a cot-death.
The function of an expert witness is not to bolster any particular case put forward by the prosecution but to provide unbiased evidence on the basis of their expert knowledge so it would be rather shocking if Sir Roy Meadow’s evidence would have remained unchanged had he in fact had an adequate education in statistics sufficient to understand the error of the testimony that he gave in that regard. This is particularly so in the light of the guidance given to expert witnesses by Mr Justice Cresswell in the Ikarian Reefer some years before.
Of course as Jules Ritchie comments this is not invariably practiced and as Waney Squier discovered in shaken baby cases Judges and professional bodies can often be biased in their approach to a defence expert witness who becomes too enthusiastic advancing alternative expert theories contradicting orthodox prosecution theories that in fact have rather less scientific underpinning than was claimed.
If my memory serves me well, Roy Meadow was an expert witness for the prosecution so I expect his testimony would have remained unchanged. That’s why one needs expert witnesses for the defense to counteract the expert witnesses for the prosecution!
What is needed is for more people to have a feel for magnitudes, to be able to visualise them, and your list would help accomplsh that.
I suggest understanding of geometry, volume, area, forces, energy, trigonometry and perspective. Inaccurate surveying combined with inability to think in 3 d produces many engineering mistakes including thise made by builders. Many people get lost because they lack any orienation skills, understanding bearings would help.
An understanding that energy has to be stored would be a massive improvement.
It is also helpful to have some knowledge of practical measurements, precision, tolerances and error bars. So that when someone tells you (I made up the example here) that the UK inflation rate is 9.75% you really understand that the uncertainty on this sort of measurement can easily be +/-10% – in other words that an “increase” from 9.75% in one month to 9.81% the next might easily be a decrease.
The danger in an increasingly digital world is that the inummerate take the super precise numbers we get out of computers and digital devices at face value.
I think what Rishi Sunak is calling for is not really “more maths”, but rather more “practical numeracy”. Something that could usefully be learned in school. But in fact, something I only really learned in the school science, design and technology and university engineering lab work. I’m not convinced this stuff is taught anything like as well as it used to be when we did more manufacturing. The lessons apply equally to everyday economics and finance.
Maybe, but how many people learn all these things in primary school and then forget them again before they enter the world of work? Plenty, I’d wager, and that alone would justify Sunak’s measures.
So you’re content that the worlds of physics, chemistry, and a lot of modern biology, are forever closed to most people.
Sally Clark would have not had her life wrecked had Sir Roy Meadow had a better education in statistics. The problem is often not what we don’t know but what we think we know but actually don’t. A little learning can be a dangerous thing if wrong and delivered with sufficient confidence by a man with a distinguished reputation.
What is needed is for more people to have a feel for magnitudes, to be able to visualise them, and your list would help accomplsh that.
I suggest understanding of geometry, volume, area, forces, energy, trigonometry and perspective. Inaccurate surveying combined with inability to think in 3 d produces many engineering mistakes including thise made by builders. Many people get lost because they lack any orienation skills, understanding bearings would help.
An understanding that energy has to be stored would be a massive improvement.
It seems to me that there is a fundamental misunderstanding of what and to which age math should be taught in schools. Before anybody accuses me of being anti-STEMM let me say I’m a MD/PhD, a practicing scientist in the area of biophysics and use plenty of math in my work.
The truth is that the only things people need to know in terms of math (and the only thing they need to remember as adults) are the following:
(a) basic numeracy in terms of being able to add, subtract, multiple and divide (i.e. not hav to be reliant on a calculator).
(b) understand the concept of percentages. What does percent mean.
(c) Have a very basic understanding of statistics and statistical significance: i.e. understand the difference between mean, median and mode, know what a standard deviation is, know the difference between two measures that is required for significance (differ by greater than the sum of 2 standard deviations), and know the difference between standard deviation and standard error of the mean, and appreciate that the standard error of the mean only provides information regarding the precision but not accuracy with which a mean is determined (i.e. the difference between the true mean and the measured mean).
Basically that’s it. And the truth is that nobody who doesn’t make regular use of mathematics in their work lives can be expected to retain or remember anything more. It’s just like anatomy in medical school: 2 weeks after the 1st year exam everybody has forgotten all their anatomy except the real basics – then if they want to become surgeons and pass their FRCS exam they have to spend a year relearning their anatomy!
Sorry but you have got this completely wrong! The problem is those children who just don’t get maths, for whatever reason, and go through life not getting it and suffering because of that. If you haven’t got basic numeracy, which is all you need (ie understanding of basic number relationships, percentages, statistics and how spreadsheets work etc) by 16, then studying a higher level after 16 is totally and utterly pointless, if fact way less than pointless but a waste of everyone’s time and cause of unpleasant frustration! Improving basic maths education before 16 is what is required. Quite what that has got to do with entrance requirements at Oxbridge a couple of hundred years ago is a mystery to me.
Well all students in Ireland, and across most of Europe, study maths up until leaving school at 18 and it doesn’t seem to do them any harm. If you haven’t got basic numeracy by age 16, maybe you need to stick at it.
It is emphatically NOT true that basic numeracy skills are all an adult needs in an advanced industrial economy, where political agendas are justified on the basis of statistics and probability, and products and services are marketed in the same way. With only basic arithmetic you are utterly at the mercy of the general process of advocacy masquerading as advice.
If you read Innumeracy by John Allen Paulos, for instance, you will find an explanation of how Bayesian statistics produces apparently self-contradictory explanations for the results of mass testing for diseases. The example he used was for AIDS testing (the book is about 30 years old) but it came in to relevance recently in the pandemic where one commentator on the news got clean away with claiming live on air that although the various Covid tests have a 2% error margin, it doesn’t matter because the false positives are cancelled out by the false negatives. This howler of a mistake was never challenged, and therefore succeeded in almost certainly assisting in giving more public confidence to the pandemic approach than it ever deserved.
The reason it’s wrong is this: the proportion of false negative to false positives depends not just on the accuracy of the test, but the real incidence of the disease in the population. If it is the case that only about 1% to 2% of the population have active Covid infections at any given time, it follows that the false positives will greatly outnumber the false negatives, thus providing the illusion that the infection rate is much higher than it really is.
It is also why in practice someone unfortunate enough to have received a positive HIV test, one possessig a 98% accuracy rating, in reality has about a 50% chance of actually having the disease, once you correct for the population bias effect.
The point here is not that every school leaver ought to be qualified to operate a Bayesian statistical analysis, it is that they ought to be capable of spotting obvious fallacies in the arguments and claims made by others and to defend their own ideas without making those same mistakes. The present situation in which school leavers may be incapable of this while having been educated in more “esoteric” (read “useless”) subjects is completely indefensible.
Of course it’s not what every adult needs and no more, but it is all most people need. School leavers at 16 are all educated in maths way beyond what most will ‘need’, in the sense that they have been given that education, the problem is that a sadly significant proportion still don’t get it.
My point is that nonetheless most school leavers are less adept in maths than they actually need to be. You are confusing qualifications with education. They are not interchangeable in the context of this debate.
My point is that nonetheless most school leavers are less adept in maths than they actually need to be. You are confusing qualifications with education. They are not interchangeable in the context of this debate.
Though I agree it’s worth educating people about the base rate fallacy, I’d also point out that in the UK, the PCR tests didn’t have an False Positive Rate of anywhere near 2% (assuming that’s what your “2% error margin” refers to). We can tell this by taking the actual positive rate when prevelance was very low (during the summer months) as an upper bound on the true FPR. See ONS’s Coronavirus (COVID-19) Infection Survey pilot: England, 17 July 2020 which says “For example, in our most recent six weeks of data, 50 of the 112,776 total samples tested positive. Even if all these positives were false, specificity would still be 99.96%” (and so the FPR 100% – 99.96% = 0.04%). ONS’s samples were tested in a Lighthouse lab.
When the prevelance was about 1%, the probability that you had SARS-nCOV-2 given a positive PCR was about 95%, assuming an FPR of 0.04% and a false negative rate of about 30%. See previous discussion 2 years back: https://unherd.com/thepost/i-am-utterly-confused-about-the-oxford-vaccine/#comment-57927
In general, the pandemic was an object lesson in innumeracy and its perils, and basic arithmetic wasn’t what was needed (so we probably need a better word than “innumeracy”, but never mind). Rather, people didn’t understand probabilities (especially conditional probabilities like FPRs and the like), exponential growth, and lacked statistical knowledge (for example, what “life expectancy” means). There were also basic failures of logic: I remember someone arguing on here that the PCR test had a huge FPR and that there were hardly any PCR positives in Australia despite lots of testing, so their continued lockdown was unjustified.
Of course it’s not what every adult needs and no more, but it is all most people need. School leavers at 16 are all educated in maths way beyond what most will ‘need’, in the sense that they have been given that education, the problem is that a sadly significant proportion still don’t get it.
Though I agree it’s worth educating people about the base rate fallacy, I’d also point out that in the UK, the PCR tests didn’t have an False Positive Rate of anywhere near 2% (assuming that’s what your “2% error margin” refers to). We can tell this by taking the actual positive rate when prevelance was very low (during the summer months) as an upper bound on the true FPR. See ONS’s Coronavirus (COVID-19) Infection Survey pilot: England, 17 July 2020 which says “For example, in our most recent six weeks of data, 50 of the 112,776 total samples tested positive. Even if all these positives were false, specificity would still be 99.96%” (and so the FPR 100% – 99.96% = 0.04%). ONS’s samples were tested in a Lighthouse lab.
When the prevelance was about 1%, the probability that you had SARS-nCOV-2 given a positive PCR was about 95%, assuming an FPR of 0.04% and a false negative rate of about 30%. See previous discussion 2 years back: https://unherd.com/thepost/i-am-utterly-confused-about-the-oxford-vaccine/#comment-57927
In general, the pandemic was an object lesson in innumeracy and its perils, and basic arithmetic wasn’t what was needed (so we probably need a better word than “innumeracy”, but never mind). Rather, people didn’t understand probabilities (especially conditional probabilities like FPRs and the like), exponential growth, and lacked statistical knowledge (for example, what “life expectancy” means). There were also basic failures of logic: I remember someone arguing on here that the PCR test had a huge FPR and that there were hardly any PCR positives in Australia despite lots of testing, so their continued lockdown was unjustified.
Well all students in Ireland, and across most of Europe, study maths up until leaving school at 18 and it doesn’t seem to do them any harm. If you haven’t got basic numeracy by age 16, maybe you need to stick at it.
It is emphatically NOT true that basic numeracy skills are all an adult needs in an advanced industrial economy, where political agendas are justified on the basis of statistics and probability, and products and services are marketed in the same way. With only basic arithmetic you are utterly at the mercy of the general process of advocacy masquerading as advice.
If you read Innumeracy by John Allen Paulos, for instance, you will find an explanation of how Bayesian statistics produces apparently self-contradictory explanations for the results of mass testing for diseases. The example he used was for AIDS testing (the book is about 30 years old) but it came in to relevance recently in the pandemic where one commentator on the news got clean away with claiming live on air that although the various Covid tests have a 2% error margin, it doesn’t matter because the false positives are cancelled out by the false negatives. This howler of a mistake was never challenged, and therefore succeeded in almost certainly assisting in giving more public confidence to the pandemic approach than it ever deserved.
The reason it’s wrong is this: the proportion of false negative to false positives depends not just on the accuracy of the test, but the real incidence of the disease in the population. If it is the case that only about 1% to 2% of the population have active Covid infections at any given time, it follows that the false positives will greatly outnumber the false negatives, thus providing the illusion that the infection rate is much higher than it really is.
It is also why in practice someone unfortunate enough to have received a positive HIV test, one possessig a 98% accuracy rating, in reality has about a 50% chance of actually having the disease, once you correct for the population bias effect.
The point here is not that every school leaver ought to be qualified to operate a Bayesian statistical analysis, it is that they ought to be capable of spotting obvious fallacies in the arguments and claims made by others and to defend their own ideas without making those same mistakes. The present situation in which school leavers may be incapable of this while having been educated in more “esoteric” (read “useless”) subjects is completely indefensible.
Sorry but you have got this completely wrong! The problem is those children who just don’t get maths, for whatever reason, and go through life not getting it and suffering because of that. If you haven’t got basic numeracy, which is all you need (ie understanding of basic number relationships, percentages, statistics and how spreadsheets work etc) by 16, then studying a higher level after 16 is totally and utterly pointless, if fact way less than pointless but a waste of everyone’s time and cause of unpleasant frustration! Improving basic maths education before 16 is what is required. Quite what that has got to do with entrance requirements at Oxbridge a couple of hundred years ago is a mystery to me.
There’s an elephant in the room here… the scarcity of good Maths teachers. If you’re lucky enough to have been taught by good teachers with a real enthusiasm for the subject, your chances of picking up enough to see you through life is much improved over those whose teachers who were just going through the motions. I suppose the same can be argued for any subject, except that having the kind of understanding of Maths and of how to impart it just seems more rare. (No stats to back that up!)
What do others think?
The problem with Rishi’s plan then, is that it’d take a generation to bring to fruition and there’d still be a danger that those extra recruits into Maths teaching will bore the pants (or skirts) off schoolkids, thus wasting everyone’s time.
I disagree.
There’s certainly a shortage of maths teachers. But not a shortage of people who could teach maths.
There are a lot of people who are in their 50s and perhaps 60s who are retired or semi-retired who could take on some of the teaching here. I’d consider it myself at some point – provided the school environment was tolerable. I think a lot of older people are going to be needing some extra income in the coming decades.
Whether that fits into the current educational system and the rather rigid way it’s organised is another matter. But I suspect that will have to change anyway.
Fair point. I suppose the kind of older recruits you refer to might also have acquired the life skills to teach in a way that was more enthusiastic than a worn-out teacher who’d been on the education treadmill since their own schooldays. I suppose my view was influenced by having too many of those myself, albeit many years ago now.
Fair point. I suppose the kind of older recruits you refer to might also have acquired the life skills to teach in a way that was more enthusiastic than a worn-out teacher who’d been on the education treadmill since their own schooldays. I suppose my view was influenced by having too many of those myself, albeit many years ago now.
I disagree.
There’s certainly a shortage of maths teachers. But not a shortage of people who could teach maths.
There are a lot of people who are in their 50s and perhaps 60s who are retired or semi-retired who could take on some of the teaching here. I’d consider it myself at some point – provided the school environment was tolerable. I think a lot of older people are going to be needing some extra income in the coming decades.
Whether that fits into the current educational system and the rather rigid way it’s organised is another matter. But I suspect that will have to change anyway.
There’s an elephant in the room here… the scarcity of good Maths teachers. If you’re lucky enough to have been taught by good teachers with a real enthusiasm for the subject, your chances of picking up enough to see you through life is much improved over those whose teachers who were just going through the motions. I suppose the same can be argued for any subject, except that having the kind of understanding of Maths and of how to impart it just seems more rare. (No stats to back that up!)
What do others think?
The problem with Rishi’s plan then, is that it’d take a generation to bring to fruition and there’d still be a danger that those extra recruits into Maths teaching will bore the pants (or skirts) off schoolkids, thus wasting everyone’s time.
Rishi’s not necessarily wrong about Maths but the real problem with the speech was the total absence of a vision for the future of the country. We don’t need more mediocre managerialism, we need inspiration and action.
Rishi’s not necessarily wrong about Maths but the real problem with the speech was the total absence of a vision for the future of the country. We don’t need more mediocre managerialism, we need inspiration and action.
Comparing illiteracy with innumeracy in this context is idiotic. No one is asking children to study English till 18 and GCSE level maths is a perfectly good level of maths education. What Rishi wants is to make sure children have “analytical skills”. Well, math is only one small part of analytical skills. Creativity and critical thinking are required too. As for your assertion that there’s some kind of STEM snobbery, given that the number of young people taking humanities subjects at all levels keeps plummeting I think that any snobbery is actually directed at the arts.
Comparing illiteracy with innumeracy in this context is idiotic. No one is asking children to study English till 18 and GCSE level maths is a perfectly good level of maths education. What Rishi wants is to make sure children have “analytical skills”. Well, math is only one small part of analytical skills. Creativity and critical thinking are required too. As for your assertion that there’s some kind of STEM snobbery, given that the number of young people taking humanities subjects at all levels keeps plummeting I think that any snobbery is actually directed at the arts.
Humanities grad here. Hated maths at school. I think the trouble is that the old system of having a rounded education has been destroyed (perhaps irretrievably) by intense specialisation. It isn’t enough to have a modern languages degree any more as back in the day modern languages often meant you knew several to a decent standard – which allowed post-university exploration. Nowadays modern language undergrads (me included) only learn 1 language to a high standard. We had postgrad students in our language department who only spoke/read one language.
I don’t know if the clock can be turned back.
It will ultimately have to be. British 16 year olds specialise to a ludicrous degree, before they know who or what they are. An awful lot of Britain’s problems stem from this. The breadth of ignorance can be extraordinary. It’s taken 60 years or more to reach this sorry state, but reversing it will have to start sometime.
The obsession with intense specialisation in modern education does seem in some ways to do harm to both ends of the learning spectrum. Whilst in some ways it allows those who are particularly skilled in one area to focus on that, it means that a lot of pressure to tick all the boxes for maths and english skills in a shorter time frame is imposed upon everyone, but especially those who aren’t gifted in those areas.
Those who struggle with maths or English are frequently held back under current systems, given more time, but penalised by being told they can’t do A levels until they achieve a certain grade in maths and English in spite of the majority of what those qualifications test being unrelated to actual literacy and numeracy.
It’s also bad for those who like me are all rounders with the potential to be polymaths. The only subject I ever struggled with in school was physical education, was considered gifted in maths, English and languages from early on in my schooling, and acquired my maths GCSE by the age of 14. However, once I was shunted from school into the world of the sixth form, I struggled, as not only was I expected to pick just a few subjects to focus on that would be tailored to just one degree subject, I would have to learn those in a very strict time scale, with no real allowances for variance in health, circumstance, etc.
Now in my late 30s, I have multiple degrees, I have studied both STEM and humanities, and walk an interdisciplinary path in academia, but I had to take a very roundabout route that most with the potential simply would not be able to follow, and I have suffered economically for that.
You say that modern language undergrads only learn one language to a high standard. I think you are right : that language is their native tongue!
What you should have said, I think, is that they only learn one additional language – and I would dispute whether that is to a high standard.
In my day (fifty years ago) a modern languages degree was a means to study literature – the language skills were regarded as a rather pedestrian necessity, a dull means to an intellectal end.
After all, learning to speak French is not an academic achievement – lots of extremely stupid French people do it far better than the usual UK graduate.
It will ultimately have to be. British 16 year olds specialise to a ludicrous degree, before they know who or what they are. An awful lot of Britain’s problems stem from this. The breadth of ignorance can be extraordinary. It’s taken 60 years or more to reach this sorry state, but reversing it will have to start sometime.
The obsession with intense specialisation in modern education does seem in some ways to do harm to both ends of the learning spectrum. Whilst in some ways it allows those who are particularly skilled in one area to focus on that, it means that a lot of pressure to tick all the boxes for maths and english skills in a shorter time frame is imposed upon everyone, but especially those who aren’t gifted in those areas.
Those who struggle with maths or English are frequently held back under current systems, given more time, but penalised by being told they can’t do A levels until they achieve a certain grade in maths and English in spite of the majority of what those qualifications test being unrelated to actual literacy and numeracy.
It’s also bad for those who like me are all rounders with the potential to be polymaths. The only subject I ever struggled with in school was physical education, was considered gifted in maths, English and languages from early on in my schooling, and acquired my maths GCSE by the age of 14. However, once I was shunted from school into the world of the sixth form, I struggled, as not only was I expected to pick just a few subjects to focus on that would be tailored to just one degree subject, I would have to learn those in a very strict time scale, with no real allowances for variance in health, circumstance, etc.
Now in my late 30s, I have multiple degrees, I have studied both STEM and humanities, and walk an interdisciplinary path in academia, but I had to take a very roundabout route that most with the potential simply would not be able to follow, and I have suffered economically for that.
You say that modern language undergrads only learn one language to a high standard. I think you are right : that language is their native tongue!
What you should have said, I think, is that they only learn one additional language – and I would dispute whether that is to a high standard.
In my day (fifty years ago) a modern languages degree was a means to study literature – the language skills were regarded as a rather pedestrian necessity, a dull means to an intellectal end.
After all, learning to speak French is not an academic achievement – lots of extremely stupid French people do it far better than the usual UK graduate.
Humanities grad here. Hated maths at school. I think the trouble is that the old system of having a rounded education has been destroyed (perhaps irretrievably) by intense specialisation. It isn’t enough to have a modern languages degree any more as back in the day modern languages often meant you knew several to a decent standard – which allowed post-university exploration. Nowadays modern language undergrads (me included) only learn 1 language to a high standard. We had postgrad students in our language department who only spoke/read one language.
I don’t know if the clock can be turned back.
I was pretty poor at most things including Maths until I went to college. Once it was linked to a real world situation, it seemed pretty straight forward. So for once I agree with Rishi.
It is amazing how many media personalities actively agitate against maths. They might have got the hang of it if they had come at it from another angle.
I was pretty poor at most things including Maths until I went to college. Once it was linked to a real world situation, it seemed pretty straight forward. So for once I agree with Rishi.
It is amazing how many media personalities actively agitate against maths. They might have got the hang of it if they had come at it from another angle.
The real problem with the proposal is that it’s at exactly the wrong stage of education; it’s far too late, children’s attitudes are too entrenched, and the sorts of maths appropriate at that age are inappropriate for what most people need in the real world. A far better bet would be to insist that no pupil leaves primary education without a solid grounding, and demonstrable achievement, in literacy, numeracy, reasoning, and social behaviour. That would provide a firm platform for the secondary and subsequent stages.
The real problem with the proposal is that it’s at exactly the wrong stage of education; it’s far too late, children’s attitudes are too entrenched, and the sorts of maths appropriate at that age are inappropriate for what most people need in the real world. A far better bet would be to insist that no pupil leaves primary education without a solid grounding, and demonstrable achievement, in literacy, numeracy, reasoning, and social behaviour. That would provide a firm platform for the secondary and subsequent stages.
I hold a viewpoint that most who read it will consider off the wall bonkers: I think a very significant proportion of people can be taught most things to a decent standard if the people in question are motivated enough and take enough time. This includes maths or any component of STEM or a new language or draw and paint or cook to a near professional standard. I mean by this largely cognitive activities and I exclude activities that require high end physical components – like becoming good at a sport without better than average reactions or play the violin to a good standard when you don’t have perfect pitch etc.
Many people have told me my belief that most people can be taught most things is unrealistic nonsense. I nevertheless persist in believing that. My observation is the big variation between people is the speed with which they comprehend something and can apply it – which in effect is a strong indicator of the wide spread in abilities you see in individuals. If given enough time, most people can understand far more than they think they are capable of. They don’t because they are slow off the bat, and they don’t have a strong enough innate interest in abstractions to get past the inertia and persist for a long time. There are others who can’t do it because they are stuck in loops in their heads: circumstances, backgrounds, events, history etc, and although all of that can be got past, it requires a lot of effort to unpeel all that unless you pay someone to help. To illustrate my point, the person who can understand the quantum tunnelling effect in semiconductors today is no different from the person who was stacking hay on a two acre farm all their lives a couple of millennia ago. I have come across young people (in India this was) who were literally shovelling goatshit from one end of a village to the other, but half an hour of chat made clear they would be capable of anything any college graduate could do if they had been through the same education paths. This is in effect people who need to be ‘directed’ – as in, given the option they would wile away the years stuck in a groove of habits doing nothing.
The thing which changes this, is that most people when young enough to be coercible, are forced into school and college by their parents or govt for eight hours a day for a decade and a half minimum. Much rarer are people who are innately quick at comprehension in a particular subject because they are so obsessively absorbed in it that they gravitate towards first expertise and then sometimes beyond, into innovation and originality in their field of interest, much faster than everyone else.
I believe it is here we can find the missing piece into teaching things to people for whom interest in a particular subject, say maths, is not innate. The culprit for my money is the industrialisation of education – something which has happened for very good reasons indeed but is now ripe for revolution. Imagine you could teach each individual child or adult one-on-one – bespoke teaching on a per personality basis which is explicitly designed to plug the comprehension gaps an individual teacher can see in their individual tutee. Well, you get much, much, better outcomes. The private education industry, which goes varying degrees down this path, proves the point. I’m not saying you will make someone interested in STEM, merely that you can teach it – although you might even awaken interests that weren’t there before comprehension came. The reason it doesn’t happen for the bulk of people is because bespoke is impractical and expensive, and most individual teachers have neither the expertise nor motivation to get into the heads of a large number of tutees to see where the blocks are.
And finally, my point is this: today instead of teachers we should start to focus on technology – I believe algorithms are perfectly capable of getting into the heads of people (who allow them to), better than any teachers, and improve all aspects – memory, comprehension, even originality which I’m firmly convinced can ramp up the level and complexity to which people teach themselves. Our current addiction to discourse within the virtual social worlds created by algorithms, proves this point. And if the algorithms are going to get into our heads regardless, we may as well use that to effect constructive rather than harmful changes to ourselves, by actively constructing technology which improves up learning.
A very interesting comment. I agree that most/all people would learn better if provided personalized tuition although, as you recognize, that would be prohibitively expensive. I do believe, however, that there is a range of innate abilities and, even with personalized tuition, people would reach their own natural limit of achievement.
Your suggestion about AI-based education disturbs me. AI currently monitors our internet activity and selects the ads we’re shown accordingly. I’ve no doubt technology will (or already has) advance to the point of providing on-line tutoring programs that would set lessons and questions, analyze our responses, and figure out the basic flaws in our reasoning and comprehension, and adjust subsequent lessons and questions accordingly. The AI would, in effect, get into our heads. I’m not so much concerned about the program itself, as the people who analyze the program and what they learn about the cognitive processes, limits, and biases of each person. That is an advertiser’s dream, and also a government’s dream. The potential for abuse is endless.
Agreed there is huge potential for abuse, and in response we have to push for legislative frameworks that enshrine privacy. It’s not as though companies who want to sell us things are not going to profile us for targeted selling anyway, they do it via offering their software for free and we love things that appear seemingly free. What I’m also hoping is that more sophisticated technologies arise to assist with assessing exactly what all the software we use is getting upto and where data about us is ending up – although I appreciate using technology to counter technology in this way is getting just a tad circular.
Agreed there is huge potential for abuse, and in response we have to push for legislative frameworks that enshrine privacy. It’s not as though companies who want to sell us things are not going to profile us for targeted selling anyway, they do it via offering their software for free and we love things that appear seemingly free. What I’m also hoping is that more sophisticated technologies arise to assist with assessing exactly what all the software we use is getting upto and where data about us is ending up – although I appreciate using technology to counter technology in this way is getting just a tad circular.
A very interesting comment. I agree that most/all people would learn better if provided personalized tuition although, as you recognize, that would be prohibitively expensive. I do believe, however, that there is a range of innate abilities and, even with personalized tuition, people would reach their own natural limit of achievement.
Your suggestion about AI-based education disturbs me. AI currently monitors our internet activity and selects the ads we’re shown accordingly. I’ve no doubt technology will (or already has) advance to the point of providing on-line tutoring programs that would set lessons and questions, analyze our responses, and figure out the basic flaws in our reasoning and comprehension, and adjust subsequent lessons and questions accordingly. The AI would, in effect, get into our heads. I’m not so much concerned about the program itself, as the people who analyze the program and what they learn about the cognitive processes, limits, and biases of each person. That is an advertiser’s dream, and also a government’s dream. The potential for abuse is endless.
I hold a viewpoint that most who read it will consider off the wall bonkers: I think a very significant proportion of people can be taught most things to a decent standard if the people in question are motivated enough and take enough time. This includes maths or any component of STEM or a new language or draw and paint or cook to a near professional standard. I mean by this largely cognitive activities and I exclude activities that require high end physical components – like becoming good at a sport without better than average reactions or play the violin to a good standard when you don’t have perfect pitch etc.
Many people have told me my belief that most people can be taught most things is unrealistic nonsense. I nevertheless persist in believing that. My observation is the big variation between people is the speed with which they comprehend something and can apply it – which in effect is a strong indicator of the wide spread in abilities you see in individuals. If given enough time, most people can understand far more than they think they are capable of. They don’t because they are slow off the bat, and they don’t have a strong enough innate interest in abstractions to get past the inertia and persist for a long time. There are others who can’t do it because they are stuck in loops in their heads: circumstances, backgrounds, events, history etc, and although all of that can be got past, it requires a lot of effort to unpeel all that unless you pay someone to help. To illustrate my point, the person who can understand the quantum tunnelling effect in semiconductors today is no different from the person who was stacking hay on a two acre farm all their lives a couple of millennia ago. I have come across young people (in India this was) who were literally shovelling goatshit from one end of a village to the other, but half an hour of chat made clear they would be capable of anything any college graduate could do if they had been through the same education paths. This is in effect people who need to be ‘directed’ – as in, given the option they would wile away the years stuck in a groove of habits doing nothing.
The thing which changes this, is that most people when young enough to be coercible, are forced into school and college by their parents or govt for eight hours a day for a decade and a half minimum. Much rarer are people who are innately quick at comprehension in a particular subject because they are so obsessively absorbed in it that they gravitate towards first expertise and then sometimes beyond, into innovation and originality in their field of interest, much faster than everyone else.
I believe it is here we can find the missing piece into teaching things to people for whom interest in a particular subject, say maths, is not innate. The culprit for my money is the industrialisation of education – something which has happened for very good reasons indeed but is now ripe for revolution. Imagine you could teach each individual child or adult one-on-one – bespoke teaching on a per personality basis which is explicitly designed to plug the comprehension gaps an individual teacher can see in their individual tutee. Well, you get much, much, better outcomes. The private education industry, which goes varying degrees down this path, proves the point. I’m not saying you will make someone interested in STEM, merely that you can teach it – although you might even awaken interests that weren’t there before comprehension came. The reason it doesn’t happen for the bulk of people is because bespoke is impractical and expensive, and most individual teachers have neither the expertise nor motivation to get into the heads of a large number of tutees to see where the blocks are.
And finally, my point is this: today instead of teachers we should start to focus on technology – I believe algorithms are perfectly capable of getting into the heads of people (who allow them to), better than any teachers, and improve all aspects – memory, comprehension, even originality which I’m firmly convinced can ramp up the level and complexity to which people teach themselves. Our current addiction to discourse within the virtual social worlds created by algorithms, proves this point. And if the algorithms are going to get into our heads regardless, we may as well use that to effect constructive rather than harmful changes to ourselves, by actively constructing technology which improves up learning.
Arithmetic is little more than learning verbs in a language. Core concepts people use everyday are scale, ratios, optimisation, trends, accounts, and rates of change. If you can’t work with these, then it’s difficult to see how you can have an informed, or even a useful view of tons of issues. For instance, environment, taxes, regulations, budget-making or any complex systems. For instance, how much do you spend on schools or nurses? What’s the scale difference between solar and nuclear? What’s the optimum tax level? Or how many seeds do you plant? How much do you invest in a pension?
If you’re happy for other people to make those decisions, then by all means skip out of the relatively simple maths taught at school.
Arithmetic is little more than learning verbs in a language. Core concepts people use everyday are scale, ratios, optimisation, trends, accounts, and rates of change. If you can’t work with these, then it’s difficult to see how you can have an informed, or even a useful view of tons of issues. For instance, environment, taxes, regulations, budget-making or any complex systems. For instance, how much do you spend on schools or nurses? What’s the scale difference between solar and nuclear? What’s the optimum tax level? Or how many seeds do you plant? How much do you invest in a pension?
If you’re happy for other people to make those decisions, then by all means skip out of the relatively simple maths taught at school.
The problem with maths and why people “hate” it is that it’s often taught badly.
When children have reading problems there’s all kinds of innovative ways to help them. But if they struggle with math they are just told they’re useless at math.
In my view math should be taught properly, that includes embedding math in history and art and other subjects, and taught by charismatic competent teachers
Unfortunately I have no confidence this will happen.
You are so right!
You are so right!
The problem with maths and why people “hate” it is that it’s often taught badly.
When children have reading problems there’s all kinds of innovative ways to help them. But if they struggle with math they are just told they’re useless at math.
In my view math should be taught properly, that includes embedding math in history and art and other subjects, and taught by charismatic competent teachers
Unfortunately I have no confidence this will happen.
We need to get back to basics. My daughters curriculum is all over the place, she started reception last year, for example they did castles which was based around ‘prince’s, princesses and knights’ (i think a slightly inaccurate description of the medieval world, it was more Disney than history) then ‘how things have changed in living memory’ now they are talking about the old local shoe factories. It’s all over the bloody place and really abstract. Nothing follows on from the last thing. They have named all the classes after the planets but never covered them in a lesson as far as I know. Class sizes of 40 are too big. They do loads of superfluous assemblies, the free play business they started last year for reception where the children just get to ‘choose their activity and learn through play’ is just a ticket for them to run errant around the classroom. I thought it was absolutely ridiculous.
Now, I had a letter on Wednesday saying there’s an explosion in strep A, flu and covid and they aren’t to go in with a temperature or if they are at all unwell. If they are unwell don’t go out. If you have to go out wear a mask etc etc. So, when the next thing goes around, we are basically being asked to isolate. The local doctors sent out a message one day before Christmas saying they were ‘overwhelmed and had exceeded capacity’ so not to go that day. I get that the NHS around here anyway is struggling and that’s fine but none of this fills me confidence and its very difficult to plan work etc. It’s all well and good saying they’ll throw money and maths at it but they have to be able to actually attend for starters, we don’t know what we’re doing from one month to the next since she started last September, everyone was in and out of isolation last year at school, they had to shut because the teachers all got it. I’m just waiting for the next thing to go around now and it will be sorry the teachers are ill we’re closed. Crazy.
We need to get back to basics. My daughters curriculum is all over the place, she started reception last year, for example they did castles which was based around ‘prince’s, princesses and knights’ (i think a slightly inaccurate description of the medieval world, it was more Disney than history) then ‘how things have changed in living memory’ now they are talking about the old local shoe factories. It’s all over the bloody place and really abstract. Nothing follows on from the last thing. They have named all the classes after the planets but never covered them in a lesson as far as I know. Class sizes of 40 are too big. They do loads of superfluous assemblies, the free play business they started last year for reception where the children just get to ‘choose their activity and learn through play’ is just a ticket for them to run errant around the classroom. I thought it was absolutely ridiculous.
Now, I had a letter on Wednesday saying there’s an explosion in strep A, flu and covid and they aren’t to go in with a temperature or if they are at all unwell. If they are unwell don’t go out. If you have to go out wear a mask etc etc. So, when the next thing goes around, we are basically being asked to isolate. The local doctors sent out a message one day before Christmas saying they were ‘overwhelmed and had exceeded capacity’ so not to go that day. I get that the NHS around here anyway is struggling and that’s fine but none of this fills me confidence and its very difficult to plan work etc. It’s all well and good saying they’ll throw money and maths at it but they have to be able to actually attend for starters, we don’t know what we’re doing from one month to the next since she started last September, everyone was in and out of isolation last year at school, they had to shut because the teachers all got it. I’m just waiting for the next thing to go around now and it will be sorry the teachers are ill we’re closed. Crazy.
Surely what all students need teaching about is critical thinking and working out where the facts actually lie. So many parrot mainstream media without any research or investigation. Never looking sideways to other sources of possible information. I only have to hear my own nieces and nephews (rarely) discussing current affairs and govt instructions to realise that they know nothing really.
Surely what all students need teaching about is critical thinking and working out where the facts actually lie. So many parrot mainstream media without any research or investigation. Never looking sideways to other sources of possible information. I only have to hear my own nieces and nephews (rarely) discussing current affairs and govt instructions to realise that they know nothing really.
Maybe if people had better Maths than a 12 year old they wouldn’t be so easily fooled by government plots, statistics, and ‘models’. And maybe they could assess on their own some of what the ‘scientists’ say. After all, Maths used in medical papers is not very advanced either.
But maybe we rather not being able to understand and let the experts tell us what to do
Maybe if people had better Maths than a 12 year old they wouldn’t be so easily fooled by government plots, statistics, and ‘models’. And maybe they could assess on their own some of what the ‘scientists’ say. After all, Maths used in medical papers is not very advanced either.
But maybe we rather not being able to understand and let the experts tell us what to do
Hear hear hear! Hooray for at least one voice that recognises the shocking attitude of elites and media alike towards both mathematics and numeracy (two separate issues). I saw some fool on TV opine a few days ago that algebra was also about long division, and not just about ‘a equals x’. I find such attitudes truly scary and alienating.
Hear hear hear! Hooray for at least one voice that recognises the shocking attitude of elites and media alike towards both mathematics and numeracy (two separate issues). I saw some fool on TV opine a few days ago that algebra was also about long division, and not just about ‘a equals x’. I find such attitudes truly scary and alienating.
Rishi would be doing ordinary kids a greater service if he mandated Finance as a core subject. But of course mass ignorance maintains his advantage. Pegg’s right in that all the math skills you need to function can be drummed into you by the age of about 12. The problem is that in many cases they aren’t. Rishi’s going to have to find enough decent math teachers. In my whole school career I only ever had one math teacher who inspired me. But let’s not get into the whole teacher recruitment crisis thing. The article reminds me of those people who excel at team sports lecturing the rest of us how about enriching team sports are.
‘The problem is that in many cases they aren’t’
Hit the nail on the head.
‘The problem is that in many cases they aren’t’
Hit the nail on the head.
Rishi would be doing ordinary kids a greater service if he mandated Finance as a core subject. But of course mass ignorance maintains his advantage. Pegg’s right in that all the math skills you need to function can be drummed into you by the age of about 12. The problem is that in many cases they aren’t. Rishi’s going to have to find enough decent math teachers. In my whole school career I only ever had one math teacher who inspired me. But let’s not get into the whole teacher recruitment crisis thing. The article reminds me of those people who excel at team sports lecturing the rest of us how about enriching team sports are.
Interesting how advanced maths skills, which most probably won’t be needed by most adults, are being fetishised, while modern languages, which also won’t be needed by most adults, have been totally sidelined.
I don’t think we are talking about ‘advanced’ maths skills – probably no more advanced than long division!
Iteresting that you mention modern languages : in my experience, both as a student and a supportive parent, both these subjects are equally badly taught.
I don’t think we are talking about ‘advanced’ maths skills – probably no more advanced than long division!
Iteresting that you mention modern languages : in my experience, both as a student and a supportive parent, both these subjects are equally badly taught.
Interesting how advanced maths skills, which most probably won’t be needed by most adults, are being fetishised, while modern languages, which also won’t be needed by most adults, have been totally sidelined.
At least three “left-leaning” comedians have been on Twitter wailing about this, and didn’t manage one single joke between them.
At least three “left-leaning” comedians have been on Twitter wailing about this, and didn’t manage one single joke between them.
Simon Pegg is a mega jerk. He epitomises everything that is imbalanced and unpleasant about the Woking Class.
Simon Pegg is a mega jerk. He epitomises everything that is imbalanced and unpleasant about the Woking Class.
If I can make any (small) claim to academic success, it is in the fields of Aesthetics and Art History. For the senior school Me, Maths was a perplexing dark art.
Nevertheless, I bumped into it again in my researches into Beauty. I discovered all these mathematicians speaking about Elegance. Later, I found that the BBC had surveyed the public on their vote for the Most Beautiful Equation (Dirac’s, since you ask). Later still, a mathematician friend told me of how she numbers in nature (Fibonnaci, I believe).
I still don’t understand it. The way those equations always end up equaling 0 simply seems like a con. And yet I feel like my view of the world has expanded and deepened. My awareness that another truth is ‘there’ has grown.
I think that more than anything else, this experience finally saw off in my mind the distinction between Arts and Sciences. But I doubt if this awareness is what Mr Sunak seeks.
If I can make any (small) claim to academic success, it is in the fields of Aesthetics and Art History. For the senior school Me, Maths was a perplexing dark art.
Nevertheless, I bumped into it again in my researches into Beauty. I discovered all these mathematicians speaking about Elegance. Later, I found that the BBC had surveyed the public on their vote for the Most Beautiful Equation (Dirac’s, since you ask). Later still, a mathematician friend told me of how she numbers in nature (Fibonnaci, I believe).
I still don’t understand it. The way those equations always end up equaling 0 simply seems like a con. And yet I feel like my view of the world has expanded and deepened. My awareness that another truth is ‘there’ has grown.
I think that more than anything else, this experience finally saw off in my mind the distinction between Arts and Sciences. But I doubt if this awareness is what Mr Sunak seeks.
In Ireland, every student studies Maths in some form up to the end of secondary school at 18 or so. Essential skills.
interesting
Innumeracy enabled the befuddling and manipulation of the vast majority of the population during the pandemic – remember those dodgy graphs, the death tallies, the general belief that whole counties could shut down for month after month with people paid to stay home and do nothing but stuff themselves and there not be any dire consequences? I am convinced that twenty years ago the public would not have gone along with the insanity of lockdowns and being told to stay home. I thought we had arrived at peak Age of Stupid but it appears we have much farther to go thanks to the vast army of useful idiots made up of the likes of Peg.
Attitude and perspective are more foundational than concepts and processes. More important than ‘filling up the bucket’ with formulae and techniques, is ‘lighting the fire’ of interest, appreciation and confidence in thinking about mathematical problems. Less scope, better taught would be more rewarding for the pupil, the teacher, and society.
What is lacking is teaching of perspective, geometry and forces. Many of the mistakes in building/construction are due to faults in surveying, inability to think in 3 dimensions and understand the forces.
The failure of technical education is due to Arnold of Rugby in the 1850s. He realised public schools could either follow a classics route or maths/engineering as taught at Woolwich Military Academy. Arnold chose classics. Up to the mid 1870s the land owners were happy to develop technology. It was the Agricultural Revolution which was based upon soil improvement – drainage, manuring,marling and sanding and selective breeding which enabled the Industrial Revolution to occur. When the Royal Rociety was formed, land owners attended and supported the use of science to enlarge the economy, especially farming.
It was the landowners who supported Newcomen and the Duke of Bridgewater paid for the canals designed by Brindley to move his coal.
However, the decline of rural incomes due to food from New World post 1830s meant by 1870s aristocrats had become anti-new money, especially manufacturing . Also investment overseas brought greater returns than in the UK.
From 1914, the Marxist Middle class adopted an anti trade and technology attitude. The PPE degree became a favourite of the Left, not Engineering.Gladstone had a Double First in Greats and Maths from Oxford. The Classics and Maths combination, whicht Cambridge was Mathematical Physics, was considered the greatest intellectual challenge up to 1914.
Engineering is about overcoming challenges. The greter the challenge, the greater the achievement. In mining, oil and construction one is working with tough practical men in dirty, arduous and dangerous conditions where mistakes kill. Young Engineers have to accept being criticised, even threatened, when they make mistakes.
It is difficult to think of any London Chatterati who could survive workinging tough in mines, oil rigs or constructions sites as an engineer.
Many, if not most, mining, civil and oil engineers were keen rugby players and or boxers at university, Profs Alec Skempton FRS and Vaughan FR.Eng of IC come to mind.
Col Bill Hudson is good example of 1930s Mining Engineer,
Bill Hudson (British Army officer) – Wikipedia
The London Chatterati lack the Renaissance qualities of people like Brunelleschi and Michelangelo who designed and built most of St Peter’s, Rome or toughness of a Col Bill Hudson.
If schoolchildren have not grasped simple maths by age 16, two more years of staring blindly at numbers will make little difference. Make a comparison with literacy: if a pupil cannot read fluently by 16, that is not going to be fixed by a couple of extra years of failing to read, reinforced by resentment.
The problem of numeracy can only be fixed by better teaching in the early years, which is easy to say, but not easy to implement. I can say it needs to be done, but I do not know how, because although I have a reasonable level of numeracy (probably up to A-level standard) so I understand the subject, I do not have teaching skills. I admit that I would not want to teach literacy for the same reasons.
Can I say, to put this further into context, that I have lectured and trained, with some success, in finance subjects for both professional exams and on MBA courses, but teaching, proper teaching, requires a different skill set.
One further point. I refuse to believe that anyone is incapable of learning some mathematical (or arithmetical) skills. I am sure we have all seen people who are under-educated and “can’t do sums” but who can sort out scoring at darts at lightning speed, and who have no problems with understanding betting odds! I am more willing to accept that some people cannot learn to read than that there are people who cannot learn to count.