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Posts from the ‘schools’ Category

Apr 9

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John Mason’s Conference Thoughts

John Mason, Professor of Mathematics Education at the Open University, was the closing speaker at this year’s MA-ATM combined mathematics education conference.

The central theme of the talk was the importance of reflecting upon experiences in order to unify them. We don’t often seem to learn from experience alone Prof. Mason exhorted; we learn incrementally, unifying experiences with one another, gradually gaining awareness of a greater whole.

Unifying experiences does not happen by chance; or rather, it should not. As teachers we must act as faciliators of this reflective process. One way to achieve this is to offer students familiar patterns of problems which are then developed and extended, and the richness drawn out of them through reflection.

The associated prensentation to the talk, with examples of such activities can be downloaded from Prof. Mason’s website, or by clicking on the link below:

Powerpoint: Closing Plenary at the MA-ATM Conference

Of course, this presentation does not do justice to an impassioned talk from such an experienced educator!

There was a great deal of truth in Prof. Mason’s talk. One of the main things that I will take away from the talk was my reflection during the talk that as a teacher I found myself too often concentrating on the activity in quantity, searching to find new activities and new ways of approaching a topic. I would find them on the internet, or in books, or by asking others. By contrast, the activities considered in Prof. Mason’s talk could be found only by taking the mathematics seriously and doing the mathematics for yourself. He searched for activities in quality, searching for ways of reusing the familiar but provoking new thought within that structure. From this, students are in a position to draw upon previous experiences, become familiar with areas of mathematics, and begin to unify their experiences. That is a lesson worth (re)learning!

Feb 29

Primitives Article

Cover of Mathematics Teacher 207

In this month’s Mathematics Teacher magazine is an article about prime factorisation by me. It discusses an idea for teaching and learning about prime factorisation that minimises ‘telling’ and maximises students mathematical exploration.

Dave Hewitt, a lecturer in Mathematics Education from the University of Birmingham (and my PGCE mentor a few years ago), has written a series of articles about separating the arbitrary (or contingent) and the necessary and mathematics, and teaching by ‘telling’ only those things which are arbitrary. The idea is that students need to engage and discover for themselves the necessary connections and patterns in mathematics, but the arbitrary are not discoverable in the same way, and so need to be told to people.

This position has influenced my thinking about mathematics education, particularly with respect to algorithms. My conjecture is that using an algorithm involves no mathematical thought; at best, it is an exercise in arithmetic. However, where an algorithm exists there is likely to be a kernel of really interesting mathematics, and creating an algorithm to perform a particular function involves a great deal of mathematical thought. The goal of the investigation was to capture the interesting maths in an interesting way, that the students can engage with, and which they can learn from.

The accompanying software can be found in the primitives section of this website.

Nov 17

A new voice calling for exam overhaul

The Education Guardian reports that the Specialist Schools and Academies Trust urge school exam overhaul. It is encouraging to hear another voice added to the growing clamour for change.

The SSAT argue that the government has “consistently exaggerated the technical rigour of national assessments and the GCSE“. They argue that by changing the curriculum and therefore changing the content that is being tested, it becomes extremely problematic to maintain and compare standards.

The SSAT also argue that there are testing cause a degree of stress and that the level of continued stress that students are exposed to has become unreasonable and counter-productive. In place of the SATs they suggest using sample testing of randomly selected pupils to monitor performance.

The response from the DCSF is staggering: “… we are not looking at sample testing of randomly selected pupils … It is hard to see how any sample of children could be truly representative of one school … the idea that children are over tested is not a view that the government accepts … we don’t believe that in this day and age parents can be expected to have hidden from them the real achievements of their children at school.”

If the governmental body responsible for our curriculum do not understand sample testing, then I am deeply concerned with the science curriculum; if do not understand how sample testing can give representative data, then they do not understand science. Science is based wholly upon the statistical analysis of sample data. Given a sample and the overall population size, we can very accurately calculate how representative that sample is. Simply, this argument is nonsense.

The original premise for introducing SATs was as a means of measuring schools performance. The DCSF statement concedes that they have now become GCSEs for younger students – performance assessments for the students and their parents to measure themselves with.

Despite this the government does not accept that children are over tested. I am absolutely and utterly convinced that the government is wrong about this. Sadly, there is no easy way of measuring what level of stress is acceptable to expose children to. However, I would have thought that until tests GCSEs, the natural inclinations of all parents and teachers would be to minimise unnecessary stress. This is not the government’s inclination.

Oct 25

It’s the teachers, stupid

In the October 19 2007 Times Educational Supplement, the lead headline is “It’s the teachers, stupid”. It reports the findings of a report by McKinsey, a global consultancy firm that argues that the most important factors in educational excellence is the teachers.

The findings are quantified: around the world the top educational systems are found in South Korea, Finland, Singapore and Hong Kong. In these countries, teachers come from the top 5%, 10%, 30% and 30% of the graduates respectively. As a comparison, in the USA teachers come from the bottom 33% of graduates. The figures aren’t specified for the UK, though it is considered ‘between the two extremes’.

Their conclusions are that the only way to improve the outcomes of pupils is to improve the quality of instruction. When a profession is high-status, top graduates want to do it and the quality of their instruction improves.

Having read this article yesterday, this morning on Radio 4′s Today programme I heard a lady talk about one of the changes between when she grew up and now: when she was at school she was told that (as a woman) she could become “a teacher or a nurse” whereas now she might have aspired to be a “doctor or a lawyer”. The status levels are clear, and still entrenched. Doctors and lawyers are high-status professions. A teacher is respected, but is essentially a carer in some important way. I can’t believe that in Finland or South Korea these unfortunate couplets would trip off the tongue so readily.

I am glad that McKinsey has produced this report, because ministers are liable only to listen to a big consultancy business. My heart sinks to imagine how much money has been thrown at this consultancy giant to point out the mind-blowingly obvious. What is scary to me is that ministers appear to be genuinely unable to appreciate these truths without a consultancy-led statistically-backed study, whereas surely a moment of rational reflection shows their conclusions to be self-evident.

Oct 23

Tests are Counter-Productive (shock?)

Channel 4 News has recently run a major report about how low-achievers are being left behind in the school system.

It is encouraging that the media is starting to pick up on the reality that testing and league tables helps only the government and not the students. As far as I am concerned, this is patently obvious for the majority of teachers in schools. The testing regime was a top-down initiative which never really had the students’ best interests at heart.

In the report, Mary Hilton of Cambridge University argued that in their last year of primary schools, children in England are “trained and drilled for the tests and its disastrous”. Ask any parent whether they would prefer their child to experience motivating and engaging ideas in classrooms or test revision, and they would all want the engaging ideas… that is unless they had become caught up in a system whereby they worry that their child will be disadvantaged in some way by not being drilled for the test.

This is a problem: testing regimes bootstrap themselves; by introducing a mandatory testing regime, everybody must be seen to perform at least at their level of expectation within that regime, but everyone will strive to perform better. Therefore increasingly attention will be diverted towards the regime. More and more people spend more and more time focussing on the test rather than on what the test was introducted to test.

SATS help the government because they make measurable the achievements of schools. One ought to have reason to pause at this idea. What exactly has been measured?

The improvement that any student achieves while at school is due to a combination of three factors: the speed of their natural development, the nourishment (in every sense) and education that their parents provide, and the education that the school provides. At the very best measuring students’ academic performances does not measure what the school adds to the students. The clearest example of this is that in comfortable middle class areas where, other things being equal, parents tend to have more time and more knowledge about how to educate their children, schools perform better than in deprived areas. In what sense can SATs be thought to be comparing the two schools’ performances by comparing their SATs results? Value Added measurements attempt to get around that problem, but it is not really clear that they do.

Do tests actually measure understanding? At their most sophisticated, testing measures understanding by asking questions which catch students off guard or are unusual in some way. Then the student must adapt using what they know to this new scenario. There is a good reason why at around 16-18, as learners begin to move into an abstract sphere of understanding, that the first meaningful tests that students sit occur in cultures around the world. Before then, tests are likely not to measure understanding.

Driven by the desire for all testing to be standardised and comparable, tests have increasingly become tests of memorisation. Testing 11 year olds will inevitably test learnable skills not creative understanding. Thus, SAT questions are familiar and routine. Performance in answering routine questions can be improved through drill. It is not unreasonable to argue that one of the things tests actually measure is the amount that a child has been drilled for the test.

What is worse, Channel 4 News reports that experts argue that the testing regime is actually particularly bad for lower achievers at school. Not only are they counter-productive, they are particularly counter-productive for students at the bottom of the pile. One can only hope that the clamour to overhaul this current system will grow and grow.

Oct 2

Tories tackle Schools & Social Mobility

The Tories appear to have come up with a good idea for tackling the thorny problem of encouraging social mobility through the education system. My natural inclinations are not conservative, nevertheless, their idea has merit I think, and deserves serious consideration.

Financialy, students from disadvantaged backgrounds will be worth more to schools than ones from socially more advantaged backgrounds, reports Anthea Lipsett in the Education Guardian.

The only good example of genuinely encouraging upward social mobility through the education system was the post-war Grammar School System, which enabled students from poor backgrounds who were good enough to get into grammar schools the same opportunities to succeed academically as their more socially advantaged peers. Unfortunately however, the grammar school intake tended to be largely from socially advantaged backgrounds to start with, which in turn meant that large numbers of socially disadvantaged students ended up going into the Secondary Modern system. Over time this became politically unsustainable, as the Secondary Moderns seemed to be ‘scrapheaps’ for the less advantaged children.

However, scrapping this system and introducing the Comprehensive School System has not reversed this sort of trend. Now the opportunities for the few socially disadvantaged students to go to grammar schools have disappeared, but the majority have not benefited as a result. Students tend to go to their local schools, but local schools in socially deprived areas have problems attracting the best staff, encounter more students with behavioural and learning problems, and have lower expectations.

Worse, when a school becomes successful, more affluent parents move closer to it for the sake of their children, reinforcing the divide by ensuring that the students from more advantaged backgrounds go to the already-successful schools.

The Tories’ proposal is to incentivise schools to take students from socially disadvantaged backgrounds by recognising that they, on average, need more money to help educate them and so attaching to them a higher amount of funding.

In part, the levels at which the funding is set for different groups, and how it is calculated will determine the success of the scheme. I rather expect that if implemented politicians will thoroughly under-estimate the difference in funding required to offer genuine equality of educational opportunity to every student, not least because the true level of funding required would probably be huge!

Sep 22

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Online Marking System Farce

BBC News today reports that "Online marking systems ‘faulty’". Prima facie evidence is that with the growth of online marking there has been a corresponding increase of complaints about grades from teachers.

Exams are an inexact method of assessing students’ abilities. Teachers know their students thoroughly and are able to gauge with a very good degree of accuracy how they should perform in exams. When differences between expected performance and actual performance start become too widespread, then there is a problem with the examination system.

John Bangs, head of the NUT is reported as saying "They are not able to annotate the scripts by hand, there’s a time constraint and you can’t take into account youngsters who do quite a lot of writing and don’t fill in the standard box that online marking demands. So legitimately there’s a question whether or not online marking is missing some of the achievements of youngsters." There is also reported a trend towards less well paid, less well qualified examiners.

Technology has a worrying tendency to make things more uniform than they might otherwise be. Marking an exam can be a complex business, and it seems reasonable to contend that someone whose performance is good but unusual could be at a disadvantage in the new marking regime.

Sep 20

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The Minimax Principle at KS2 & KS3

Scientific-Computing.Com’s recent blog articles "Beyond the Prisoner’s Dilemma" and "Global warming and the Prisoner’s Dilemma" are interesting examples of using the logical structures of game theory as starting points for logical thought at younger levels.

The blog conversation starts with the big environmental issue of global warming and this friendly video where the protagonist explains the application of minimax to the global warming debate. He argues, in a nutshell, that given uncertain future consequences of humanity’s impact on the planet, and given also a choice of decisions about how to act against those potential consequences, it makes the most logical sense to exclude the catastrophic choice of doing nothing to prevent global warming by acting as if global warming were a certainty.

I like how the minimax principle here facilitates students’ understanding by offering a powerful structure for considering different possibilities. Because minimax is so clearly structured and relatively easy to grasp, it is the sort of idea, like the Venn Diagram, which ought to be a constantly recurring feature of students’ education. In Mathematics, it bears close resemblance to the Carroll diagram, which is a similarly undervalued structure for understanding issues.

Sep 19

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Computer Games in Education

Firaxis Games, the makers of one of the greats of computer gaming Civilisation, discuss on their website the growing trend for computer games to be used in the educational arena. It is encouraging that educators are starting to understand the potential of technology to educate, though I suspect that the use of commercial games as educational tools is an transitional step before bespoke educational games begin to be produced with production values that begin to approach those of commercial games.

One of Firaxis’ contributors Kurt Squire proposes Civilisation as a good model for learning about World History. There is an interesting tension here. On the one hand, a game like Civilisation engages students in such a way that they build a sophisticated model of the game in order to succeed at it. That is good educationally to the extent to which the game models genuine historical processes. It is not clear that the ‘history’ that Civilisation presents is particularly convincing.

While Kurt Squire argues that Civilisation “represents world history not as a story of colonial domination or western expansion, but as an emergent process arising from overlapping, interrelated factors”, it does still give an essentially American – or at least New World – view of history. Land is virgin territory until moved into by the great civilisations; pre-colonial Afrians, native Americans, native Australian Aborigones do not have a story. Intellectual and technological progress happens linearly; the Middle ages and the loss of Roman and Greek learning cannot happen. There is no potential for a European type of historio-political scenario; states are the size of continents.

On the other hand, if one ignores the problems with the historical model, it does offer a ‘big picture view’ of history. Could such a grand model of historical processes be so readily expressed without the means of technology? Certainly the answer is yes, though it would take an extremely talented teacher, and those are notoriously thin on the ground.

The pipedream is for someone to create a game with production values on a par with Civilisation, but which takes as its starting point an historical model that aims at accuracy. This of course, is rather like desiring an historically accurate documentary that looks and sounds like a Hollywood movie, but there will surely be moves towards higher production values in educational software in the future.

Sep 15

School testing regime attacked

Today’s Independent runs this headline on page 27, heading an article by their Education Editor Richard Garner on Dr Paul Kelley’s new book Making Minds.

The Independent quotes Dr Kelly on the SATs sat by every student at 7, 11 and 14: "Testing every child has, overall, a negative on the learning outcomes and attitudes of children. Repeated practice tests reinforced the low self-image of the lower-achieving students. The feedback from teachers often hurts children’s feelings rather than helping them understand their weaknesses. Children often responded by reducing their efforts towards further learning and focussing on performance in tests."

It is encouraging to hear Dr Kelly say this, which seemed apparent to me and to many of my colleagues as soon as we started training to teach. It is important that he says it too. The more high profile criticisms of the current testing regime, the more the government will have to listen.

The current testing regime comes from an array of misguided notions about the appropriate means of assessing schools, teachers and students. It is easy to think that those who argue against the current regime are against testing per se. Not so; the criticism of the testing regime for younger students does not imply a criticism of the idea of testing at 16 and 18.

Richard Garner disputes Dr Kelly’s argument that ‘rising achievement’ can be explained by examinations having been made easier. Garner argues that the rise in perceived achievement is explained by teachers becoming ever more adept at coaching for exams. I’m inclined to think that a little of each is more or less right. I discuss a similar idea in my post Playing Politics with Education.

Dr Kelly has a host of other things to discuss in Making Minds too, from the hours that schools open to the ages at which language acquisition is most acute. It is encouraging that research into neurological science is starting to have an impact on educational thinking. I will post more on these ideas once I’ve got my copy!

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