Sir Simon Jenkins:

Like much of the public realm, British maths is “in crisis”. The country is languishing alongside America way down every league table. Evidence of this was cited in a new poll from YouGov, measuring the public’s knowledge of maths, science and English. In maths, roughly a third of those surveyed had no idea how to calculate a mode, a median, a “line of best fit” or the area of a circle.

I seriously doubt this poll, since it implies that two-thirds did know the answers. All on whom I tested it failed, including myself.

If you don’t know your mode from your median then you’re not going to get very far with the statistics about public policy, are you?

Which might explain the newspapers in this country: not only is a journalist admitting he doesn’t know he’s proud of it too.

Hardly anyone knows how to do these, in my experience. In a recent experiment, out of four colleagues only 1 could tell me what seven times nine is. And she is Iraqi.

Area of a circle? Maybe 1 in 10, and that’s probably optimistic.

Maths isn’t “in crisis”: shitty state education is in crisis.

IanB: Times Tables I remember–we had to memorise them in the Sixties.

Area of a Circle? Can’t quite recall the formula–but I haven’t had occasion to use it in 45 years so not too surprising.

I would need to do a bit of revision about the “best fit” question (assuming it is least squares or something similar). The rest are pretty ok.

Are what we are seeing here, the outcome predicted by Snow’s “Two Cultures” ?

The first thing to look at is how well the teachers know the subject they are teaching. The people I know who went into teaching did so largely because they were otherwise stuck in dead-end jobs they hated, and don’t particularly like teaching either but need the money.

I can do that but I shouldn’t expect 99% of the population to need to do a least-squares regression analysis, so why include something like that in the list?

Right, I have a Maths A level from days of yore which included statistics.

Area of a circle – easy.

Median – easy.

Mode – had to google to remember what it meant.

Line of best fit – no idea what that is.

Most people don’t need to know or remember this stuff. The idea that unless the general public knows what “line of best fit” is and how to work it out is standard Maths knowledge is fucking ludicrous.

I think you’re all being too clever. The line of best fit probably just means drawing a line with a ruler through most of the dots except the outliers, about in the middle, like at junior school.

I remember mentioning this before by the way, but to this day I am still baffled as to why we did addition and multiplication etc of matrices at Middle School. I can’t imagine what application was intended. Useful if you’re going to do Quantum Mechanics, not much use if you work at Poundland.

By the way, public policy normally doesn’t use mean, median or mode, but “the average”, which is defined as an imaginary person or family who will be better off after the budget.

Average is handy because you can define it more precisely after the fact based on what your audience wants to hear.

Ignorance is bliss – as the superlative Mr Ecks said, the purpose of ‘state education’ is ‘to prepare leaders for the coming struggle’ – not inculcate knowledge

The Indy has a sample survey. Doesn’t appear to be the same as the full thing. http://www.independent.co.uk/news/education/only-30-per-cent-of-adults-can-answer-this-question-can-you-a6918791.html

I blame the smoking ban!

In days of yore, people used to go down the pub and play darts and calculate complicated finishes, and you had to score a match in order to play. Or they would be able to work out who was stiffing who on the round. Then they would go down the bookies and put on each way yankees and such and workout what the odds were.

Now, darts is a spectator sport on the telly and betting is passive on-line casino stuff and drinking is a couple of cans of Stella in front of the box.

Ruined the country’s math skills, it has.

The area of a circle cannot be expressed with absolute accuracy in numbers as Pi is an approximation, therefore the area cannot be “calculated”.

” The nation needs, and therefore pays most for, more executives, accountants, salesmen, designers and creative thinkers.”

Markets work today in Simple Simon world.

“Any league table that has China at the top, Britain at 26th and America at 36th tells me something”

That communist governments make up stats?

Kevin: I remember a Bash Street Kids story stating (almost) exactly that! This Kids were crap at maths in school, but in the yuuff club after school were playing darts and snooker and were doing multiple subrtactions and projected future additions in their head.

Whatever happened the the Schools Mathematics Project? That taught me maths based around real-world applications like bus timetables, wallpapering, shopping, mortgages and stuff.

@ BraveFart

Pi is *not* an approximation but it is an irrational number so any rational number used as an answer in calculating the area of a circle with a rational number as its radius can only be an approximation.

Kevin B,

“Ruined the country’s math skills, it has”

That was the easy stuff. Pounds, Shillings and Pence is a Maths assault course, as are pounds and ounces, and all Britons needed to be comfortable with using F and C interchangeably.

The older generation can do mental arithmetic in their heads (geddit?), while the younger are still struggling with 7 x 8

I did A Level Maths and cannot remember. any. of. it.

Certainly not how to differntiate and integrate.

In my 25 years in IT I only needed to be able to think in Hexadecimal and multiply by 1024.

Jack C nails it.

Bring back Imperial and £sd.

Fish and Chips, Bread and Butter, Tea–9-1/2 d–Before the War.

It’s lines of best fit, under the posher name of regression analysis, that tell you that bee hives cause cancer. Or other such fairy tales.

By the way, public policy normally doesn’t use mean, median or mode, but “the average”, which is defined as an imaginary person or family who will be better off after the budget.Never an individual person and always a “hard-working family”.

Why focus on maths like this?

What proportion of the population has ever had to know what a complex conjugate is? Or any of the English Language stuff that’s taught from age 14 onwards?

How many of the people you run into on the street have needed to know any Shakespeare? Or to know what’s in “Of Mice and Men”? Or anything else in English Literature?

Personally, the knowledge of how an Oxbow lake is formed, or the primary exports of Patagonia has turned out to be rather less than fundamental in my life, and I doubt I’m rare in that sense. Goodbye, Geography, at least in the sense beyond the most basic.

I learned French at school, along with about 99% of my age-peers. If more than one in twenty of them can remember more than twenty or so words in French, I’d be stunned.

And so on.

Looks to me like “Journalist says Maffs is hard, it’s unfair, we shouldn’t be expected to know it, it’s like Orwellian, or something.”

Sir Simon

If you asked people 10 questions on he median, how many would the average person answer correctly….on average?

And would you be an outlier or just the usual innumerate arsehole writing for the Guardian?

Math is inherently useful training in logic and thinking in sequential syllogisms.

If you cannot do those things you cannot think and math is the only method I know of to test that skill in multiple ways.

Its usefulness pops out in odd places. My carpenter, grade 9 education, can use trigonometry to calculate all of his cut angles for slanted wood members.

“Ordinary hard-working family”

And still, a basic lack of simple numeracy seems to be perfectly acceptable to your average/mean/median Oxbridge-educated TV ‘journalist’. “Ooh, I was never any good at maths, hee hee” when faced with some addition or subtraction.

The last exponents of mental arithmetic are the tradesmen. I worked in IT and I was amazed at the number of people who would pull out a calculator to work out something like 15% of 300.

If the political elites were more numerate, or at least bothered to ask people who were, we wouldn’t have many of the insane policies we do. I’m not sure what the answer is, other than to get politicians to recognise a charlatan when they see one, or perhaps enable the electorate to spot a charlatan when they see one, and not elect them.

You might not need to know what a Lie algebra is, or how to draw the Coxeter-Dynkin diagram for a rhombicuboctahedron, but having a certain facility with basic mathematics and especially arithmetic is part of being a fully-developed human being.

I’ve long been of the opinion that Simon Jenkins’s unerring ability to get the wrong end of the stick in every matter on which he propounds is a testament to the fact that every compass needle has a butt end.

For IanB (March 10, 2016 at 11:58 am), who I think has just suffered a bit of temporary forgetfulness, and anyone else who cares: from Wikipedia, here are some uses of matrices beyond just quantum mechanics.

“Applications of matrices are found in most scientific fields. In every branch of physics, including classical mechanics, optics, electromagnetism, quantum mechanics, and quantum electrodynamics, they are used to study physical phenomena, such as the motion of rigid bodies. In computer graphics, they are used to project a 3-dimensional image onto a 2-dimensional screen. In probability theory and statistics, stochastic matrices are used to describe sets of probabilities; for instance, they are used within the PageRank algorithm that ranks the pages in a Google search. Matrix calculus generalizes classical analytical notions such as derivatives and exponentials to higher dimensions.”

I would add, from my own work interest, that matrix arithmetic and matrix algebra are key to communications theory – as in modems and stuff for connecting computers together. Also for the digitisation of speech (linear predictive analysis) – as used (in extended form) in mobile phones etc. Linear prediction theory is also heavily used in statistics, as applied to economics and elsewhere. Matrices are also very important in navigation, eg SATNAV, without which we would all now be currently lost.

Best regards

Best fit on a graph? I bet most people would do better with a freehand sketch. Regression analysis is for bores and economists.

(Which is also why a lot of companies have ditched their wizz bang network calculations and gone back to the ladies in the secretarial pool)

BraveFart – “The area of a circle cannot be expressed with absolute accuracy in numbers as Pi is an approximation, therefore the area cannot be “calculated”.”

I think you have got this the wrong way around. If I have a circle whose area is exactly one square foot, it follows, inevitably, that the radius cannot be known.

Although I think we have an explanation for why there is so much gang violence in this country. Clearly the fact they continue to sell in ounces and the like means none of them really have a clue how much is being sold so they constantly think they are being ripped off by their peers and so end up stabbing each other. I think we need to think of the Vibrant children and reintroduce proper maths teaching and Imperial measures both.

Would love to know how to calculate a mode or median. Don’t you do it by inspection rather than calculation?

Like others I had to look up mode, which I immediately forgot, as I haven’t had to use it since school. I can’t say that school failed me because it is my fault that I don’t remember a now useless fact.

Personally the best math classes I took were the ones that didn’t need a calculator. While getting the right answer is very important in building a bridge it doesn’t matter much in the education process. Schools need to be teaching the theory. Once you understand that 6×8 is the same as 8+8+8+8+8+8 it no longer matters if you’ve memorized 48. It was only once I started living and had to figure out the answer frequently that I bothered memorizing something I could fairly easily look up.

LY-

I disagree. If you have to serially add small numbers, you’re going to be awful slow at both mental and written arithmetic. It’s like trying to write fluently when you can’t spel. Or know the rules. of Grammar!?

Familiarity with small number additions, multiplications etc I also find to be essential to confidence and capability; multiple sub-calculations or look-ups (8+8+8+8, or counting the number line) are more points where errors can be made and make the whole calculation more daunting as the algorithm now has many more steps to it.

Moving back to be more general in criticism of Simon Jenkins, everyone’s understanding of maths (like that of any other major subject) should be much more than can they do a few simple things. How about a bit of a grasp as to why the subject (and most other subjects) is important.

On this, I recollect a wonderful comment stream at Samizdata from 2008, following the post entitled: What Use is Maths?

Best regards

Ian B,

Trapper Keeper folders had a handy table. When we had word problems instead of memorization tasks I would just look up the value and I understood the problem. Instead of seeing each individual calculation as a hard unchanging fact I now see a dynamic structure.

When I had to take a test I simply relied on x10 to get a starting point and added or subtracted from there. Since I could add and subtract far faster than other kids my age I was still able to finish early. I would get 6×8 by doing something in my head like this:

8*5=40

40+8=48.

But that is how I learned to do math.

I found the memorization tasks to be so dull I rarely learned anything. I still do not understand the point of having to write out the numbers from 1 to 1000. As soon as I understood that 1+1=2 and 9+1=10 I had the concept and was ready to move on.

I fully admit that there were times that I made a mistake due to the extra calculation. Much more common are the times that I think 48 and instead write 84. Everyone has a different way of learning and memorization wasn’t very effective for me.

Or you could have just remembered that six eights are forty-eight and got on with life instead of having to break down six into five plus one, multiply by ten, halve it, then add the other eight.

You’re probably quite clever, so this burden was tolerable. For people less gifted, that’s a major diversion in the algorithm, especially if you’re doing (for instance) a long multiplication and have to keep doing this breakdown over and over.

582 * 178 is only 177 serial additions after all. Off you go.

And then, I admit, sometimes I wonder if I’m being an old fart. I was horrified to discover the other day that schools are dropping cursive handwriting. But what’s the use of it? I never use it any more. I use a kind of semi-joined-up scrawl for notes on bits of paper, and that’s it. I can’t help feeling though that the end of proper handwriting is one step closer to the fall of civilisation.

But maybe I’m just an old fart.

Ian B: 582 * 178 = 380*380 – 202*202 = 144400 – 40804 = 103596. Simples. (Cough)

Given a modern environment where you can’t move for tripping over something that has a calculator function, the modern obsession with rows of questions on long mul/div/add/sub in school homework baffles me. Guess it’s low effort for the teachers to mark for the time taken by students.

Are what we are seeing here, the outcome predicted by Snow’s “Two Cultures”?I think Snow was about half right. In the common room of my Mathematics department, conversations can frequently be heard about maths, of course, but also about novels, music, politics (both contemporary and philosophy of), the theatre, history and a wide variety of other topics. I dare to predict that it may be rare for a similar breadth of spirit to be on show in a History or Literature common room.

“Would love to know how to calculate a … median. Don’t you do it by inspection rather than calculation?”

If you have two candidates for the median, a common convention is to adopt their mean as “the” median. Thus

1, 2, 3, 4:

your candidates are 2 & 3, so you report the median as 2.5.

“582 * 178 is only 177 serial additions after all. Off you go.”

No it’s not, its about three.

582 times 100, that’s 58200

need another 70 of them, 70 is 30 less than 100, so knock 30*582 off 58200, 3*582 with a 0 on the end, 1500ish, 17460, so 116,000ish minus 17,000ish, sort-of 99,000-ish

need another 8 of them, call it ten of them, another 5820, so about 106,000. Three significant figures, close enough for carpentry.

178=200-20-2

“Would love to know how to calculate a mode or median. Don’t you do it by inspection rather than calculation?”The mode is the number that appears most often. The median is the number exactly half way down the list after you sort it.

The mean, of course, is just add’em up and then divide by the number of numbers.

The hardest question here is to get the line of best fit. To do that, subtract the mean from all the points and write the resulting coordinates in two columns. Add a third column which is the x and y values multiplied. Add a fourth which is the x values squared. Then add up the two columns and divide one by the other. This is the gradient of the line of best fit, which passes through the mean point.

For example, say the points are (1,6), (2,8), (3,13). Subtract the mean (2,9) from all the points and write down:

-1, -3, 3, 1

0, -1, 0, 0

1, 4, 4, 1

The gradient is(3+0+4)/(1+0+1) = 7/2 and the line passes through the point (2,9). So draw a straight line through the points (2, 9) and (4,16). (i.e. the point 2 along and 7 up from the mean.)

It sounds complicated, but it’s really no harder than long division.

Maths is like any skill. You can get by without it, but it enables you to do things that otherwise you would have to rely on somebody else for, which gives you more power over your world. Do you trust someone else to do your numbers for you? To cook your dinner for you? To supply your water? Your health care? To wire your electrics?

We all only have time to learn a few skills, and must rely on the rest of society for the rest. But to get that aid, we have to have skills that the rest of society needs, that we can trade for all that help. So which skills should we acquire?

I would never venture to tell anyone else that any particular skill is or is not essential for them to have, or criticise them for not having it. People can and do get by without maths. But it is the foundation of so much of modern technology, and rare enough as a skill, that it is a particularly easy skill to trade. The more people have it, the more modern technology we can create and use, which is good for everyone. It seems like a particularly good deal, but perhaps not for everyone.

Nevertheless, I’ve never understood the *pride* people express in being bad at maths. I’m not sure if they’re trying to make themselves and each other feel better about not having a skill they think they ought to have, or whether it’s resentment, or false modesty, or some sort of emotionalism / anti-intellectualism, or what.

mean, median, mode use them every day.

area of a circle, know how but would need to check my fallible memory for the value of pi. On the other hand my calculator has a button for pi. Best-fit Line? 45 years since my stats o’level and that was probably the last time I needed to know how. If a hand drawn line is not good enough any spreadsheet program can draw a graph and calculate a regression line

john77, that is how I think of it.

When I learned division in 2nd(South Carolina) and 4th grade(Virginia) grades multiples of 2 is when knowing multiples of 2 became useful.

You may be asking why I learned more math at younger age in South Carolina than in the, better on paper, Virginia public school system. In South Carolina I was put into math classes for the next grade. When we moved to Virginia an SJW had me take some tests that put me in with the slow kids. The reason for the change was that when I was asked to draw a picture of my family I started with the, easier to draw, new puppy. Obviously because I drew an animal before a person I had some sort of disorder.

@ NiV

Yes if you are only considering straight lines – in some cases you want the curve that best fits the data which is why regression analysis is designed to work with curves as well as straight lines.

@ LY

I should thank heaven that my IQ was never tested by drawing a picture of my family – I should have been put in with the so-called “mental defectives” (now called “those with learning difficulties”).

@NiV

I have a suspicion that *pride* in being bad at maths, incompetent at DIY, clueless at car maintenance, etc, is all about class.

Back in the day, the fact that the idle rich schooled themselves in the arts and humanities demonstrated that they did not need to acquire skills that could be leveraged to make a living. Essentially, scientists and engineers were seen as practically ‘trade’, and demonstrating skills in those areas clearly illustrates a low-born background.

That’s the only reason I can think of for all those graduates in the arts and humanities feeling that they are justified in condescending to the people that have actually built the technological world in which they are pleased to pursue their pointless meanderings.

“Yes if you are only considering straight lines – in some cases you want the curve that best fits the data which is why regression analysis is designed to work with curves as well as straight lines.”True. But I was trying to keep things simple.

You can also do it with splines, planes, surfaces, hyper-surfaces, vectors, matrices, polynomials, rational functions, infinite series, fractals, and lots of other brain-bending stuff. Mathematicians do that sort of thing for fun.

But I didn’t want to scare people off. The point is that it’s not any more difficult or complicated than any other bit of basic maths – just unfamiliar. Even something as simple as addition can be made complicated.

“Back in the day, the fact that the idle rich schooled themselves in the arts and humanities demonstrated that they did not need to acquire skills that could be leveraged to make a living.”Were those like the days of Lord Kelvin, Lord Cavendish, and the Lady Augusta Ada Byron?

You may be thinking of more recent times, but my impression was that only the rich could afford the copious spare time and money needed to conduct research into scientific topics without immediate practical use. Everyone else was too busy scratching out a living doing subsistence farming.

But yeah. It’s a possibility.

Two out of three ain’t bad. Kelvin was ennobled for his work not born with a title.

The lack of a need to acquire useful skills does not prevent their acquisition. I don’t suppose the aristocrats gave a toss about who studied what and why. The way they behaved, however, certainly influenced the nouveau riche and the middle classes, who always sought to ape their ‘betters’.