The crisis in education gets deeper by the month. The government keeps urging teachers to try harder, but sensible people know that putting heavy pressure on children is a certain way to drive out genuine education. We have the classic symptoms of a paradigm (education as learning) in crisis.
Education means leading the child from the parochial values, enthusiasms and emphases of the home and local area towards the grand enduring 'values, enthusiasms and emphases' of the mature society. This isn't "learning" so much as "joining" and "becoming proud" of the latter.
We have had more than two millennia of our classic mathematical culture, but during the 20th century it nose-dived into a morass of confusion and contradiction. The result was that mental paralysis gripped the foundations of maths for the first half of the 20th century. Then the opportunity for reform arose (the Curriculum Reform movement around 1960) and the maths hierarchy unconsciously put too much emphasis on formalism, hyper-abstraction, rigour and knowing-your-stuff. That meant that the approach in schools could only be "learning". There was no hope of "joining" or "becoming proud of" it.
Then came the catastrophe of 1972 when the maths hierarchy's credibility caved in. They had backed 'Modern Maths' to the hilt and Rene Thom told the ICME at Exeter in August 1972 that is was all based on a fallacy, trying to get children to run mathematically before they could walk.
The result, after a delay, was Practical Maths for Schools, which tries to maintain the notion that you do maths to achieve practical results in the real world. That, too, for different reasons, can't be a suitable target for education. It is supposed to 'empower' the pupil, but of course the kind of power it flaunts is banal and boring. It can't be a 'culture' anyway, if it is chiefly about empowering the individual. It is just nuts and bolts learning which is even less educational than the 'modern maths' which preceded it.
Because maths is recognised as the most difficult subject in the curriculum, it claims the high ground and it tends to set the pattern for other subjects. (Once maths had its 'modern maths' revolution in the early 1960s all the other subjects tried to follow suit!)
So 'learning' has become ---improbably in an age in which people have less need to "learn" facts than ever before--- the official aim of education.
My thesis is that we can only solve the general crisis in education by returning to an educational form of maths.
We need a new, exciting view of maths which is capable of being a target for genuine education.
There is such a view, the extended Peircean view, of maths as the investigation of promising practical and theoretical hypotheses. (Some of the theoretical hypotheses are inside maths itself.) It has been around for about thirty years and was worked out in some detail in the Mathematics Applicable project of the 1970s. It implies that we teach maths as a meld of imagination and mathematics, because you only get the best results when both are working together.
Both the pure and applied sides of the maths hierarchy jumped on it and virtually stamped it out. Its publications were rubbished mercilessly. They (the two hierarchies) were not having any fundamental rethink about what "maths" centrally was.
The extended Peircean view of maths is what we need in schools, but our chances of getting it into operation by planning or design are negligible, because now the government has thrown its full weight behind the misguided hierarchies.
Nevertheless, education is in the father and mother of all crises, and in this kind of situation who knows what may happen?
You can learn more about this by emailing chrisormell@compuserve.com or write to Ingleside-Ashby P.O. Box 16916, London SE3 7WS for details about extended Peircean publications. A personal monthly ejournal is http://ourworld.compuserve.com/homepages/chrisormell