This is the question asked by a *Guardian* article of 17 July.

"Hundreds of schools and colleges in England are failing to enter any pupils for science and maths A-levels, official figures show.

"The data has been published by the Department for Education (DfE) for the first time as part of a government bid to encourage young people to take science and maths past the age of 16. It reveals the percentages of students at each school and college who are taking A-levels in these areas, seen as vital by ministers, partly due to increasing demand for workers with science, technology, engineering and maths skills.

"An analysis of the figures shows that 79 institutions entered no pupils for maths A-level in 2012-13 and a further 892 entered no pupils for further maths. No student took biology at 161 schools and colleges while at 217 none took chemistry and at 306 no pupils studied physics at A-level."

I can't yet prove this, but I am suggesting that 'school improvement' is the reason for this decline and that the link is with the explosion in the attainment of A*-C grades in GCSE maths driven by the marketisation of the education system.

Students quite rightly do not generally take A Level sciences without also taking A Level maths.

I know from my own research that in specific 'highly improved' schools, C grades in maths have been obtained at the expense of higher grades, especially B. They have also been achieved at the expense of E and D grades, but that is another equally important story.

I once had a telephone conversation with the head of one such highly improved school who told me that that getting a C grade at GCSE maths was best treated as 'a rite of passage' for young people, like passing the driving test. The driving test is a classic example of a criterion referenced exam where behaviourist teaching methods based on practise, repetition, memory and multiple entries work.

These are the same methods that unbanded entry, 'improved' schools with an intake deficit of able pupils, are forced to use for maths teaching in pursuit of 5ACEM, regardless of whether or not the Wolf criteria are applied, as in Henry's last post.

I describe in more detail how these behaviourist cramming methods work here and here.

Sue Johnstone-Wilder and Clare Lee have been working in this area for some years. This paper describes their approach and concerns.

Johnston-Wilder S & Lee C (2010), Developing mathematical resilience, BERA Annual Conference 2010, 1-4 Sep 2010, University of Warwick

You can read it here.

Their work, like that of Guy Claxton is based on the ideas of 'learning resilience' and 'capacity for learning'. The former is all about the acceptance and expectation on the part of the learner that mistakes and failures are an essential, integral part of the process of 'deep learning', which as a consequence, is of a 'slow' (Kahneman System 2) nature, rather than 'fast' (Kahneman System 1).

See my post here.

Developing 'Capacity for Learning', according to Guy Claxton, should be the aim of all schooling, rather than behaviourist remembering stuff and regurgitating it in crude recall-driven exams. You can read about Claxton's ideas here.

Johnstone-Lee and Wilder, Claxton, Kahneman, the Eton College based 'slow education' movement and until the current domination in England of the education marketisation paradigm, virtually all mainstream learning theorists, are within the 'developmental' (think Piaget and Vygotsky) rather than the behaviourist (think Skinner) school.

To return to my hypothesis as to why A Level maths uptake is in decline, I am proposing that it is because the growth of mathematical understanding in school children requires very carefully designed developmental teaching programmes and skilful maths teachers with the requisite deep understanding of both their subject and how children can be helped to understand 'hard stuff'.

**This is not what the 'heroic' and much currently celebrated champions of school improvement are about. Deep learning is not facilitated by extending KS4 back into years 8/9 and early/multiple GCSE maths entries. **

The 'top twenty' schools in Henry's list are, as he points out, a mixed bunch. Not all of them are maths 'crammers'. I know that Mossbourne Academy is not, because I have past year's full subject-by-subject, grade-by-grade GCSE results. Without these it is impossible to tell how a school gets its 5ACEM. Mossbourne can achieve outstanding results without cramming because of the Hackney banded admissions system.

**However, OfSTED should be making the critical judgements and should not be handing out 'outstanding' status to schools that put headline results before deep learning. The Trojan Horse issue shows that OfSTED can be 'blind' to issues it is not looking for.**

**OfSTED needs to be looking hard at the schools that fail to develop pupil's cognition sufficiently to enable and encourage take up of A level maths and sciences.**

"Hundreds of schools and colleges in England are failing to enter any pupils for science and maths A-levels, official figures show.

"The data has been published by the Department for Education (DfE) for the first time as part of a government bid to encourage young people to take science and maths past the age of 16. It reveals the percentages of students at each school and college who are taking A-levels in these areas, seen as vital by ministers, partly due to increasing demand for workers with science, technology, engineering and maths skills.

"An analysis of the figures shows that 79 institutions entered no pupils for maths A-level in 2012-13 and a further 892 entered no pupils for further maths. No student took biology at 161 schools and colleges while at 217 none took chemistry and at 306 no pupils studied physics at A-level."

I can't yet prove this, but I am suggesting that 'school improvement' is the reason for this decline and that the link is with the explosion in the attainment of A*-C grades in GCSE maths driven by the marketisation of the education system.

Students quite rightly do not generally take A Level sciences without also taking A Level maths.

I know from my own research that in specific 'highly improved' schools, C grades in maths have been obtained at the expense of higher grades, especially B. They have also been achieved at the expense of E and D grades, but that is another equally important story.

I once had a telephone conversation with the head of one such highly improved school who told me that that getting a C grade at GCSE maths was best treated as 'a rite of passage' for young people, like passing the driving test. The driving test is a classic example of a criterion referenced exam where behaviourist teaching methods based on practise, repetition, memory and multiple entries work.

These are the same methods that unbanded entry, 'improved' schools with an intake deficit of able pupils, are forced to use for maths teaching in pursuit of 5ACEM, regardless of whether or not the Wolf criteria are applied, as in Henry's last post.

I describe in more detail how these behaviourist cramming methods work here and here.

Sue Johnstone-Wilder and Clare Lee have been working in this area for some years. This paper describes their approach and concerns.

Johnston-Wilder S & Lee C (2010), Developing mathematical resilience, BERA Annual Conference 2010, 1-4 Sep 2010, University of Warwick

You can read it here.

Their work, like that of Guy Claxton is based on the ideas of 'learning resilience' and 'capacity for learning'. The former is all about the acceptance and expectation on the part of the learner that mistakes and failures are an essential, integral part of the process of 'deep learning', which as a consequence, is of a 'slow' (Kahneman System 2) nature, rather than 'fast' (Kahneman System 1).

See my post here.

Developing 'Capacity for Learning', according to Guy Claxton, should be the aim of all schooling, rather than behaviourist remembering stuff and regurgitating it in crude recall-driven exams. You can read about Claxton's ideas here.

Johnstone-Lee and Wilder, Claxton, Kahneman, the Eton College based 'slow education' movement and until the current domination in England of the education marketisation paradigm, virtually all mainstream learning theorists, are within the 'developmental' (think Piaget and Vygotsky) rather than the behaviourist (think Skinner) school.

To return to my hypothesis as to why A Level maths uptake is in decline, I am proposing that it is because the growth of mathematical understanding in school children requires very carefully designed developmental teaching programmes and skilful maths teachers with the requisite deep understanding of both their subject and how children can be helped to understand 'hard stuff'.

The 'top twenty' schools in Henry's list are, as he points out, a mixed bunch. Not all of them are maths 'crammers'. I know that Mossbourne Academy is not, because I have past year's full subject-by-subject, grade-by-grade GCSE results. Without these it is impossible to tell how a school gets its 5ACEM. Mossbourne can achieve outstanding results without cramming because of the Hackney banded admissions system.

## Comments

At first he was getting "U" and was told that, if he got another U he would be off the course. The next test was graded U but when I looked at the marking no marks had been given for follow through, so a careless error in the first line would get him 0, even if all the method was correct. He took this back to the school and was allowed to stay.

There have been several issues. The most problematic has been that, although quick and bright, he has been taught to the tests and by rote - given a rule and told to apply it with, apparently, little explanation. Another problem has been that topics in A level have not been linked to earlier work. For example, the introduction to division of algebraic expressions was not introduced with a revision of division of number.

It would be easy to criticise the teaching but the impression I get is that the school, a converter academy, is desperate to be able to claim a 100% pass rate and, therefore, is trying to force anyone who may fail off the course.

Fortunately, my neighbour's grandson has made so much progress that he should be fairly safe. I am not tutoring him in any normal sense. I cough when he makes silly mistakes, sometimes ask him to explain what he is doing and sometimes make him do preceding work before tackling the work he has been set.

It is sad that other students at that school who don't know a retired Maths teacher are either paying for private tuition or have been thrown off the course, without being given a chance to make progress. What a loss to the country and so much for equality of opportunity - his mother could not afford private tuition fees.

Maths is hard work for him but if he is 'in practice' he does well. He's moved around between Set 1 and Set 4 and the Set, for maths only, which suited him best was the Set which involved lots of reinforcement and practice. He may get to ‘deep learning’ in Maths, but I’m not too fussed if he doesn't. A recognition of the problems and a toolkit of ways to solve them may be as far as he gets. The school has provided that, and in that case I do not believe it has been at the expense of B (or higher) grade passes (last year 30% A/A* Maths GCSE).

For him, science is a completely different proposition. He loves it, and will read about scientific developments and watch (TV) and listen to (radio) science programmes and also watch a ton of sci-fi programmes. His capacity for learning, and deep learning, in that area is self-driven, and generally supported by the school (and at home).

In terms of developing capacity for learning, the school (which I think does a really good job overall) is hindered/constrained by the need to 'perform' at GCSE results.

My son is not a cert for a STEM set of A level subjects. But he would be if A levels included around 6 subjects, with 3 at a basic (for 6th form) level and 3 at a higher level (like the International Baccalaureate).

Developing/supporting deep learning for every student, across a range of subject areas, is simply not possible in a publicly funded school while they remain judged by the exam/target driven system. That still falls to a few teachers who go above and beyond, and sometimes to family and friends. That’s a crying shame.

To be honest Roger, I think I’ve just repeated the gist what you posted, albeit in a different way.

I do think maths ability/results and scientific curiosity and rigour are sometimes not as closely aligned as the promoters of the STEM acronym would have us believe though. Perhaps that's a different subject.

The problem for your son with his 'get by' in maths approach of 'recognising the sort of problem' then 'applying the right toolkit' that he has leaned by rote and practise is that he will increasingly find even in school maths lessons that it is difficult to correctly recognise the category of problem he is dealing with.

I am not arguing like Carol Vordeman that all people can be taught to understand maths at a high level if they are taught 'properly'. The Bell Curve' distribution of human variation surely applies. If your son has indeed been failed by his maths teaching, and I am not saying he has, then I think the problem lies in the area described by Johnstone-Wilder and Lee (apologies to all for mangling their surnames in my post) in their paper that I have linked to. It is more a question of 'resilience' rather than 'explanation'. I am sure we can all recall the sorts of maths textbooks which provide banks of 'practise' questions of the same sort. I remember huge blocks of quadratic equations to factorise. The star pupils could produce neat solutions in two columns (page folded) of their exercise books, all completely free of error and alterations acknowledged by neat ticks all in a tidy column, followed by an 'excellent work' comment by the teacher on each page and heaps of praise by the parent.

This follows from exactly the same approach in primary school.

What Johnstone-Lee and Claxton are advocating (I think - I hope to be corrected if I have got this wrong) is that children's maths lessons should involve far more time struggling with problems that they can't do rather than those they can. The learning context would be groups of 5 - 6 pupils discussing with each other how to tackle the problem, with the teacher providing prompts and suggestions. Dead ends and mistakes should draw as much praise from the teacher as correct answers. Johnstone-Wilder and Lee's idea of getting children to produce video's and powerpoint presentations for each other is also worth experimenting with.

I anticipate the reaction from maths teachers of, 'we haven't got time for all that, there is a syllabus to cover'.

Therein lies the crux of the problem. We need a lot more 'slow' learning and a lot less high stakes 'pressure'.

I know this is all very simplistic. I also admit to being a science teacher not a maths teacher. I think Shayer and Adey's Cognitive Acceleration through Maths Education (CAME) may also have a lot to offer.

Maybe if your son had experienced a lot more of this, which is much more like the science he loves, he might now be in a better place with his maths.

There is also the issue of biological clock cognitive development. I am July born and therefore was always one of the youngest in the class. I am sure this made a difference to me. There are lots of things in maths and science I could do with ease when I was older that I could not do when younger. Being in a school that recognises developmentalism would of course help.

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