A libertarian inclined blog for teachers and learners of all ages. Comments, emails and links to other educational stuff welcome.
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Category archive: Maths
She expressed extreme pessimism about computers in education. She said that pretty much all the vast amounts of money spent on computers in education so far has been wasted, and that all further expenditure on computers will likewise be money down the drain. They spend enough time staring at screens as it is, without them being encouraged to stare at yet more screens when they ought to be learning things. Computers do not encourage concentration. They destroy it.
As for me, I don’t know. Really, I don’t know. I’m just passing on what she said.
If you want an old-school school, hers sounds pretty good, and there are still places going spare. She talked about the Synthetic Phonics stuff that I have already researched, and clearly knew her stuff. She has been asking around about a similarly good approach to maths, but has not yet found how that ought to be done.
She also said that during the last year or so, regular state schools have maybe been making some actual progress in the literacy department, what with the literacy hour, and with word getting around about Synthetic Phonics. This despite the obfuscations spread by the government, who don’t want to admit how wrong they have been in the quite recent past.
Yesterday was the hottest day of the year, and everyone at Kings Cross Supplementary seemed to be in a bit of a mood, certainly me. Small Boy’s disposition was particularly negative, it having been severely aggravated by the fact that his little Nintendo games machine was doing something “mysterious”. He used this word over and over again. I am impressed that at his age he knows such a word, and its precise meaning, but I couldn’t solve the problem, which was making the games machine work as Small Boy thought it should. Also he was coughing a bit, and I have yet to learn the medical diagnostic skills that are evidently part of the skill set of a Real Teacher. Was Small Boy actually ill, or just reluctant to have yet more Education done to him, after a day spent having it done to him at his regular school?
We looked at maps of the world in a map book I had brought with me, and he pointed out different countries. I persuaded him to allow me to pronounce country names that he didn’t know. Namibia. Zimbabwe. Libya. He pronounced ones he did know. Morrocco. Egypt. Then he wrote, very badly, a list of countries, one of which was “United”. But I guess that names of countries are often rather confusing. How was he to know that United was part of United Kingdom when the Kingdom bit was quite a lot below the United bit?
Small Boy used interesting arguments to explain that he needed no more Education. I can already read, he said. He came dangerously close to saying: “I already know everything”, which is obviously blasphemy if you are being Educated, and I subjected him to a big speech about he obviously had More To Learn because Everyone Has More To Learn. (It never ends. It’s a permanent treadmill. You are Educated and Educated and Educated. Then you die. Welcome to the twenty first century, kid. One of the more depressing things about being a teacher is the things you hear yourself saying.)
Smart Boy and Smart Girl both prefer talking with me to having Education done to them, but Miss Head Teacher was adamant. They must do sums in the class.
The most memorable moment of the evening for me was when Mr Maths also made a speech. “Smart Girl, why are you wandering around? Sit down in your place. If everyone wandered around, there would be Anarchy instead of Order.” It was like in a movie, where the script writer has completely abandoned realism in order to explain the Underlying Point Being Made In This Scene, except that Mr Maths really said that. I’m afraid I was not much help to him, probably because I am an anarchist. But eventually I was able to contribute to the imposition of Order with the necessary mixture of prison guarding and maths tuition. So I guess that means I’m not an Anarchist any more.
Seriously though, one interesting educational issue did crop up, which concerns the methods used to teach things like long division and “long multiplication”. (I’d never heard of that one before.) Every teacher and every school seems to use a different method for these things. There’s the “grid” method, and various others I can’t remember the names of. Do different methods confuse, for doing something like multiplying 57 by 34? Or do different methods throw light on the underlying things that are really going on, the way that speaking several different languages is supposed to make children cleverer by giving them an instinctive philosophical grasp of what language is (and is not) that other children are denied? I suspect that the clever kids – and all the kids at Kings Cross Supplementary seem pretty smart to me - do actually gain a bit from having sums that they find easy taught to them in an unfamiliar way.
Just after writing all that, I went in to the Civitas Office to find out how I was doing, in their opinion. They were nice, but the message was unmistakeable. Less Anarchy, please. More Order.
As already reported in this earlier posting, I have been reading Nick Cowen’s Civitas pamphlet entitled Swedish Lessons. It consists of three chapters, the first being about Sweden’s education reforms, the second about Britain’s current educational problems, and the third proposes British solutions. The chunk that follows is from chapter two, about what’s going wrong with British education. Things aren’t that bad, says Cowen. But they’re getting rather worse, and here (pp. 48-52) is one of the reasons:
GCSEs and A-levels, the current official indicators of what makes a good school and what defines a successful pupil, are bad measures of how well pupils are doing. Yet the government treats exam results as a proxy for school productivity, with the Department for Schools, Children and Families, the Qualifications and Curriculum Authority and the Office for Standards in Education (Ofsted) placing primary emphasis on good exam results representing success and achievement. Under this regime the actual skills and abilities of pupils come to be disregarded.
This problem becomes more acute when the interests of pupils come to be directly at odds with the interests of the school as judged by the exam and assessment system. The continual drive to improve results creates a damaging incentive for schools to find qualifications that are likely to produce good results with the least amount of effort and talent. General National Vocational Qualifications (GNVQs) taken at the same time as and often in lieu of GCSEs offers perhaps the most widely used ‘loophole’ used to drive up standards on paper while not actually tackling students educational outcomes. Professor Smithers of the University of Buckingham’s Centre for Education and Employment Research found that thousands of students took courses in these ‘quasi-academic’ subjects, which include science, information and communication technology and business. However, ‘entry to the more practically-sounding fields is miniscule. Hospitality and catering, manufacturing, construction, retail and distributive trades, land and environment together account for only 1.2 per cent of the Intermediate GNVQ’. Indeed, over half of all the GNVQs taken are in the single subject, ICT. Smithers has also noted that the influence these subjects have had on results is significant: ‘from 2001 the proportion achieving five good GCSEs themselves has plateaued at about 50 per cent and the increase [up to 2005] has been through intermediate GNVQs which count as four GCSEs’. David Brown, a reitred head teacher, calculated that since GNVQs are valued so highly compared to GCSEs, studying the ICT GNVQ was 13 times as effective in boosting a school’s league table position as studying maths.
A-levels have suffered a similar commute to easier subjects that appear to offer improved results for schools. From 1996 to 2007, the number of A-level entries has increased by nearly 100,000. However, this increase has not been reflected in traditional subjects. In fact, many have declining numbers of entries: physics, French and German have all registered reductions of more than 4,000, 10,000 and 3,000 respectively. By contrast, psychology has increased by 30,000; media & film studies by 16,000 and PE by nearly 12,000.
Officially, qualifications in all A-level subjects are worth exactly the same but, as Peter Tymms and Robert Coe of Durham University have demonstrated, some A-level subjects are less demanding than others: ‘It is perfectly clear from our research that two A-levels are not equal, with some more severely graded than others.’ Their research found that students with Bs in JSCSE history, economics, geography, English language and literature, sociology and business studies went on to attain C on average in the same subjects at A-level. However, Coe and Tymms found that those with Bs in GCSE maths, computing, German, French, chemistry, physics and biology were more likely to get Ds at A-level.
The result is not just a case of students themselves choosing easier subjects. There is evidence that some schools have been actively discouraging pupils from taking subjects that are deemed more challenging and are therefore less ‘safe’ for league table purposes. An ICM survey commissioned by the Association of Colleges in 2006 showed that 55 per cent of students felt that teachers steer them towards courses in which their school does best, rather than what they needed.
It is hard to predict exactly what the long-term consequences of disregarding challenging subjects will be, but a number of experts have described their fears. Richard Pike, chief executive of the Royal Society of Chemistry, has argued that schools are discouraging students from taking maths A-level. He noted: ‘This contrasts starkly with countries like China, in which mathematics is seen as integral to the sciences and to the nation’s economy.’
David Hart, then general secretary of the National Association of Head Teachers, argued that ‘soft’ subjects may be helping students get into higher education but that ‘in the long term I’m not sure it does very much for their career prospects’. Robert Kirby-Harris, chief executive of the Institute of Physics, has also argued that exams present a ‘crazy situation’ in which A-level students are opting for subjects which have ‘poor career prospects’. In addition, Kathleen Tattersall, chair of the Institute of Education Assessors, has described how history, in particular, is becoming an endangered subject as more students opt for subjects such as media studies and photography.
The irony is that this focus on exam results and regulated assessment is meant to ensure high standards of teaching in all schools, but the flaws in the system have created incentives that act to undermine standards and to direct the efforts of both teachers and pupils in the wrong direction. Of course, there are still very good teachers and some very good schools in the maintained sector, and there are many successful pupils. However, the structures and incentives operating at the centre are working against those successful outcomes rather than for them. It means, for example, that when a school begins to struggle, its first priority is not to concentrate on getting genuinely better outcomes for their pupils, but on creating better outcomes on paper, the ones that are acceptable to the central bureaucracy.
Hence, the very mechanism designed to assure some quality in every school has led, when implemented systematically, to a lower quality of education being generated in practice.
An early factual claim in Reform’s document is simple: “about 40% of mathematics graduates enter financial services”. This - we are invited to agree - is a good thing. The report’s reference for 40% is a simple link to prospects.ac.uk, which isn’t very informative as it’s rather a large website. Chasing through the pages there, you will find “What Do Graduates Do?”, and then the maths page. There were 4070 maths graduates in their sampling frame of 2006. Only 2010 of those, however, are in UK employment (1.5% are working abroad, and the rest are studying for a higher degree, or a teaching qualification, or unemployed, or unavailable for employment, and so on).
Of those 2010 - not 4070 - 37.9% are indeed working as “Business and Financial Professionals and Associate Professionals”. So correct me if I’m wrong – I’m always eager for that to happen – but by my maths 2010 x 0.379 = 761.79, and that divided by 4070 = 0.1871, but let’s round up like the angry maths profs did and say that about 20% of maths graduates enter financial services. Not 40%. I call this “arithmetic”. For a bunch of people complaining about the substitution of woolly modern notions like “relevance” and “applied maths” in place of high end mathematical techniques, they don’t make a particularly good advert for their own skill set.
I’ve added the link in that.
After criticising what he believes to be other arithmetical errors, and errors of other kinds, in the report, Goldacre ends by saying:
I’m happy to agree that maths is economically useful, that maths exams are dumbing down, that people avoid difficult school subjects, and that humanities graduates who think maths is uncool are bores. What I would like is someone who can be bothered to sit down and reinforce my prejudices without perpetrating crass errors of overinterpretation and getting the basic arithmetic wrong. I’ve never fully seen the point of them, but I suspect that’s what thinktanks are there for. Again, I may be wrong.
No, I think that’s about right. Think tanks exist to supply facts to support your preferred prejudices. They translate reasonable opinions, held for other reasons to do with your overall worldview, into pseudo-deductions from only the facts of the particular matter being dealt with. The more honest ones are also honest about their prejudices, and don’t only do this. The seriously bullshit ones do nothing else. (See this, by me.)
London: Britain is all set to get its first fully state-funded Hindu school by September 2009.
The Krishna Avanti Primary School in Harrow in north-west London, will have Scripture Reading, Vedic Math, Sanskrit and Yoga as part of its curriculum.
On Saturday, a traditional bhumi pujan ceremony was held before starting the construction of the £13.5-million project.
“This gives Hindu parents a choice. Parents from other religions have a choice so it’s fair that the Hindu parents, too, have an option,” says Nitish Gor of I-Foundation, a Hindu charity closely associated with the Hare Krishna Movement, which will run the school.
It’s the “fully state-funded” bit that I object to. If these Hindus were paying for their own school, I’d have no objection. But should the British state be paying for this kind of thing? The report linked to and quoted above notes that some British teachers unions object to such schemes on the grounds that they divide communities. I wonder. I suppose much depends on what exactly they teach about the other bits of the community.
Also, what on earth is “Vedic Math”?
The Telegraph reports:
GCSEs are “considerably” easier than tests sat 50 years ago as questions are simplified to make them more relevant to modern teenagers, it said.
Reform, an independent think tank, said the traditional emphasis on algebra, arithmetic and geometry has been dropped in favour of questions focusing on real-life situations. It added that pupils can now gain a good grade with fewer than half the marks needed in 1990.
Reform also claimed that the lack of rigour has led to fewer students studying maths at sixth-form and university - leaving the British economy vulnerable to competition from China and India.
So, it would seem that “real-life” situations are not relevant. Oh dear.
I’m an individualist about stuff like this. It may matter to the Prime Minister than Britain’s children are slipping down the international league tables, but an individual child isn’t going to be unemployable merely because he doesn’t have a PhD in maths. Okay, less rich maybe, but will he starve?
Maybe the answer is much better teachers and much bigger classes. In other words obscenely high salaries for the best maths teachers in the country. That’s only going to happen in the private sector. So I say, eliminate the teaching of maths altogether from state schools (according to the Reform report good progress is already being made along these lines), and tell the parents it’s up to them to buy it elsewhere. Just kidding.
Or maybe I’m not kidding. Seriously, maths as showbiz. If you ran maths classes in huge conference centres, charged a fiver a head per class, packed them in, but wanted them to keep coming back time after time because the show was actually very good - the children liked it and their parents liked it - what would it consist of?
I have been having a look at your blog and though you might like to hear about our new site www.tutpup.com which has free maths and English games for students.
Our site is completely free, has no ads, does not require players to disclose any personally identifiable information and allows students to play competitive head-to-head games with their friends/classmates or students from around the world.
We also provide tools for teachers where they can set up and manage their classes as well as seeing how their students are performing at school and at home.
I thought that this may be of interest as our aim is to help as many kids (wherever they are) to improve their basic maths and English skills and this seemed to fit with the libertarian leaning of your blog.
Yes, Richard Taylor, this is just the kind of thing that does interest me, a lot. Feel entirely free to keep me and my readers informed of progress with this. It’s obviously a world away from this kind of thing, but some of the simplest and most basic games are among the most successful and addictive, yes?
As I keep saying here, sooner or later someone is going to make something like this work in a very big way.
Today I was at Hammersmith Saturday again. Apparently there was some confusion in parental minds about whether this was the half term break, which for Hammersmith Saturday is not this week (as it already is for regular schools) but next week. Present were a mere five pupils, and five teachers (assuming I count), plus one teacher’s daughter, who joins in as a pupil or not as she pleases. So, I was pretty much surplus to requirements. I myself will not be attending Hammersmith Saturday for one Saturday in mid-June. When I revealed this news to Other Man Teacher today, he hardly panicked at all.
So, what did I actually do today? One thing I did was sit down and, as a pretend pupil, do some of the arithmetic tests that Miss Maths sets her charges. I did this because (a) it will make me better at teaching arithmetic, which I want to get better at, and (b) because it does the children good, maybe, some of them, the ones who care, to see just how very very quickly, compared to most of them, mental arithmetic can actually be done by someone who is quite good at it. As I told Miss Maths, Rachmaninoff used to teach the piano by just himself playing the piano to his pupils. He didn’t make his pupils play, or tell them how to play. He just played. He set a standard. I was, in a somewhat more mundane setting and far more mundanely, attempting the same technique. It didn’t work, though. The ones that didn’t care didn’t care. The ones that might have were busy doing their own sums.
But the main thing I did was just get to know a few of the children who were there that little bit better.
I have long held to the theory that one of the Great Educational Divides in Humanity is between People Who Were Confused At School, and People Who Were Bored At School. Education Theory, for instance, is either elaborated to solve the problem of Confusion, or of Boredom, the Traddists being the ones who were Confused and the Progressive being the ones who were Bored. Two of the girls present were classic “I’m bored!” pupils. “I’m bored,” they said. “This is boring.” But one of the boys in particular is a classic Confused type. He doesn’t mind being bored, so long as he knows what he is supposed to be doing, and is left to get on with it. Children are different from each other.
Talking of children being different, another basic divide in educational theory concerns whether education means focusing on strengths, or on weaknesses. Are teachers supposed to bring out spikes of super-achievement from their pupils, while those same pupils continue, e.g., to do sums by counting on their fingers? Or are teachers supposed to home in on weaknesses and try to correct them? Miss America, who is a very capable and much loved teacher of English at Hammersmith Saturday, is, so it appears to me, a weakness correcter. My lazy, fun-loving instincts tend towards playing to strengths and dealing with alleged weaknesses by just going around them. My understanding of a lot of home educators is that they feel this way too, not just out of laziness and not wanting to have perpetual fights, but because they think it’s for the best. (I recently read an HE-er’s posting about a son who learned to hand-write very well but in his own good time, without being pressurised. But, I can’t now find this. It has a picture of his writing. Anyone?)
So, for instance, those two Bored Girls were being driven almost foetal-position with the tedium of the sums that Miss Maths was giving them. So after their ordeal, to cheer them up, I just sat down and had a conversation with them. This worked well. They are both highly witty and stimulating conversationalists, and conversing with them is playing to one of their strengths. (Women love to talk.) They soon cheered up.
My playing-to-strength way of teaching arithmetic would be to find out what a kid really, really cares about, and find the arithmetic in that. Miss Actress, for instance, would be asked things like: how many lines are there in this Shakespeare play? How much money did Angelina Jolie get for her last film? If she got this for her last film, and this for the one before, and this for the one before that, etc., how much did she make in the last decade? Things like that. And as for all those boys who are going to be international footballers ... (By the way, the England team is going to have thousands of young men in it in fifteen years time.) Well, the Premier League is an absolute hotbed of arithmetic. I learned a lot of my mental arithmetic listening to cricket commentaries on the radio, and reading the scores in the newspaper.
Well, that is what I would do with the Bored ones. With the Confused ones, I simply let them get on with their arithmetic, helping them with any confusions.
Hub caps and phone photographs
Tim Worstall on the uses of maths
Kings Cross Supplementary Headmistress gives the thumbs up to Nintendo Maths Training
Neil Turok on teaching the best maths students in Africa
Me teaching very young children and me teaching slightly older children
Smart Boy looks up Don Bradman on the internet
Therefore God exists
Talking maths with Michael Jennings
Busy doing education stuff but not education blogging
The girl who was in The Wonder Years is now a math wizz
What use is maths?
Maths on a Russian pavement
Learning by assisting
Boris Johnson on maths and personal debt
Woodhead on GCSEs and on centralisation
Easy with Eve
Handwriting is essential if you want to add words to pictures and for doing maths