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Education

Why Learn Maths?

Brian Micklethwait asks:

But what about the kind of maths that really is maths, as opposed to mere arithmetic, with lots of complicated sorts of squiggles? What about infinite series, irrational numbers, non-Euclidian geometry, that kind of thing? I, sort of, vaguely, know that such things have all manner of practical and technological applications. But what are they? What practical use is the kind of maths you do at university? I hit my maths ceiling with a loud bump at school, half way through doing A levels and just when all the truly mathematical stuff got seriously started, and I never learned much even about what the practical uses of it all were, let alone how to do it.

I also get that maths has huge aesthetic appeal, and that it is worth studying and experiencing for the pure fun and the pure beauty of it all, just like the symphonies of Beethoven or the plays of Euripides.

But what are its real world applications? Please note that I am not asking how to teach maths, although I cannot of course stop people who want to comment about that doing so, and although I am interested in that also. No, here, I am specifically asking: why learn maths?

Well?

I would split the subject into two. For past a certain level, it most certainly is two entirely different disciplines. The first is pure maths. For those who like it (most definitely a subset of the population) it\’s glorious, beautiful, engaging, even thrilling. It\’s also a description of the universe as it ought to be. Any connection between results and the real world is entirely coincidental: pure mathematicians are the original "yes, that\’s all very well in practice, but is it true in theory?" people. Once you climb into the higher realms (well past A levels) the value is like that of poetry. That\’s not to say that more practically useful things don\’t come from it, of course they do, but it\’s not done for its practicality nor will anyone attempting to do it for its practicality do very well at it. 

Statistics rather reverses this. Looking at it in one way it\’s rather like, yes, well, this is all very well in theory but is it true in practice? We go out and gather real world information and then examine it to see what it tells us. While we might think that x happens because of y, we actually want to find out whether that is true. Or does y happen because of x? Or do they both happen because of a? Or are they simply correlated rather than caused by any of them? And many statistical tests are designed to work out how important our result is.

There\’s two things that statistics are extremely useful for. The first is to teach you how to gamble: that\’s the root of the whole subject anyway. Seriously, it really started with people trying to work out how to win at cards and dice. Things like the Fibonacci series, which explains things as varied as the placing of petals on a flower and possibly the curling of a wave, also explain the liklihood of throwing a 4, 5 or any other number with a pair of dice. From that we derive ! and so on.

But the second thing it\’s extremely useful for is politics. The standard intro by some pantywaist who wants to steal your liberty, livelihood and freedoms is "research has shown that….". Statistics enables you to evaluate whether research actually has shown (the death rate from Ebola is 80% so yes, clamping down on movements and civil liberties during an outbreak can be justified) or not shown ("the part time pay gap for women is 40%", no, it isn\’t, that\’s comparing the wages per hour of part time women against full time men. Comparing part time women against part time men gives us 11%.) the point that the speaker is trying to make.

Which of the two you are good at, which you prefer doing, largely depends upon your mindset at the beginning. I\’m not very good at either, but I do struggle to understand the statistics side as well as I can for defending those liberties, livelihoods and freedoms from those who would steal them on spurious grounds seems to me rather important.

Oh Dear

Good grief, are students nowadays really like this?

On Saturday I stood at Warwick University\’s union bar. I had been speaking at a rather excellent student conference and the organisers had invited me to join the students for the evening. Large numbers of the 400 students present were standing without anything to drink, unable to afford the highly-taxed lagers that were on sale. As a result, students stood in straight lines listening quietly to the live band. No one was smoking, which of course would have been illegal.

Well Done Gordon

Gordon Brown lays out his plans to deal with the challenges of globalisation.

To build a world-class teaching workforce, we will shortly announce our proposals for a new masters qualification

Wrong! As teachers themselves seem to think, postgraduate education courses are one of the problems, not one of the solutions.

And from Tim Worstall, unusually, something about education I think most teachers would agree with: we knew the \’academic\’ component of our post-grads in education was a waste of time, taught as we were by a bunch of people who could hack it neither as teachers nor academics, peddling out-dated theories that I would decline to describe as \’liberal\’*. We all knew the only thing worthwhile in the whole damn year was the actual teaching practice.

Abolish education degres entirely and simply make teacher training 6 weeks of teaching practice. You might want to say that you can only teach in a secondary school if you\’ve got a degree in something or other, you might not (would one of the new cookery teachers need a degree? Or would someone who has run a kitchen for 20 years but now getting a little creaky around the knees be a better hire?), but the year or more of theoretical education about education needs to go.

Mind Boggling

Point one:

We will never go back to selection

Point two (the next part of the same sentence):

but you could have a situation where 11-year-olds with a particular talent in a certain subject or the potential to go to a certain university are encouraged at an early age.

Leading to:

Potential Oxbridge students should be identified at 11 and given special mentoring throughout their school years to help them compete for a place, the Government\’s access tsar has proposed.

So when is selection not selection?

Two Stories on Education

Much burbling about "fairness", "equity":

In a key test case, Brighton will become the first city in England this year to employ the system as a tie-breaker at all of its over-subscribed secondaries. It is believed other areas may be encouraged to follow suit in an attempt to bring greater transparency to the admissions system.

The new admissions code bans schools from interviewing children and parents, or asking for extra information designed to weed out pupils from poorer homes who may be more difficult to teach.

Jim Knight, the schools minister, warned it was "unacceptable that children may be missing out on school places" 12 months after the new rules were imposed.

And elsewhere:

Failure to teach children the three Rs at a young age is damaging the British economy, according to a report published by Cambridge University today.

Productivity lags as much as 25 per cent behind economic competitors such as Germany, France and the United States because workers lack basic reading, writing and numeracy skills, it is claimed.

Those productivity numbers I\’m sure are wrong but leave that aside.

I can\’t help thinking that if less effort was expended on the "fairness" side of things rather more might be on the "teaching" side. It isn\’t the most difficult thing in the world, to teach the basics of readin\’, \’ritin\’ and \’rithmetic, given that the ankle biters are there for five years on a compulsory basis.

We Musn\’t Discriminate Now, Must We?

A report from the education front lines:

The report, Able Pupils Who Lose Momentum, found shortcomings in the 37 primaries across England visited by Government advisers.

One of the key problems uncovered by researchers was the failure to put children into ability sets or groups. Even when children were put in classes with children of similar abilities, clever children were still grouped with other "lower ability" pupils when carrying out work.

"Children often worked exclusively in mixed-ability groups and rarely worked with children who were making similar rates of progress," the report said.

Still insistent that children are a tabula rasa, that there are no innate differences in ability. Can we please, sometime soon, get back to the idea that all children should indeed be taught to the limits of their ability, but that ability varies?

Ms. Riddell

Most amusing. Three points:

One of the most welcome parts of Balls\’s children\’s plan is the renewed commitment to abolish child poverty by 2020. If that happens, and it will take some investment, then many ogres of childhood may melt away.

Could we please get this straight? This wll not be investment. It will be current spending. We\’re not going to be able to spend billions up to 2020 and then stop, considering the problem solved. We\’re going to have to go on spending those billions forever, until the end of time. For each new generation of children will require exactly the same corrective taxation and benefits handouts to alter the market incomes outcome to the desired one.

Health, fitness and weight are all class issues. Obesity and heart disease are plagues of the poor. It is no accident that far more children are overweight in the UK, with its sclerotic social mobility, than in the fairer Nordic societies.

OK, we\’re on the page where the education system does or does not lead to social mobility. So can we please actually have a look at what those fairer Nordic societies actually do in their education systems please? Sweden has a pure voucher system for education financing. Finland has a modification of vouchers (and, to what will most assuredly be a fit of the fainting vapours from educationalists, divides children at 15 into academic and vocational streams, at different schools: this is Grammars and Sec Mods, just at a later age). Denmark has a private school system both larger than the UK\’s and also funded considerably by the State:

The private independent schools (frie grundskoler) play an important role in Danish education. There are around 430 private schools situated all over the country, and approx. 11% of a cohort go to private schools for primary and lower secondary education.

Primary and lower secondary education is free of charge at municipal public schools. The private schools charge a fee, and the average for non-boarding schools is DKK 13,000 per year. Both the government and the municipality contribute considerably to the cost of operating the recognised private schools. 

Primary and lower secondary education is governed at municipal level, and it is the obligation of the municipality to ensure that all children receive education. 

Both private schools and continuation schools receive a substantial state subsidy.

Oh, and note that it is organised locally, not nationally. So if we\’re going to try and change the UK education system to get to that fairer outcome, can we please start adopting some of the policies which lead to that fairer outcome? Like, umm, vouchers, subsidy of private schools, sorting the academic from the vocational? Or is real world evidence not acceptable these days?

Critics say it\’s not in the gift or remit of the state to confer happiness. Why not? When it has proved so adept at making children unhappy – by piling on too many jail sentences, Asbos, exams, dead-end schools and unreal expectations – it also bears a duty to be an agent of a better life.

Err, if the State is making people uinhappy then surely we don\’t want it to potter off and try and make them happy in other ways: what we\’d actually like it to do is stop making people unhappy, isn\’t it?

Being Vile About the Sutton Trust Report

So we had the Sutton Trust report.

Parental background continues to exert a very significant influence on the academic
progress of children:
o Those from the poorest fifth of households but in the brightest group at age three
drop from the 88th percentile on cognitive tests at age three to the 65th percentile
at age five. Those from the richest households who are least able at age three
move up from the 15th percentile to the 45th percentile by age five.
o If this trend were to continue, the children from affluent backgrounds who are
doing poorly at age three would be likely to overtake the poorer but initially bright
children in test scores by age seven.
o Inequalities in degree acquisition meanwhile persist across different income
groups. While 44 per cent of young people from the richest 20 per cent of
households acquired a degree in 2002, only 10 per cent from the poorest 20 per
cent of households did so.

But we\’ve also got this:

The problem with this famous Eyferth study, which formed the backbone of Flynn\’s Race, IQ, and Jensen, is that it was a study of children. So? After Flynn wrote this book, behavioral geneticists gradually made the amazing discovery that the heritability of IQ (and many other traits) sharply rises as children grow up, while family effects on IQ fade out.

Now I have no idea whether that last is in fact true, but if it is it provides us with a way of interpreting the Sutton Trust\’s results. A way that will be most un politically correct. Children of the poor do badly in the educational system because they are dim. That dimness being a genetic problem, one which becomes apparent as they age.

It is, in fact, the exact opposite of the Trust\’s thrust. It isn\’t that a bad environment hampers the children of the poor, it\’s that we only find out about their dimness as they grow older.

No, I don\’t think I like that conclusion either but what if it is actually true?

What if, say, the educational mobility of the 50s through 70s was a one off event? That there were those with the brains but not the opportunity to rise, that once the opportunity arose they did in fact rise but that there\’s no more such to come?

All depends rather on the heritability of IQ I guess and that\’s something that creates a firestorm whenever it\’s mentioned.

As I say, I\’m not sure I like that conclusion but I\’m absolutely certain that it will enrage all of the right people.

Correlation and Causation

One would have to have a heart of stone not to laugh here:

Despite billions being invested in education, children born in deprived homes are no more likely to escape the poverty trap than they were 30 years ago, it is claimed.

That isn\’t laughing material, to be sure, but this is:

Comparing a series of research papers carried out over the past 50 years, it found a sharp fall in social mobility between 1958 and 1970.

Everyone in the debate agrees that it is education which creates even the possibility of the desired social mobility. The Grammar School/Secondary Modern system was progressively scrapped from the 50s to the 70s in favour of the Comprehensive system. This, it was insisted, would lead to greater social mobility.

In fact, social mobility fell, not rose.

Correlation or Causation?

Your call.

Faith Schools

Yes, I know the arguments about indoctrination on the taxpayers\’ shilling but:

The academic superiority of faith schools was underlined today as they dominated top positions in new league tables for 11-year-olds.

Two thirds of the 250 primaries in England achieving "perfect" test results were Church of England, Roman Catholic or Jewish schools.

Despite making up just a third of schools nationally, faith schools increased their hold on the top places from 44 per cent two years ago to 66 per cent in 2007. Last night, they hailed the results as a testament to good teaching and discipline.

Is it possible that at least some of the hatred from people like Polly T is that they actually do teach pupils better ? Thus showing up the rest of the comprehensive system?

Education System Problems

Something of an indicment of the current way of doing things, don\’t you think?

Sex education lessons are so poor that most teenagers have no idea about sexually transmitted diseases or pregnancy, according to new research published today.

I understand about the problems with teaching 20% of them to read: it\’s not, after all, a natural activity. \’Ritin\’ is also a bit odd.

But you\’ve got to have a really bad education system if you can\’t teach teenagers to fuck properly.

Simple Answer

A quarter of graduates do not have full-time jobs more than three years after getting their degrees, according to government figures.

The Higher Education Statistics Agency, which examined the career progression of 24,000 people, also found that 20 per cent of those who were employed were not working in graduate occupations.

So too many are getting a degree then.

Absolutely Agreed Polly!

It\’s time to end faith and grammar schools that damage children\’s chances and limit most parents\’ choices.

It is absolutely the time to remove the limits on most parent\’s choices. Of course, we shouldn\’t do that by the method you advocate, which is that pupils are assigned to a school, rather, we should work the other way around. We should maximise parents\’ choices by slapping a voucher on the back of every kid and letting parents choose as they wish.

As they do in Sweden.

Academic Selection

Yes, I understand Labour\’s (perhaps "the left\’s" is better) hatred of private schools, I can even get my head around the dislike of Grammars (a single competetive exam at 11 years old might not be the very best way of predicting future academic success, for example) but this is astonishing:

However, the Department for Children, Schools and Families insisted that grammar schools left poor children behind. "The Government has never been in favour of academic selection and never will be," said a spokesman.

That\’s vastly stronger and as such near insane. Not even selection within schools? A math prodigy is to be taught the same syllabus as someone who will never be more than marginally numerate? If we are to have no academic selection at all then I guess that means the end of special needs education, doesn\’t it? The end of schools specialising in the arts? Stage schools and the like?

Am I reading too much into that one phrase or are they really that barkingly egalitarian?

Ballotting on Grammar Schools

Something that slightly puzzles me here:

Labour is set to reignite the political row over selective education by making it easier for disaffected parents to force the closure of their local grammar schools.

Jim Knight, the schools minister, has instructed officials to look at how to simplify the balloting process by which schools can be forced to drop selection under a 1998 law.

Why is there no mention of being able to have a ballot to enforce selection? Is it simply because the article doesn\’t mention it? Or is it not actually possible to ask for such a ballot. And if the latter, why not?

Teacher Training Days

So surprising, eh?

Sending children home from school to allow teachers to train is a waste of time, a leading academic says.

Pupils in England lose about a week of schooling every year as staff take "inset" days to brush up on the latest teaching techniques and Government reforms.

But research claims there is "depressingly little evidence" that it has any effect on teaching standards.

So teaching teachers the latest trendy educational nonsense doesn\’t improve teaching. Fancy that!

Joined up Government

That is, I believe, what we were promised a decade ago, isn\’t it? So the first lines of two stories in The Telegraph today:

Private schools could lose their multi-million pound tax-breaks unless they help state-educated pupils get into universities such as Oxford and Cambridge, it was disclosed yesterday.

The number of failing schools has soared by almost a fifth this year, new figures showed yesterday.

None of those failing schools, as far as I can see, are in the private sector.

So, is it joined up thinking to remove subsidy friom what works and to spend more on what does not?