## Why we lag behind East Asia in maths

The Institute of Education report comparing attainment in maths in England with East Asian countries recommends, among other things, that for us to catch up requires:

" a shift of school and pupil incentives away from reaching floor targets (e.g. a C grade in GCSE mathematics)".

How can this make sense? To explore this apparent paradox let us look at the example of Mossbourne Academy, a school with superb results at GCSE and AS/A2 in maths.

According to the current prospectus, in 2012, 88 percent of Y11 obtained at least a C grade in GCSE maths, and 38 percent at least an A grade.

Mossbourne admits pupils in Y7 on the basis of banding administered by the LA through the The Learning Trust. The Mossbourne Admissions policy is designed to fill four ability bands based on Cognitive Ability Tests (CATs), which all Hackney pupils take in Y6. Each band contains 25 percent of the national ability distribution. Assuming the 2012 Y11 had an ability distribution corresponding to the Mossbourne Admissions Policy to achieve this pattern the CAT score boundaries would be as follows.

Band A 110+

Band B 100-109

Band C 90-99

Band D below 90

This provides a mean intake CAT score of 100, the national average.

We can therefore estimate the CAT scores that correspond with Mossbourne's GCSE results in maths.This is possible because of the very strong correlation between CATs and GCSE especially in maths. If 88 percent obtained at least a C then just 12 percent didn't. The CAT score for the 12th percentile is 82. So about half of the Mossbourne Band D pupils are likely to have obtained a C grade GCSE in maths. Using the same estimation argument, the A grade CAT score threshold is 105 (the 62nd percentile), so about half of Band B are likely to have obtained at least an A grade, as well as all of Band A.

So what is the significance of the Grade C for A Level maths at Mossbourne? The answer is none at all. According to the prospectus, the normal minimum requirement for admission to the AS maths course in Y12 is an A grade at GCSE, and in a Mossbourne year group of 200, 76 pupils would have been likely to have met this requirement in 2012.

So GCSE Grade C at Mossbourne is not a high stakes target for pupils wanting to progress to A level courses. However it certainly is for league tables and OFSTED. Without at least 88 percent at Grade C+ in English and maths then the league table figure could not be above 88 percent. However, is this likely to have distorted teaching and learning at Mossbourne? Certainly not, there are enough pupils in each ability band for the school to provide well-matched teaching for every pupil including the most able,withour risking a low C+ pass rate. There is also a strong 'gifted and talented' scheme. So whatever the failings of maths teaching in England compared to East Asia they are certainly not down to Mossbourne.

But Mossbourne is not a typical urban comprehensive school. The vast majority of such schools cannot achieve a mean intake ability profile that matches the national average of 100. In fact a more typical urban comprehensive might be working with a mean intake CAT score of 90 (the 25th percentile). Even if such a school could match Mossbourne's quality of teaching then only the pupils with a score above 82 (the 12th percentile) would be likely to get a C grade at GCSE. Given the extra pastoral demands on such a school then it would be holding its breath every August in case its maths GCSE C+ figure fell below 40 percent, which could happen just by chance. The consequences of this would be high stakes indeed: the head asked to resign, an 'in need of improvement' judgement from OfSTED and a 'failure' label in the local press, followed by severe recruitment problems the following year leading to an even more depressed intake ability profile. Note that this disaster could befall a school whose standard of teaching was as high as Mossbourne's.

I have known many, many comprehensive schools whose mean intake CAT score is less than 90. Most of Gove's 'bottom 200' are likely to be in this category. Even if they wished to preserve teaching matched to pupil abilities, such schools cannot take the risk of falling below the floor target so they must prioritise the C grade for ALL of their pupils by teaching for this outcome even if this sacrifices higher grades.

This then is why the Institute of Education report citing the C grade floor target as a likely reason for underperformance of English pupils is correct. Note the counter-intuitive nature of this conclusion. Putting high stakes pressure on schools to get C grades LOWERS standards.

Providing differentiated teaching does not necessarily require rigid setting or streaming especially where very able pupils are thin on the ground. There is a lot that can be achieved through flexible groupings and additional small group tuition as well as approaches that are effective with a wider ability range. There are many expert maths teachers that happily make such methods effective.

So what is Michael Gove's response to this argument? It is to state that the current C grade threshold set at the 12 percentile in effective schools like Mossbourne is too low. In this he is certainly correct, if only because of not leaving much space for grades D - G. But what would be the consequence of raising it, say to the current Mossbourne A grade entry threshold of the 62nd percentile. Would this raise standards? The answer must be a resounding 'NO'. All it would do is distort teaching and resource allocation in the other direction. With the 12th percentile no longer a high stakes target why waste effort on such pupils? Given that PISA and other international tests, not to mention the education systems in East Asia, have no such high stakes distortions, the English system would remain as far adrift as ever, with the added disadvantage of growing numbers of innumerate pupils at age 16.

If Michael Gove wants to raise standards in English schools then making the exams harder is not the answer. He needs to abolish high stakes testing and the league tables they generate. Only then could we move towards the best practice of our East Asian competitors.

" a shift of school and pupil incentives away from reaching floor targets (e.g. a C grade in GCSE mathematics)".

How can this make sense? To explore this apparent paradox let us look at the example of Mossbourne Academy, a school with superb results at GCSE and AS/A2 in maths.

According to the current prospectus, in 2012, 88 percent of Y11 obtained at least a C grade in GCSE maths, and 38 percent at least an A grade.

Mossbourne admits pupils in Y7 on the basis of banding administered by the LA through the The Learning Trust. The Mossbourne Admissions policy is designed to fill four ability bands based on Cognitive Ability Tests (CATs), which all Hackney pupils take in Y6. Each band contains 25 percent of the national ability distribution. Assuming the 2012 Y11 had an ability distribution corresponding to the Mossbourne Admissions Policy to achieve this pattern the CAT score boundaries would be as follows.

Band A 110+

Band B 100-109

Band C 90-99

Band D below 90

This provides a mean intake CAT score of 100, the national average.

We can therefore estimate the CAT scores that correspond with Mossbourne's GCSE results in maths.This is possible because of the very strong correlation between CATs and GCSE especially in maths. If 88 percent obtained at least a C then just 12 percent didn't. The CAT score for the 12th percentile is 82. So about half of the Mossbourne Band D pupils are likely to have obtained a C grade GCSE in maths. Using the same estimation argument, the A grade CAT score threshold is 105 (the 62nd percentile), so about half of Band B are likely to have obtained at least an A grade, as well as all of Band A.

So what is the significance of the Grade C for A Level maths at Mossbourne? The answer is none at all. According to the prospectus, the normal minimum requirement for admission to the AS maths course in Y12 is an A grade at GCSE, and in a Mossbourne year group of 200, 76 pupils would have been likely to have met this requirement in 2012.

So GCSE Grade C at Mossbourne is not a high stakes target for pupils wanting to progress to A level courses. However it certainly is for league tables and OFSTED. Without at least 88 percent at Grade C+ in English and maths then the league table figure could not be above 88 percent. However, is this likely to have distorted teaching and learning at Mossbourne? Certainly not, there are enough pupils in each ability band for the school to provide well-matched teaching for every pupil including the most able,withour risking a low C+ pass rate. There is also a strong 'gifted and talented' scheme. So whatever the failings of maths teaching in England compared to East Asia they are certainly not down to Mossbourne.

But Mossbourne is not a typical urban comprehensive school. The vast majority of such schools cannot achieve a mean intake ability profile that matches the national average of 100. In fact a more typical urban comprehensive might be working with a mean intake CAT score of 90 (the 25th percentile). Even if such a school could match Mossbourne's quality of teaching then only the pupils with a score above 82 (the 12th percentile) would be likely to get a C grade at GCSE. Given the extra pastoral demands on such a school then it would be holding its breath every August in case its maths GCSE C+ figure fell below 40 percent, which could happen just by chance. The consequences of this would be high stakes indeed: the head asked to resign, an 'in need of improvement' judgement from OfSTED and a 'failure' label in the local press, followed by severe recruitment problems the following year leading to an even more depressed intake ability profile. Note that this disaster could befall a school whose standard of teaching was as high as Mossbourne's.

I have known many, many comprehensive schools whose mean intake CAT score is less than 90. Most of Gove's 'bottom 200' are likely to be in this category. Even if they wished to preserve teaching matched to pupil abilities, such schools cannot take the risk of falling below the floor target so they must prioritise the C grade for ALL of their pupils by teaching for this outcome even if this sacrifices higher grades.

This then is why the Institute of Education report citing the C grade floor target as a likely reason for underperformance of English pupils is correct. Note the counter-intuitive nature of this conclusion. Putting high stakes pressure on schools to get C grades LOWERS standards.

Providing differentiated teaching does not necessarily require rigid setting or streaming especially where very able pupils are thin on the ground. There is a lot that can be achieved through flexible groupings and additional small group tuition as well as approaches that are effective with a wider ability range. There are many expert maths teachers that happily make such methods effective.

So what is Michael Gove's response to this argument? It is to state that the current C grade threshold set at the 12 percentile in effective schools like Mossbourne is too low. In this he is certainly correct, if only because of not leaving much space for grades D - G. But what would be the consequence of raising it, say to the current Mossbourne A grade entry threshold of the 62nd percentile. Would this raise standards? The answer must be a resounding 'NO'. All it would do is distort teaching and resource allocation in the other direction. With the 12th percentile no longer a high stakes target why waste effort on such pupils? Given that PISA and other international tests, not to mention the education systems in East Asia, have no such high stakes distortions, the English system would remain as far adrift as ever, with the added disadvantage of growing numbers of innumerate pupils at age 16.

If Michael Gove wants to raise standards in English schools then making the exams harder is not the answer. He needs to abolish high stakes testing and the league tables they generate. Only then could we move towards the best practice of our East Asian competitors.

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