Note: This is an updated version of a post that first appeared on 7 September 2015. It includes data published by Exeter Mathematics School in response to the original version, as well as answers to some follow-up questions I posed on Twitter.
My attention was drawn to a recent Spectator article by Alison Wolf ‘What I’ve learned helping to found a specialist free school’
Wolf led the project to establish the King’s College London Mathematics School and is now a governor of the academy trust that runs it.
KCLMS is one of only two university-sponsored 16-19 maths free schools in existence, the other being Exeter Mathematics School. Both opened for business in September 2014.
The previous Government planned to establish 12 of them but there was little interest from the HE sector and, despite rumours of at least one more school in the pipeline, none has yet materialised.
Both schools are highly selective. Minimum grade requirements were in place for this first cohort:
- At KCLMS candidates needed an A*/A grade in GCSE/IGCSE maths, an A*/A grade in GCSE/IGCSE physics or double award science and five more qualifications at grade C or above, ‘normally including English’.
- At Exeter they needed an A* grade in GCSE maths, an A*/A grade in GCSE physics or double award science and six [further?] GCSEs at grade C or above, ‘normally to include English at a grade B’.
At Exeter only learners predicted to meet these minimum criteria were invited to take a mathematical aptitude test which, for this first year at least, seems to have been identical for both institutions. (The School has subsequently confirmed that six of its 2014 intake – 18% – undershot their predicted GCSE grades in maths or physics, in all cases by one grade.)
They were also assessed on the basis of a written application, references from a tutor and an interview:
‘…to further explore mathematical and problem solving ability and to ensure that the learner has realistic expectations in terms of workload and commitment expected and passion for the topic’
Only learners who ‘scored highly on the aptitude test’ were invited for interview. If oversubscribed with candidates meeting the test threshold, priority was given to ‘interview answers and the candidates’ potential to thrive and succeed on the course’.
For September 2014 entry Exeter had a PAN of 30 and admitted 34 students.
Those at KCLMS followed a similar selection process. The current Admissions Policy (the 2014 version is no longer available online) says all applicants take the aptitude test prior to their GCSEs but only those ‘with a high score’ (unspecified) in the test:
‘…will be invited to interview to assess further a candidate’s ability to benefit from the experience of attending a specialist mathematics school’
Participants receive two interview scores, one for mathematical understanding and one:
‘…to assess to what extent the school is likely to add value in terms of making a difference to their future careers’
Offers are made on the basis of the test score and the two interview scores, all three of which must be above the (unspecified) thresholds, which can vary from year to year. Offers are conditional on achieving the minimum grades and conditional offers may be set higher than these minima.
If the School is oversubscribed places are awarded to those with the highest ‘weighted average’ scores. (Four scores are mentioned, but the fourth is not explained. Nor is the weighting.)
In AY2014/15 KCLMS admitted 69 students against a PAN of 60.
Neither School gives explicit priority to learners from disadvantaged backgrounds. KCLMS’s current Admissions Policy says simply:
‘All places…are offered on the basis of academic ability and aptitude’.
Exeter’s 2014 Admissions Policy offers a tangential policy with no specifics attached:
‘EMS is committed to widening participation and broadening access to high quality mathematics education. As such, we will target our recruitment in areas which have high levels of deprivation and in schools for which provision is currently limited, such as those without 6th forms’
September 2015 AS level results
At KCLMS all students take A levels in maths, further maths, physics and AS computing in Year 12 (economics is introduced from 2015 as an alternative to computing). They also complete an EPQ in Year 13.
At Exeter all students take A levels in maths, further maths, physics (or computing from 2015) and one further AS level (from a choice of 30) which they can also pursue at A2. In 2015, Year 12 students sat 6 maths modules – C1, C2, M1, M2, S1, S2 – so completing AS Mathematics but not AS Further Mathematics.
KCLMS supplies a results page and a press release which provide the following facts (my commentary is in square brackets):
- Over 97% of students achieved an A grade in maths [so 67, all but two of the cohort]
- 90% of grades in maths and further maths combined were As [so there were 124 A grades, meaning that 57 students – some 83% – achieved a grade A in further maths]
- 80% of all grades across all four subjects were B or better [so 55 awards were at Grade C and below]
- 72% of students achieved AAB or better [so 50 students, meaning that 19 (28%) were at ABB or lower. This presumably takes no account of the results in computing.]
- ‘Comparing GCSE grades to AS grades, students have on average attained 1.8 grades higher across their subjects than predicted by national data’ [The source and basis of these predictions are not specified. It is not clear whether these are personal predictions or derived from general assumptions about progression from given GCSE grades. The statement appears to mean 1.8 grades across 4 subjects, so an average of 0.45 grades higher per subject.]
Exeter was initially far less open about its results. There was a brief statement on the School’s website and another on its Facebook page. But the press release issued in response to this post provides more detail. I also obtained some further clarification via Twitter.
Initially we knew that:
- All 34 students passed all three AS levels.
- According to the website 97% [so all but one] met or exceeded their predicted grades in maths and physics.
- According to the Facebook page, 100% met or exceeded their target in maths and 94% [all but two] did so in physics.
Now we also know that:
- 91% of the intake (all but three students) achieved an A or B grade in AS mathematics. (The scatter graph shows there were 5Bs, 2Cs and one D, suggesting that 76% achieved grade A.)
- 80% achieved an A or B grade in physics. (The scatter graph suggests that 22 students – 65% – were awarded grade A, six grade B, two grade C, three grade D and one grade E.)
- 51% achieved an A or B grade in the additional subject taken at Exeter College (Unless some students opted out of a fourth AS level this must mean 17 of the 34 students, which is of course 50%).
- On the basis of the modules taken to date, the School expects 80% of the intake to achieve grades A or B in further mathematics at AS level.
- 38% (so 13 of the 34) achieved AAB+ at AS level in maths, physics and their additional subject. However, the School predicts that 76% will eventually achieve AAB+ in AS maths, further maths and physics.
- According to ALIS ‘On average, EMS students achieved a grade higher in both Mathematics and Physics than expected based on their GCSE performance’ (though this rounded statistical estimate may be somewhat misleading, as it has to be reconciled with the fact that at least 82% of the intake had A* in GCSE maths).
How good are these results?
In her piece on KCLMS Wolf throws no further light on the ‘higher than predicted’ grades. Indeed she unaccountably rounds ‘1.8 grades higher… than predicted’ up to two full grades.
She confirms that 43% of the students are girls:
‘And there are no significant differences in the results achieved by different groups – not by gender, not by ethnicity, and not by whether students are eligible for Free School Meals…’
The press release says ‘over 30% of the second intake is female, so there has been a significant decline on that indicator.
Wolf does not tell us what proportion of the initial intake is disadvantaged, whether on the basis of FSM eligibility or any other measure. Without knowing the size of the FSM-eligible cohort we cannot judge the School’s success in closing excellence gaps.
We do know from a former governor that only 85% of this intake – so 59 of the 69 – were from maintained schools, indicating that students drawn from independent schools were somewhat over-represented.
Given the minimum entry requirements it is hard to make sense of Wolf’s references to Calvin, predicted DD for maths and further maths, Kamil predicted CCDD and Glen ‘with a C grade average’.
Did the School waive these requirements for some students and, if so, how was this permissible within the 2014 admissions policy?
‘We select for potential, using our own test. But we also select by the education, and especially the quality of the A-level maths, that applicants could expect at their current school. Will coming to us ‘add value’? If not, someone else should have the place.’
The emboldened statement is not explicit in the Admissions Policy and it is surely misleading to judge ‘added value’ on this basis if the student intended to leave in any case? In this eventuality the value-added’ comparison should be with the next best school or college the student could have attended.
How much value does KCLMS add compared with, say, non-specialist institutions such as the London Academy of Excellence or Harris Westminster Sixth Form?
It is clearly possible for several students attending independent schools to satisfy the ‘adding value’ judgement, so it cannot be set particularly high.
Incidentally, the School’s Academic Exclusions Policy says:
‘Student [sic] who are not on track to attain any A*-B grades in their A2 examinations, as demonstrated by their attainment throughout their first year at the school and by their AS grades, are not suitable for the specialist environment of KCLMS and will be required to leave the school permanently.’
We do not know how many students, if any, will not be allowed to progress into Year 13.
The new data published by Exeter means that it is now more transparent than KCLMS and deserves to be commended strongly for that. In terms of performance it is not too far behind, although it seems that Exeter has a higher percentage of outlier students than its London competitor. It would be interesting to understand why this is so, given that the admissions policies were so similar.
One clue might lie in a comparison with neighbouring Exeter College (co-sponsor of the Maths School alongside the University) where, according to their Facebook page:
‘Half of our 132 students taking Maths A level get A or A* grades’.
The Principal comments:
‘We are delighted with the results across the college but the Maths and Science results particularly endorses our decision to invest in this crucial curriculum area with the development of an A level Maths and Science Centre in the heart of the city due to open this year, complementing our existing partnership with the University of Exeter on the Exeter Mathematics School which opened last year.’
Is this really a partnership or is it open competition? Will the best candidates continue to prefer the College over the Free School? What is the USP of the latter?
Overall and given the intensive selection practised by both schools, these results are broadly in line with what they should be.
Remember that, for England as a whole in 2015, the provisional percentages of all candidates achieving grade A at AS level were 35.6% for maths, 52.6% for further maths and 21% for physics.
Wolf claims that KCLMS ‘exists to nourish untapped mathematical potential’ but this appears exaggerated and rather at odds with aspects of the admissions criteria. Exeter might have slightly stronger grounds for making such a claim, but both schools could do more to prioritise the admission of talented but disadvantaged students.
I see no reason to depart from my overall assessment of a year ago: KCLMS Good; Exeter RI.
Wolf’s claims for specialist provision
On the basis of her analysis, Wolf concludes that:
‘…specialist schools work, not just because students find their tribe and learn but because teachers do the same’.
Yet she makes no effort to disentangle the impact of selection from that of specialism and her assertion raises many unanswered questions.
- Since the majority of educators appear convinced that the A level curriculum is too narrow and too specialised, what counter-evidence is there to suggest that this model is worthy of further replication?
- Might it not be likely that these students would have performed equally well – or even better – had they attended a non-specialist institution such as the two mentioned above? Would there not be additional developmental advantages to engaging with a wider cohort?
- Might the same not be true of their teachers? Is it necessarily true that subject experts thrive best in small specialist institutions? Isn’t there a premium to be gained from inter-disciplinary interaction, or else why do we persist with multi-faculty universities?
- If we accept in principle that it is in the best interests of some high-attaining students to specialise this narrowly, how do we reliably distinguish which are most likely to benefit?
- Where do we draw the line? Would the Government accept proposals from universities to establish 16-19 free schools that feature A level combinations such as English language, English literature and drama; or French, German and Spanish; or Latin, Greek and Classical Civilization? If not, why is STEM a special case?
- It would be feasible for the Government to set aside a fraction of the revenue and capital budget required for 500 new free schools for such a purpose. But would a cadre of small-scale specialist post-16 institutions give value for money during a time of austerity, either as a model of post-16 education for high attainers, or as a vehicle to promote social mobility and fair access to higher education?
- Where should such institutions be established, given that relatively few students would benefit directly and the impact on others through outreach would remain localised and limited? Should they be located in areas where high A level attainment is most depressed?
Small specialist sixth forms might play a useful national role, but only if they form part of an integrated network operating across all key stages, with responsibilities delineated and each element mutually supportive. Even in maths we are still a long way from achieving that ambition.
And even then there is deadweight. The optimal solution has to be to target long-term intervention and support directly at all students who meet specified criteria for attainment and socio-economic disadvantage, regardless of the school or college they attend and their geographical location.
We should get the very best from existing schools and colleges, with co-ordinated support from all our universities, supplementing where necessary to ensure a genuine national entitlement.
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