Sir Chris Woodhead described progressive education as “a blob”. It is also like an octopus, with tentacles in local authorities, governing bodies, unions, university education departments, quangos, examining boards, left-leaning charities and many professional associations. The tentacles are formed by loose associations of generally like-minded people, and operate, like a blob, by taking up all available space, smothering their opponents and stifling dissent. “Philosophy” is often their starting point – in this context it means points of view that are not substantiated by evidence, a sort of leftist neo-platonism.
Nick Gibb met the mathematical tentacle last week in a visit to the Advisory Committee for Mathematics Education (ACME). This operates under the auspices of the Royal Society, with a FRS in the chair, but no others as members. In 2010, it argued, following a meeting at which no FRS was present, that too much emphasis on early proficiency in calculation inhibits the development of mathematical thinking:
It is widely agreed, both by those at this meeting and in the wider mathematical community, that fluency with multiplication and division using the full range of decimal numbers cannot be achieved by many until the early years of secondary school without sacrificing understanding, confidence and interest. Learning procedures without understanding them takes a lot of time and continuous practice; the details of longer algorithms are easily forgotten. Having this as a major focus too early has negative effects on students’ confidence in mathematics.
This is not scientific argument. It was once widely agreed that the sun revolved round the earth. Neither is this view held by the "wider mathematical community", if this is taken to include mathematicians as well as mathematics educators. The mathematics faculty at Stanford University in the US, for example, has famously disowned one piece of progressive mathematics published under its name.
Rebecca Hanson gave this account of Nick Gibb's encounter with ACME on Fiona Miller’s anti-government blog, the local schools network (an official note of his speech is here.)
Well we had Nick Gibb at ACME conference today. Let’s just say he clearly deeply believes in himself. Couldn’t see anyone else looking anything short of incredulous and/or gobsmacked at his ignorance but I think we could all see why people who didn’t know much about statistics and/or maths education might think him credible.
He spoke with great passion about giving teachers professional freedom.
But the devil, as ever, is in the detail. By professional freedom he means that we should be allowed to decide whether or not to put the optional zero in the long division algorith. Meanwhile me must, of course, teach huge content by rote to KS1 children in direct contradiction of all the evidence as to what will improve education. It’s like offering someone a plaster while dropping a nuclear bomb on them and spouting with conviction about how much you care about their health.
Even more disturbingly he seems to think that telling us how long he has spent discussing and deliberating on his views (clearly without managing to achieve any insight at all) is a wise thing to do.
I include this as an illustration of the kind of thinking Michael Gove and Nick Gibb have to deal with from our opponents. The last sentence is partly accurate. Nick Gibb has spent several hours in seminars organised by the civil service, at which all views were represented and discussed on a frank and confidential basis. The comments on evidence are plainly wrong. HMI's most recent maths survey states clearly that the standard methods of calculation are the most efficient, and that older pupils' achievement in maths is limited by their lack of knowledge of number facts (which includes tables).
This report is based on first-hand evidence gained by direct observation – one of the foundations of the Royal Society – and I attended a meeting at that institution a couple of months ago at which its author faced criticism for giving aid and comfort to the government, when in fact all she was doing was telling the truth. Nick Gibb also had a fresh piece of evidence showing correlation between early success in calculation and fractions, and later success in maths. Correlation, of course is not the same as cause and effect, which are difficult to pin down exactly in education, but this study, partly based on UK evidence, does provide an argument for equipping children with these skills, and I can find no evidence to the contrary.
But then a surprise. Nick Gibb's critic provided this link to a piece of wonderful teaching she had carried out with a young neighbour she found running of school in tears. Ms Hanson carefully went back to the very beginning of the child's understanding of maths and reconstructed it in ten lessons with a brilliance and clarity that reminded me of Annie Sullivan's work with Helen Keller. However, the child's "local school" was arguably the cause of the problem rather than its solution. What was the parent to do if her daughter had not had the good luck to run into Ms Hanson?
Nick Gibb actually said this:
…the draft programme aims to ensure pupils are fluent in the fundamentals. Asking children to select and use appropriate written algorithms and to become fluent in mental arithmetic, underpinned by sound mathematical concepts: whilst also aiming to develop their competency in reasoning and problem solving.
As fundamental to our day-to-day lives as the ability to read, maths allows us to navigate the world by calculating uncertainties and predicting outcomes; spotting patterns and irregularities; by making sense of the calculations of others.
It is also to mathematics that we look first to provide opportunities in study and employment. It is the skeleton-key subject: opening doors to other disciplines and jobs, from archaeology to architecture, engineering to economics, genetics to geology. I owe my own career in accountancy to an appreciation and interest in mathematics.
But we don’t see the study of maths in the narrow terms in which it is sometimes presented: a subject that we take to simply gain employment or pass an exam.
There is – as we all know – great beauty, fascination and depth to maths. The reoccurrence of patterns in nature. The symmetry of great music and art. The inter-related numbers that together govern the shape, size and texture of the universe.
Every single young person in this country should have the opportunity to appreciate and comprehend these aesthetics. To understand how one child’s obsession with mathematics and the sequences he saw in flower petals, could one day lead to the creation of a machine that would help save Western Europe from fascism. To understand how another man’s contempt for abstract mathematics and love of algebra could inspire him to write Alice’s Adventures in Wonderland, one of the world’s most imaginative children’s books.
This is the true importance, breadth and scope of mathematics – yet over the years far too few children have been inspired to make sense of these connections, to fathom the links between maths and the great artistic and scientific movements.
This is balanced, thoughtful and imaginative. It might even be termed, in the real sense of the word, progressive. Above all, it is Conservative.