One of the things that seems to characterise Tory ministers in this government is a remarkable attraction to putting ideology and an assumption that they know best ahead of little details like “facts” and “evidence based policy”.
A good example of this comes in the form of Michael Gove’s education reforms which have been characterised by a breathtaking disregard for decades of research into what works and an aversion to listening to anything or anyone who disagrees with the reforms.
Nevertheless, I’d like to highlight the following facts about education. It would be nice if he paid attention:
Starting maths early damages educational outcomes
Another feature of the Gove reforms is the insistence on starting on basic subjects like English and maths as early as possible in the belief that this will magically boost the numeracy and literacy of students. Unfortunately, evidence shows that, because of the way that children’s brains develop, they aren’t capable of properly handling abstract concepts like algebra before the age of 14. Trying to force pupils to learn topics like algebra before that age actually permanently lowers their academic results.
Big end of year exams are bad for learning
One of the centre-pieces of the changes to GCSEs is the insistence on scrapping all coursework and modular exams and replacing them with a single three hour exam covering the entire syllabus for each subject which will have to be sat by pupils at the end of their two years of GCSE studies.
However, the flaw with this approach is that all the evidence shows that big end of year exams are a terrible way of getting pupils to memorise information.
And the reason for this should be obvious from the experience of almost everyone who’s ever sat a big exam – pupils cram for the exam shortly before they sit it and then the information goes out of their heads almost immediately afterwards.
In fact, the best way of getting pupils to remember information is to have regular, small exams (just like GCSEs had prior to the Gove reforms) to make sure that pupils are keeping up with the material – this has been found to raise overall scores by 16% and has proved so successful that Harvard University has pretty much eliminated them as a part of courses.
Academic competition hinders learning
Finland has come top of global educational rankings since 2000. The reason for this is due, at least in part, to their highly autonomous education system where there are no national league tables or exams with teachers being trusted to test and assess their pupils themselves.
And this approach is supported by evidence which shows that pupils in systems which focus on academic competition amongst pupils and on standardised academic assessment actually results in poorer mental health and academic results of pupils – mainly because they spend more time worrying about potentially doing badly in tests compared to other pupils.
So, there you have it, three important things about education systems based on evidence and research which Michael Gove should really know but which his education reforms ignore completely. It would be niceto think that someone in the education department (perhaps even Mr David Laws) might actually take note of the evidence and call a halt to the reforms in favour of evidence based policy but I doubt it will happen.
My inspiration for this piece came from this article which, despite its lighthearted tone, draws attention to serious educational research which politicians around the world seem to pay far too little attention to.
* George Potter is a councillor in Guildford
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45 Comments
I feel you’re mixing competition between schools and competition between students in a way that’s unfair. I want to see schools compete to give the best provision for pupils but it doesn’t mean I want to see pupils being forced to scrabble over each other for the best grades.
Surely we can all agree that teachers know best so we should give them to freedom to try what they think will work best? With a surplus of schools (and school places) we can have a number of systems working side by side and we’ll see over time what actually works best.
@Thomas
That’s a somewhat fair criticism but the problem is that if you have competition between schools then you need some kind of standard test to measure achievement – which in turn leads to internal pressure for pupils to do well in those standard tests. Additionally, we should be aiming for the best education in all schools rather than have a system where some are intended to do better than others.
The two links on algebra do not at first look show what you’ve said they do. The first is talking about the effects of teaching algebra to people who are bad at maths, and seems to accept others of the same age would already be learning it.
The second is talking about the effects of teaching something to everyone reducing streaming due to school procedures, and we already know streaming is a good way to not have poorer performers intimidated into giving up.
algebra is essential for computer programming, I have never heard of anything suggesting programming must only be taught to over 13s. indeed the raspberry pi is predicated on getting very young children to enjoy programming. It would be a huge result for this and other programming clubs at primary schools if it were really as harmful as you say.
Do you have better links or more studies?
Also ben goldacre had an excellent article in the guardian (iirc) on the subject of evidence based teaching, and the comments are quite depressing in showing how much work there is to do to convince people of the benefits.
@m
As a programmer myself I can adage you that algebra is not a prerequisite for programming – all you need is a very, very basic understanding of logic. Algebra is abstract mathematics – something that the brain isn’t equipped to properly understand until about the age of 13 due to the way it develops.
@m
As a programmer myself I can assure you that algebra is not a prerequisite for programming – all you need is a very, very basic understanding of logic. Algebra is abstract mathematics – something that the brain isn’t equipped to properly understand until about the age of 13 due to the way it develops.
I’ll also double check the links and post more sources when I get out of the lecture I’m in at the moment.
Well yes you can just have if then else chains, but with the pi especially you usually draw something to the screen. At that point you’re working with x and y and variables and functions.
Perhaps by algebra the literature means quadratic or simultaneous equations rather than the raw concept of variables being harmful? Is this I’m having trouble with.
@m
Well much of the programming tools aimed at young people, such as Kodu Game Lab (I’d really recommend checking it out actually) boil it down to basic logic without having to worry too much about handling complicated variables.
But yes, some variables in programming are necessary which counts as algebra but, from the educational perspective, algebra includes more complicated things like quadratic equations which were the kind of thing I started learning at age 13 or 14. Any earlier than that and pupils really struggle with the concepts.
Regarding the sources, this is a good, non technical summary of the issue with algebra:
http://www.education.com/magazine/article/higher-math-grades/
And there’s also something called the Algebra Readiness Test which determines whether a child is ready to start learning algebra yet – which most pupils won’t pass until a minimum age of 12:
http://www.cpm.org/teachers/algebrareadyTEST/
“As a programmer myself I can adage you that algebra is not a prerequisite for programming ”
Can I respectfully suggest that you’ve never actually programmed a computer then. Computer programming is algebra. A computer programme instructs a machine to compute the answer to algebraic formulae. This involves the ability of a programmer to first convert a real world problem into an algebraic formula and then describe to the machine how it is to solve (compute) that problem by breaking it down into series of arithmetic computations. I’ve spent 20 years writing computer programmes to model, analyse and control the physical world. An understanding of algebra is absolutely essential.
“Algebra is abstract mathematics – something that the brain isn’t equipped to properly understand until about the age of 13 due to the way it develops.”
According to who?
And another aspect to it is that, in order to understand algebra, you need a solid understanding of the basics of multiplication and division and all the rest – which is why it’s far better to spend plenty of time getting pupils familiar with those basics before moving onto algebra:
http://usatoday30.usatoday.com/news/education/2008-09-21-algebra_N.htm
(Apologies, by the way, for most of the sources being American – they’re just easiest to come by though the research behind them is applicable universally)
“But yes, some variables in programming are necessary which counts as algebra ”
It’s impossible to write a computer programme without variables and constants (numbers, or data as it’s known). The machine performs computations on those numbers using arithmetic according the instructions it receives (the program). I’ve no idea what Kodu Game Lab is and I suspect it has very little to do with computer programming, but I know it wouldn’t exist it someone hadn’t programmed it.
@George Potter
But that last article you posted is about trying to push less able kids into doing algebra early. You’re applying a one size fits all mentailty to teaching (‘something that the brain isn’t equipped to properly understand until about the age of 13 due to the way it develops.’) and extrapolating the idea that all kids shouldn’t be pushed into algebra on the basis that it is a wasted effort on those with lower abilities (on whom the resources would be better used in teaching them the basics of arithmetic).
Hey George.
I mostly accept your points but I’m not sure you would need a test, especially not a standard one to measure performance of schools. Personally, I’d like to see schools trying to sell themselves to parents through getting outside bodies to inspect and rate them. Over time I could see new independent bodies analogous to Which? and Money Saving Expert that the public actually trust being in a position to certify different schools to differing standards. How they achieved this would be anyone’s guess, it might involve exams, it might be pure inspection but by leaving things to schools and parents I’m sure we can find the optimal blend.
Even if we don’t want competition in schools we need a mechanism to diagnose when a school’s management is failing. Without testing we’d need a heightened inspection regime to achieve this, especially since it’s highly questionable whether the current inspection system actually works.
On a separate note, I’d question the assertion that kids can’t learn algebra until about 13/14. I think it’s worth saying that some/many kids will develop quicker and there’s nothing wrong with basic algebra a bit earlier on, e.g. “3x = 6”
As M said, your references on maths teaching do not fit your conclusions. what they do suggest is that mixed ability teaching of maths does not work because the part of the brain used by algebra develops at different ages in different children. The latest developing children fail to learn anything while the earliest are held back. Of course the studies don’t fit Michael Gove’s conclusions either.
The central concept of both programming and algebra is abstraction. I would guess this is one of those facilities that develops at different ages.
Now this explains so much! I came back from South Africa aged 11 and joined the local girls’ grammar where they’d been doing algebra and geometry for two terms. Always thought that was why I struggled, not because a) thick or b) innumerate. Now I see I was just too young. (Several people out there muttering “No, a AND b.”).
@Thomas and @Peter
Well it’s true that children develop at different rates – which is why I’d say it’s much better to implement the old Liberal policy of classes based on ability rather than date of birth. But, if we’re going to continue the system of basing classes around children born at a certain time always being in the same classes and specifying by what age children should learn what then it makes sense to make sure that we don’t start teaching anyone things before they’re ready – which the Gove reforms fail to do.
The best thing to do would be to just have classes based on ability so that children can go at their own pace – but since that’s not likely to happen at the moment then the next best thing is to do the best we can to make the current system work.
I’m not entirely sure how things are done now, I think it’s down to the schools but I was set by ability for Maths and English from the age of 7 onwards. I think we can all agree that greater setting would be a positive.
“The best thing to do would be to just have classes based on ability so that children can go at their own pace – but since that’s not likely to happen at the moment”
I was streamed at secondary school in the 1980s. I don’t know what proportion fo schools have streaming these days, but I’d guess it’s the majority. You appear to be talking about a subject, education, you have no knowledge or experience of.
I aware I’m being critical to someone who has put their name out there, while I hide behind the internet’s dream of anonymity. Thanks for engaging George.
I’ve not seen Kodu before, but I’m familiar with Scratch which seems to be doing well. Kodu does seem simpler and more restricted from a quick look which possibly makes it better, but scratch teaches constructs more useful for actual programming.
The pre-algebra test you’ve linked contains questions on subjects I would consider proper algebra, so yes if the argument under discussion is “algebra as taught in the national curriculum is too complex for most 13 year olds” I wouldn’t disagree.
I would have thought spreading out algebra over more years and starting earlier would be better than just waiting until the end, but this is where RCTs and studies come in.
As you say the studies are all from America. This is because we just don’t do it here, and for me this is the key point. We need to do more and stop damaging changes being driven by gut instinct and whim, especially as the people driving them are invariably “cleverer” than most and what they think worked for them may be very unsuitable for most people.
And now I’m not on a mobile here is the link to the guardian article I mention above. The resistance in the comments is the interesting part.
http://www.guardian.co.uk/education/2013/mar/18/teaching-research-michael-gove
@Steve
I went to school in the 90s and the 00s. I’d wager that I have far more recent and relevant experience of the education system than you do.
The new national curriculum is incredibly prescriptive: specifying exactly what children must learn by which age with a particular focus on starting on English and Maths very early and tackling more difficult subjects earlier. In this, the reforms represent a move to precisely the kind of flawed model that the Americans have and which the sources identify a problem with.
Also, regarding Kodu Game Lab, it’s a integrated development environment aimed at young children which allows them to do the basic elements of programming, creating conditional statements and variables and so on, using pre-formed elements in order to allow them to make computer games rather than forcing them to start learning programming solely through the medium of typing text and complicated syntax.
Therefore it is, along with other similar tools, a brilliant way to introduce them to the basic concepts of programming logic and breaking down complicated tasks into smaller chunks which can be programmed in a way that they can understand and find enjoyable so that they can then gradually move onto more complicated, more traditional programming rather than throwing them in at the deep end.
@Steve
Also, regarding streaming, my personal experience was that my year group was broken down into different sets for different subjects with each set moving at a different pace. That was possible under the old educational system as GCSEs in particular, with modules, allowed for that flexibility. Unfortunately, Gove’s reforms would see much greater emphasis on precisely what must be covered, and how it must be covered, for each age group which undermines the flexibility which is essential to things like streaming.
Yes, streaming is absolutely a good idea – and the reason that I disagree with Gove’s reforms is because they’ll take education backwards in teaching methods to even before the streaming methods used in the 70s and 80s. The reforms are aimed at forcing an incredibly flawed, one size fits all, method of teaching with teachers themselves being given incredibly little leeway in how they’re allowed to teach or what they should prioritise. That is a retrograde step and one which flies in the face of everything we know about what work’s best in terms of teaching techniques and methods.
George Potter
As a programmer myself I can assure you that algebra is not a prerequisite for programming – all you need is a very, very basic understanding of logic. Algebra is abstract mathematics – something that the brain isn’t equipped to properly understand until about the age of 13 due to the way it develops.
As a university lecturer in Computer Science, who has been teaching programming for 24 years, I can assure you
that there is a very close correlation between confidence with abstraction which is developed and assessed through
algebra and confidence with abstraction which is at the heart of serious programming. Have you ever heard of the
DRY principle? Isn’t that all about abstraction? Aren’t Uncle Bob’s SOLID principles also all very much about abstraction?
@George Potter
“I went to school in the 90s and the 00s. I’d wager that I have far more recent and relevant experience of the education system than you do.”
Your statement: “The best thing to do would be to just have classes based on ability so that children can go at their own pace – but since that’s not likely to happen at the moment” demonstrates a lack of knowledge of the scale of setting and streaming within secondary education in the UK. See for example: http://www.tes.co.uk/article.aspx?storycode=6047998 (and, by the way, I have taught in HE, my wife is a maths teacher and my siblings and parents are teachers – and I suspect my dad is bigger than yours, etc)
Statements such as “Algebra is abstract mathematics – something that the brain isn’t equipped to properly understand until about the age of 13 due to the way it develops.” (cited without a reference) is a stament that logically implies that you think everyone’s brain develops at the same rate with regards to one aspect of learning – the kind of thinking you then go on to attack. I’m confused.
Almost 50 years ago, if fading memory still serves, my class was introduced to simultaneous equations with two variables at age 11 or 12. Most of us coped.
@George Potter
“Also, regarding streaming, my personal experience was that my year group was broken down into different sets for different subjects with each set moving at a different pace. That was possible under the old educational system as GCSEs in particular, with modules, allowed for that flexibility. Unfortunately, Gove’s reforms would see much greater emphasis on precisely what must be covered, and how it must be covered, for each age group which undermines the flexibility which is essential to things like streaming.”
I detest much of what Gove is about, especially his micro-management and ‘i know best’ attitude and I suspect we’d actually rather agree on a lot, but please be careful about some of your bald statements – some of the ones you used earlier come across as being a bit Gove-esque. On the subject of streaming/setting – it sounds reasonable to teach kids with the same abilities together but the quick glance at the evidence I’ve taken doesn’t look that conclusive, especially in a subject, education, where it is difficult to agree upon what constitutes a useful outcome and to measure how useful they are 20 years down the line. Yes, we need better evidence and evidence-based policy, but it needs careful reported and applied. I often squirm when I hear ‘evidence-based’ these days – the expression is increasingly being used by the snake-oil salesmen.
@Matthew Huntbach
SOLID is definitely about abstraction, DRY – not so much in my opinion. But you can start teaching the basics of programming to young children without necessarily needing those principles.
After all, something like PRINT “HELLO” FIFTY TIMES isn’t particularly hard for children to grasp – all it is is going round in a circle several times. That’s a lot easier for young children to understand than, for example, simultaneous equations.
@Richard Dean
Which is the age, you’ll note, that I identified as the minimum age at which most children are capable of learning algebra – as measured by things like the algebra readiness test.
What do you mean by ‘algebra’ anyway? It’s not something you switch on one day. I did a lot of tutoring in maths at all levels some years ago, to support weaker pupils, and I would suggest that it’s best to introduce it slowly, over some years, to allow time for practice and to let it sink in. In order to do that properly, I think you have start maths a lot earlier than 13 – there are the basic skills which need to be learned in any case – basic numeracy which one should really start at five or six (starting with proper counting and simple additions), and then you slowly start to introduce more complex skills. Working out basic problems is probably the first more complex thing you start doing, still safely with defined numbers attached, and then slowly you’ll start with problems which require very simple equations, even if you don’t really notate them in that way yet.
If you wait with this stuff until 13, then many people simply won’t get enough time to even get the most basic of practice and understanding by the time they get to GCSEs.
This is such a sweeping statement, and based on studies which actually don’t bear out this conclusion (and weren’t intended to do so, either) – doesn’t look good in an article trying to advocate evidence-based education policy.
George Potter
DRY – not so much in my opinion.
It is about abstraction more than anything else. It is about saying “look – we’ve got these commonly repeated patterns so let’s abstract out the aspects where they differ, and turn them into one bit of code, specialised as necessary by parameters”.
After all, something like PRINT “HELLO” FIFTY TIMES isn’t particularly hard for children to grasp – all it is is going round in a circle several times
You’ve gone from “fifty” to “several”. That’s abstraction. Instead of having separate code for each number of times you might want to print “hello” you have one piece of code with a parameter, which could be set to 50 or to any other number.
If we really want to ensure that children from independent schools continue to out perform those at state schools we would follow George’s ideas.
I was struck by this comment “That’s a somewhat fair criticism but the problem is that if you have competition between schools then you need some kind of standard test to measure achievement – which in turn leads to internal pressure for pupils to do well in those standard tests” What on earth is wrong with internal pressure to do well on tests ?
@Simon McGrath “What on earth is wrong with internal pressure to do well on tests ?”
I think the problem is that doing well in the standard tests ends up taking priority over actually learning and developing understanding of important subjects. Finding a balance between learning and assessment of that learning is difficult but important.
“What on earth is wrong with internal pressure to do well on tests ?”
Nothing.
@Simon McGrath
“If we really want to ensure that children from independent schools continue to out perform those at state schools we would follow George’s ideas.”
Where’s your evidence that independent schools outperform state schools (for the same ability of pupil)? People that go to independent schools are more likely to get a good job, but that has more to do with the networking their parents have bought them to out-compete pupils who do not have that inherited privilege.
Goves’s proposals take us back in time so we can confidently anticipate that we will have school leavers equipped to meet the challenges of the 1940s &50s rather than the 21st century. Why the nutty obsession with competition derived from the Thatecherites in our midst? ?
The challenge is meeting the needs of individual students, encouraging individual achievement, life skills recognising that the very best teachers produce 4 x the progress of the worst. One luidicrous prescription is the 12 x table by the age of 9 er. our currency went decimal decades ago!! I have the feeling that there could (should) be a Gove/OFSTED collision brewing.
George, I’ll agree wholeheartedly with your first paragraph, but have reservations about some of your examples.
Maths.
I think the problem there is applying average statistics universally. Clearly there are some children who would have start understanding and haveing fun with algebra long before the age of eleven. The education system should allow them to do just that. So the answer is individual assessment and learning programmes, which is one on the big changes in improving comprehensive schools in the last 20 years. (Please don’t suggest that I discourage my two-year-old granddaughter’s enthusiasm for numbers and counting!)
Exams versus project work/continuous assessment.
I think you have a point there. If you’re looking for score to put on a certificate, you must know about both. Exams tell you about the ability to retrieve and use relevant information, perhaps under stress. This an important skill in many occupations – for instance, in meetings and negotiations where decisions are taken. On the other hand, project work/continuous assessment tells you about how the person can work over an extended period, maintain motivation and consistency and learn in the process. Project work/continuous assessment also gives the student some measure of his/her progress and can be an important learning tool. All jobs require both these skills, though the balance between them varies between occupations. Only a score/result that reflects both is truly useful.
Academic competition and learning
I think this is contentious. On an individual basis in a classroom, some students will be spurred on by it; some will be turned off. When it is between institutions, at best it provides them with a spur to re-evaluate their methods; at worst they distort the curriculum and teaching merely to get improved results.
Hi George,
I remember enjoying learning algebra in junior school. I also remember successfully teaching it to junior school, including SEN pupils.
I’d agree with you that much of what is crammed for exams is lost, but the same is true of most forms of learning – most trainers would agree that you’re doing well if attendees of courses remember 10% of what they’ve learnt for more than three months – never mind actually use it!
For me the major flaw in Gove’s educational reforms is the diminishing respect given to vocational/non-academic qualifications. An issue with our current school system and league tables is that schools are solely focused in getting all students through academic courses. This leaves many pupils demoralised, disengaged, and with little to show for the money and years invested. Far better that schools offer subjects their students are interested in, and which allow them to develop useful long term skills, than to try and force everyone over an arbitrary threshold deemed success or onto a poor quality university course at vast expense and little professional benefit. If anything Gove’s narrow view of education is making this worse, and it’s a waste for all concerned to only start offering an appropriate and useful education to many when they reach further education.
George Potter
Unfortunately, evidence shows that, because of the way that children’s brains develop, they aren’t capable of properly handling abstract concepts like algebra before the age of 14. Trying to force pupils to learn topics like algebra before that age actually permanently lowers their academic results.
I have now looked at the references you gave for this.
I regret to have to point out that they do NOT support what you have written here. What you have written suggests that NO children are capable of handling algebra before the age of 14, and that ALL children would have their academic results lowered by attempts to do so.
I myself was fooled by this, I did not read the actual references before commenting before, but I assume, since you had given them, that they would say what you have said they say. They don’t.
What the references actually seem to be saying is that some children are capable of studying algebra at an early age and some are not, and that forcing those who are not to study it alongside those that are damages the performance of those who are not. That is a completely different conclusion from what the words you wrote suggest.
I am particularly interested in this issue because I teach computer programming at university level and was for a long period my department’s admissions tutor. My experience of over many years is that ability and confidence with handling abstraction is the key skill in being able to write computer code at a professional level. That ability is best developed and assessed in school by study of mathematics. The evidence for this is correlating entrance results with degree results. Those who have done well in maths tend to do well in the degree. Those who have done badly in maths tend to do badly in the degree. School level qualifications in “Information Technology” are of little use for preparation for a degree in Computer Science because they do not involve development and assessment of skills in abstraction. When I was my department’s admissions tutor I had a constant battle to try and get this across to teachers and politicians, who just assumed that what we taught as “Computer Science” was what they called “Information Technology”. Every year I had to turn down hundreds of applicants, sent to me with glowing references from their teachers about how suitable this person was because of their “IT skills”, because I knew from their weak maths qualifications that they would do very badly in the degree. In fact studying Information Technology at school often tended to be negatively correlated with success on the degree, I think for the reasons 1) it gave the school students a very misleading impression of what the degree would be like 2) schools actually tended to use Information Technology as a subject to push those who were weak in mathematical skills into.
When I’ve raised this, I’ve often been told “Ah, but that’s because you teach your subject in a very mathematical way”. Which is not the case. I teach straightforward object oriented programming, the examples I use to teach it and assess it are not mathematical. There is nothing in what I teach which involves any sort of mathematics beyond GCSE level, and in fact the only bit that involves even GCSE level mathematics is the one lecture I give on efficiency where I do need to mention logarithms. Yet I find in my module, it’s prior maths experience that’s the best predictor of success. The practical programming skills I teach are in direct demand from industry – the employers are constantly telling us they can’t get enough people with these skills, I have employment agencies begging me to send them contact details of students who have done well in my module.
I am concerned that what you have written will discourage educationalists from promoting the sort of education that is needed to best develop these skills.
George Potter
However, the flaw with this approach is that all the evidence shows that big end of year exams are a terrible way of getting pupils to memorise information.
OK George. Do you know what I tell my students every week? Here it is:
EXAMS ARE NOT A MEMORY TEST
Do you get it? Here it is again:
EXAMS ARE NOT A MEMORY TEST
I have to tell my students this every week, because so many of them are stuck in the belief that they are. It would very much help if people who ought to know better did not keep saying they are. The exams I set are skills tests. Students who take a memorisation approach to them fail, and fail badly. I would say it’s one of the biggest causes of failure. Students who believe the way to success is to memorise chunks of notes or example code have got it completely wrong. That’s a bit like thinking the way to pass your driving test is to memorise all the hand movements that are made on every possible route from the driving test centre without understanding why those hand movements are made.
What is needed on a skills test is to practice, practice, practice, until it come naturally. Last minute cramming is useless. I always advise my students that they should not “revise” at all. Just keep up with plenty of practice writing code as the material is taught. Then get plenty of sleep and relaxation before the exam.
To get away from Algebra for a moment, as someone who went to school in the 80s and 90s (so, compared to George I’m ancient) I think he’s missing an important point of analysis. It’s pretty clear to me that Gove and his reforms are trying to make UK state schools more like UK private schools. You don’t have to look very hard to find people lining up to condemn the increasing “Etonisation” of the UK, but you have to accept that Eton is incredibly successful, as are many other private schools that don’t insist their pupils wear tailcoats every day. I think if you want to tackle Gove’s school reforms, the exam question is “does making comprehensive schools operate more like the existing private schools mean that, with far fewer resources, the outcomes will be similar?” I imagine the answer will be “yes a bit” in cases where the school is in a relatively affluent area, and only “maybe” in other cases.
Disclosure: I went to a private school. Not Eton.
btw – I remember doing algebra aged 11. No, I am not a genius and always struggled with maths. But the teacher told us about how you could give a number a name. It seemed a very simple idea.
@Charles Beaumont “but you have to accept that Eton is incredibly successful, as are many other private schools that don’t insist their pupils wear tailcoats every day.”
Successful because of what they do with the children they have, or simply because of the nature of the children (and parents) that they have?
The problem with the discussion so far appears to be less about Gove and more about the usefulness of Algebra for computer programming and whether Gove is right to introduce an Etonian-style curriculum to the state sector.
Firstly, on Algebra in primary schools: I think two thirds of pupils will learn Algebra quite well – some the basics, a small number will make great progress. As with any topic, a fair number who still think in a fairly concrete way in Maths, will struggle and may even be put off Maths for life by this. If that’s the risk we want to take and have another generation like mine (1970s/80s children), thrown into complex calculations before they are ready and end up detesting maths – fine. It’ll be worth it for the rest I suppose.
On Gove’s overall narrowing of the curriculum – his ‘project’ is a car crash. First of all, he has shown utter contempt for the very people he wants to implement his plans. Second, he happily ignores good practice going on in schools already and rips up the entire curriculum with a very to rewriting the entire philosophy and practice of education – without the advice of current theory and practice. He is relying on a cabal of cronies and a small group of neo-con academics to guide him (see the disastrous History programme).
I cannot get across too strongly how appalling Gove is as an education secretary – yet Liberal Democrat ministers go along with him, gently prodding him here and there.
Gove has been forced to back down on the GCSE before he was taken to court by the exam boards – this is an alarm call to those working outside education and generally thinking, ‘Oh well, I feel Gove’s heart is in the right place – we need more rigour etc..”.- you may think that Gove’s sudden reversal was strange – this is but the tip of the iceberg.
I have never known an education secretary so comprehensively alienate an entire profession, from academics and heads to classroom teachers – this is unprecedented even for Tory ministers.
Before 2010, teachers knew there needed to be reform of exams and a review of the NC but Gove is going too far and too fast – and he doesn’t care what anyone who practices in education thinks about it.
We Lib Dems should distance ourselves completely from Gove and challenge him to produce rigorous evidence to support his behaviour.
Helen Tedcastle
The problem with the discussion so far appears to be less about Gove and more about the usefulness of Algebra for computer programming and whether Gove is right to introduce an Etonian-style curriculum to the state sector.
I bring up the subject of computer programming and algebra because it’s something I know about directly, I’m arguing from evidence I’ve observed involving hundreds of students over many years. What I’ve said, however, applies to other subjects as well, maybe more so in mine, but similar in many other science and engineering subjects. Ability and confidence with abstraction are essential for these subjects, there are not enough students coming forward with the sort of school subject education that helps develop and assess them, employers are constantly telling us they are experiencing a skills shortage in these areas.
I think these needs to be understood because it is the background that Gove is working from. It seems he has heard the messages that people like me have been sending out about this sort of thing. Of course, as you say Helen, he’s gone about dealing with the problem in all the wrong way. As a result, yes, he’s damaged the case for what I actually would have wanted to see.
The point you make in your second paragraph is in fact the point the papers referenced by George Potter was making, rather than, as he suggested, that no school children under the age of 14 are capable of handling algebra. It is indeed a dilemma for educationalists. Some of us have had the naive ideal that all children are capable of handling this sort of subject, it’s just a matter of getting those who are reluctant to try (perhaps because of their cultural background) to sit down and persist at it and practice until they get it. We are reluctant, on good liberal grounds, to subscribe to the idea that there is an in-built mental difference in ability. However, my experience suggests that’s how it is, and it is roughly a division into thirds. One third can do it and get the point right away, one third just can’t and are made miserable by all attempts to get them to do it, and one third can eventually do it if you push them and find the right way to get it across to them.
The big issue is that middle third. Singling out that top third and concentrating educational resources (the grammar school model) on them won’t help the middle third. We need to find ways to identify the middle third, and ways to get them over that hump of understanding. Making them persist will work, whereas making the bottom third persist will do the opposite.
I can identify with this because at school I was in the middle third for English literature, and the other two thirds for maths and science. Pushing me to stay on studying English literature at O-level worked – I eventually got the point, and enjoy it now. Pushing me to carry on doing sports didn’t work, I hated it, and the more they made me do it and I just couldn’t, the more I hated it. It put me off, and I have a loathing for all forms of sport to this day.
Funnily enough, I was initially put into the middle stream for maths at school. I think this was because 1) I was quiet and working class 2) they interpreted my boredom at what I saw as extremely simple stuff we were being made to do as me finding it hard.
Charles Beaumont
But the teacher told us about how you could give a number a name. It seemed a very simple idea.
Yes, this is how it often is with abstract topics. There’s a simple way of putting it or explaining it which suddenly makes it “click”. I hear this all the time from my students, they tell me how one day it “clicked”, something I said or did made it all fall into place. But it isn’t that there’s one thing that works for every student. There’s not one day when I give a lecture and suddenly half the class understand what they didn’t before. Those of us who teach this subject are all searching for the magic trick which does that, but there doesn’t seem to be one. The clicks happen at different times for different students, and an analogy or way of explaining that works for one just leaves another confused.
@ Matthew Huntbach: I agree that there is nothing in principle wrong with teaching algebra to primary school children and I also agree with you that roughly two thirds of the cohort will either thrive (I would suggest the top ten %), while the rest – with persistent and good teaching will ‘get it’ after a slog.
I worry about the bottom third who may not just struggle but end up loathing maths with a passion. Having worked in an independent primary school for the past three years, I have learned a great deal about the primary education – what works and what doesn’t – (something we don’t always appreciate in secondary).
I am struck at present by just how many children are engaged with the maths and I’m convinced it’s because of the structure of progression one can see in the questions (as well as excellent teaching)- it enables children to show what they can do.
Gove wants to end this. He wants schools to return to a kind of sink or swim approach, throwing all the children in at the deep end – the weakest sink, the strongest stay afloat. Great for the bright ones and the ones with helpful parents at home. I worry a great deal about children I know who will lose out and like my generation, end up either ‘getting it’ or detesting maths with a passion. So we may well end up with more engineering graduates than history graduates but there will still be the question of those who leave school with remedial level maths.
The children I work with now have a very realistic sense of what they can do in maths and by and large they appear to enjoy it – even the average ones – not so in my day.
However, it is an independent school and the children are self-selecting ie: a higher than average wealthy parents with above average qualifications. What a contrast to the state schools I have worked in, where children on free school meals sit alongside the children of headteachers. State schools face more challenges, self-evidently but again, the Gove vision pays no heed to this.
I agree that those with high ability must be stretched – that goes on now – in fact the teacher I work with generates extra materials for these few – she also has to generate materials for those working two levels below – the level of differentiation of materials is not something teachers bothered with in my childhood. We just worked more slowly through the textbook.
I do appreciate that there is a skills shortage and we must do something about it – sensible people agree with this but as you say, Gove has gone about things in the wrong way, entirely – with a sledgehammer and with little if any regard for the excellent work or experience of primary teachers. The man is a menace but I predict that once his ‘revolution’ hits schools, there will be an enormous backlash from parents and even the Labour Party (if Lord Adonis can bring himself to criticise the Tories).