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The Roeper Review is the second Taylor and Francis publication in our selection. Articles are thought provoking and often interdisciplinary. The Roeper Review aims to enhance the development of gifted individuals and the improvement of the world through more attention to giftedness, talent development, and creativity guided by ethical awareness. The Managing Editor is Ann Ambrose, who is presumably related. Authors…are required to sign an agreement for the transfer of copyright to the publisher. All accepted manuscripts, artwork, and photographs become the property of the publisher.

This Journal also appears on a quarterly basis. The online repository stretches back to The Journal is currently published twice annually. All published articles are assessed by a blind refereeing process and reviewed by at least two independent referees.

Users have the right to read, download, copy, distribute, print, search, or link to the full texts of articles. This is the only reference to an expectation that the material to be published is original, so TDE is noticeably less insistent on this point than its peers. Ad hoc reviewers include Heller, Rindermann and Urban. However, this is open enough not to inhibit authors from making parallel use of their own work, since the license granted may presumably be of the Creative Commons variety.

Some further clarification would be helpful. As noted above, there is some lack of clarity about the rights enjoyed by authors published in the two independent journals in our sample and — even in the journals published by Sage and Taylor and Francis — it is not always entirely clear that the standard provisions apply in all respects. But what are those standard provisions?

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The two publishers set out broadly similar arrangements, but they are not identical. In both cases they seem unnecessarily complex and are difficult to interpret. I stop short of suggesting that this complexity is deliberate; nevertheless, it is highly likely that it hinders the full exploitation by authors of the flexibilities granted to them. Exceptions may exist where assignment of copyright is required or preferred by a proprietor other than SAGE. In this case copyright in the work will be assigned from the author to the society.

This may be the source of the statement I drew attention to in respect of GTC, above, but — as we shall see — there are several exemptions to this apparently blanket statement. Sage advises that authors check for any journal-specific policies though, as we have seen above, these are not always clear and explicit. In the absence of such arrangements, one must assume that the standard provisions apply. These are summarised in the general statement of policy, but the detailed version is squirrelled away in a Word document available from the penultimate hyperlink on this page.

In all these cases, Sage requires a hyperlink to the online journal where the article was first published and a standard acknowledgement. Any other requests must be forwarded for consideration by Sage. The distinction between a repository and a database is fine indeed and may simply be a matter of terminology. Greater clarity on this matter would be highly desirable.

It does seem though that the author has to place the article rather than a third party.

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These provisions are chock-full of subtle distinctions, clearly subject to legal interpretation and not at all straightforward for any intelligent layperson to understand. But it is clear that all authors of articles that appear in the seven journals published by Sage and Taylor and Francis are free to post the pre-peer review version elsewhere, in a place where it can be openly accessible, entirely free of charge.

Moreover, they can also post the peer reviewed version on the same terms following an embargo period that is, at most, 18 months from the date of publication. These rights exist now and, it would seem, entirely independent of any progress towards open access publishing of the green and gold varieties. Unfortunately, though, it seems that they are honoured more in the breach than the observance.

Open access arrangements are even more obtuse and convoluted and there is space only for a brief summary which may be misleading in some respects. These provisions can be applied retrospectively to any author who has signed a copyright agreement. Moreover, from 1 April , Taylor and Francis are offering a range of Creative Commons licenses for articles published on an open access basis:.

Reuse conditions will be subject to the license type chosen by the author. Are these two options really identical? If they are, then, what advantage exactly is being secured by virtue of a Green Open Access arrangement? Those authors who do not wish to use this service will be under no pressure to do so, and their article will be published free of charge, in the usual manner.

All existing policies on author posting of the final version will then apply. So, pending the eagerly awaited open access revolution, what steps might the global gifted education community take now to radically improve access to the stock of gifted education research, before the grass grows any longer under our feet? I cannot pretend to have conducted an exhaustive exercise, but preliminary efforts suggest that very little of the gifted education research which appears in these nine journals — or any other gifted education research for that matter — is currently also stored in repositories that are accessible to potential readers outside the institutions that house them.

Yet, as we have seen, even before the introduction of more widespread open access, there is already provision for all articles published by Sage and Taylor and Francis to be made accessible in such fashion. Assuming that other journals have adopted broadly the same terms — and those without clear terms do not stand in the way — we already have the makings of a system-wide solution. The most obvious solution would be to set up a dedicated gifted education repository to collect all gifted education research or to use a generic education research repository to undertake that task.

Several precedents already exist, but there would be running costs that could not be met by charging for access to the service, since that simply replaces one paywall with another and would anyway be prohibited by the standard terms outlined above. It is impossible to estimate the income that such a levy would generate because there is apparently no information in the public domain about the number of subscribers to each journal.

Incidentally, such data really ought to be released by publishers and refreshed on an annual basis, since authors have a reasonable right to information to help them assess how many readers a given journal is likely to attract to their article, and which is therefore likely to be the better option.

Without a levy of this kind — whether on journal subscriptions, or membership fees for organisations such as the World Council and ECHA, or both — a repository would be dependent on sponsorship and so not financially sustainable in the longer term. An alternative and more sustainable approach might just work, but it would require the full commitment of all parties and a degree of flexibility and goodwill from publishers.

The limited additional costs to publishers attributable to the extra work involved in these arrangements would be drawn from their profits. They could, if they wished, increase subscriptions to meet those costs. It cannot really be argued that this strategy would deprive publishers of any significant income as a consequence of declining demand for their journals, because they are essentially ensuring that existing permissions, already available to authors, are universally acted upon.

But instead of those rights being optional, they now become largely compulsory. Besides, their only substantive loss would be attributable to the removal of their capacity to sell access to articles and issues more than five years old which must surely be limited, since relatively few will be paying the current rates. Any loss beyond that should already be built into their business planning assumptions, albeit as a worst case scenario. Yet these comparatively slim financial losses for publishers would buy universal free access to a vast library of gifted education research ending, once and for all, the harmful and divisive practice of restricting access to those who can afford to pay.

Taken together, this basket of reforms would remove at a stroke one of my two excuses for failing to be a more productive blogger. It would help to improve the quality of gifted education research, opening it up to wider scrutiny by a more inclusive audience with a different set of expectations, more closely attuned to meeting the needs of gifted learners, their parents, carers and educators.

And it would also establish the reputation of publishers and researchers alike as more significant, more active collaborators in our collective efforts to improve radically the global incidence of high quality gifted education. Written on the eve of the Budget , this post is a progress report on the development of a network of selective maths free schools, set in the wider context of the economic arguments for investment in gifted education.

Nor is it likely that further support will be directed towards this existing initiative, given that little of the existing budget has been used up to date. I set out below the information currently in the public domain and offer a provisional yet constructive assessment of how the maths free school project is shaping up. Well-informed press reports prior to the announcement suggested that there would be at least 12 schools and the resulting network would serve as a model that might be extended to other subjects.

It was suggested that the first would be located in major cities. Some might focus solely on maths and others on a wider STEM curriculum but they would all prepare students to excel at top universities and in subsequent IT, academic or entrepreneurial careers. This is presumably available until the end of the current spending review cycle, so would have to be allocated by Spring at the latest.

But these are slightly different animals, falling outside the project under discussion because they are not supported by university maths departments. Universities can apply to set up a specialist maths Free School on their own, or in partnership with another strong education provider. Similar specialist maths schools, with significant input from universities, already operate in the United States, Russia and China. Interested universities are invited to submit brief proposals to a specialist support team whose home page says:.

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This country has some brilliant university maths departments and world-famous mathematicians, but they have become disconnected from schools, school curriculums and exams. The new specialist maths schools aim to bridge the gap between school and university maths, and in doing so, demonstrate how new approaches can bring dramatic improvements in performance that can be applied more widely. The shift from discussion of a network to a single Russian school is something of a logical non-sequitur, and it is not clear why Kolmogorov is singled out when there are so many alternative models worldwide.

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The mid-section of this post draws together currently available information about the two live projects. Not at the beginning. Once we have approved a proposal, we do offer some support to cover the costs of project management, and recruiting some staff before the school opens, in the same way we would for any Free School. It says the University announced the new school on 14 November, a month before the date of the press release. I think this must be an error. Through this broader curriculum and learning to see the world through different disciplinary perspectives, the school will foster intellectual curiosity, clear and independent thought, creativity and a sense of social responsibility.

The school roll will be students — 60 per year. The KS4 outreach programme began in September , so has a full two years of operation before the School opens, enabling it to pick up promising candidates at the start of Year There is no suggestion that graduates of the School will have preferred status in admission to the University though that might have been an option, especially for those from disadvantaged backgrounds. Potential students are invited to apply online from 30 September Further comment on the pitch of these selection criteria is provided below. It is not clear whether this is one-to-one provision.

A headteacher will be appointed in April , to take up post in September and there will be open evenings for prospective students and their families in October and November. Some are behind paywalls but those that are accessible repeat the information set out in the press release and summarised above. The person appointed to this position will be employed by the trust. Thus the material covered will be close to that in A-level maths, but the style of study will be different to that in most schools. Particular features will be:. There is much less information so far in the public domain about the parallel institution at Exeter.

These partners have also received a development grant to underwrite their project see comment above about that provision apparently being removed for subsequent proposals. The emphasis will be on applied maths, with students given the opportunity to work with academics to apply mathematical concepts to scientific research on subjects like advanced engineering. These plans are obviously still at a very early stage — although there must have been significantly more detail in the papers submitted for DfE approval — and there has been no update since the announcement.

It would have been good to have seen evidence of a fundamentally different approach. The Level and Source of Interest from Universities. Sixteen months on from the announcement, initial confirmation of just two projects — both of them still subject to approval of their funding agreements — is arguably indicative of limited interest from potential host universities, despite the very generous capital and recurrent funding available.

There may be some ideological opposition to free schools in some universities, but that is unlikely to be the principal cause of their apparent hesitancy to come forward. Part of the problem is that the Government is fishing in a small pool. Ministers have been criticised for focusing their policies exclusively on this subset of universities, on the assumption that membership defines higher education quality, when in practice there are weaknesses in some Russell Group provision and exceptionally strong provision in most if not all universities outside the Group.

Even in maths, some universities outside the Russell Group are placed highly in national rankings. In this example the top 20 includes the Universities of Bath 7 , Lancaster 12 , Southampton 16 , Surrey 18 , Loughborough 19 and Kent None are members of the Russell Group. Moreover, each has regional competitors placed higher up the rankings than they are. These are not idiosyncratic results. In the South-West, Bath is 7th and Bristol 11th. Both Kings and Exeter are therefore likely to be attracted to this initiative because they anticipate that it will help them in future to secure a relatively larger share of the best students, so enabling them to compete more effectively with their better-placed competitors.

On this evidence, the scheme is most likely to attract other Russell Group institutions with a similar mid-table profile in other regions — maybe the likes of Liverpool 35 and 41 , Birmingham 32 and 26 , York 30 and 21 , Sheffield 29 and 26 and Manchester 26 and It might help the Government to spell out explicitly that they are not interested solely in Russell Group institutions, recognising that excellent maths provision exists elsewhere.

It might also help to offer some explicit guidance on the thresholds that they expect such maths departments to exceed. The trouble is that there is a bewildering array of alternative models already being pursued by universities:. It is quite likely that many potentially interested and eligible universities have already backed a different model and are reluctant to expand their portfolio at this stage. Some — such as Warwick University — will be relying on other initiatives to secure a stronger share of the best undergraduates.

That would be a tidy sum no doubt, but surely covered substantively by a development grant and the recurrent funding available. Set in this context, the apparent decision to withdraw a development grant from new applicants seems rather puzzling. The arguments for and against selection are well-rehearsed and I will not repeat them here. It seems that selection at age 16 is somewhat less contentious than selection at age 11 with selection at 14 a largely untested assumption. Nevertheless, most of the arguments against and for selection remain in play regardless of the age at when that selection takes place.

We can see this writ large in current debate about fair access to university and its impact on social mobility. It seems unlikely, therefore, that selective universities would harbour an ideological opposition to selection at age The pitch of the selection is critical. Some aspects of those requirements are currently unclear, even for the school at the most advanced stage of development. This places the pitch of selection on a par with the traditional assumption for grammar schools though the reality is now far different and highly differentiated.

There is an obvious trade-off here between excellence and equity. If selection is pitched too highly, it will become impossible to recruit sufficient students from disadvantaged backgrounds, because high attainment is found disproportionately amongst those from comparatively advantaged backgrounds. As I have suggested, this could mean that the provision is unfairly monopolised by the middle classes. On the other hand, if it is pitched too low, students will be admitted who are not the very highest achievers and so are relatively less likely to achieve the A level grades they need to secure places in the most competitive university maths departments.

Gifted educators know that this issue boils down to the critical distinction between attainment and ability. These schools need to find the right blend of admissions arrangements such that they can recruit:. The debate over specialisation is less polarised. Historically there has been argument that the typical A level student experiences a rather narrow curriculum compared with his peers in many other countries, including several of those perceived to have the most successful education systems. The specific issue in this context is that students attending these schools are likely to have an even narrower curricular experience than their peers in other English schools and colleges.

If the KCLMS precedent is followed, they will have an extremely constrained choice of A levels — indeed no choice at all — compared with what would be available in a typical sixth form, even in a small rural school. There are references to curricular provision beyond maths and physics in the KCLMS plans, but it is not clear how they will be implemented in practice, beyond the option of an AS Extended Project.

It has to be open to question whether a small sixth form containing 60 students in each year group, all taking the same three A level choices, is the optimal solution for many students who, as a consequence, will not be exposed to ideas and perspectives from peers experiencing an entirely different subject context.

There will be limited opportunity to bring out the inter-disciplinary connections that are so often of interest to gifted learners, to undertake cross-curricular collaborative learning with peers who can bring to bear strength in other subject areas. It is not necessarily a given that these students will be weaker mathematicians than peers with just that one string to their bows. Moreover, the KCLMS proposal is guilty of a different kind of narrowness in that it is avowedly anti-acceleration, so ignoring opportunities to utilise the close relationship with a university to enable school-age students to pursue undergraduate study.

This reflects a strong strand of thinking in parts of the UK maths education community which believes that acceleration is most definitely not in the best interests of students. The KCLMS approach will probably be unattractive to some of the very highest achieving young mathematicians, who will see this as placing an artificial cap on their progress. It will also mean that KCLMS is very different indeed to some comparable institutions in other parts of the world where accelerated study is actively encouraged.

I note in passing that it is as yet unclear whether these schools will admit already-accelerated students aged under Especially since the benefit under this model is largely confined to an annual cohort of around students 12 x 60 assuming there are 12 schools all the same size as the first two.

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In order to roll out the same model, further funding tranches of this magnitude would be required for every additional 12 schools added to the network — there would be few if any economies of scale. It is likely that this model was adopted because: the Government wanted to increase the stock of free schools; the available capital funding could not be diverted to cover running costs; and it was felt that the infrastructural work involved in building the new schools would itself have a positive impact on economic growth. It would be quite wrong to criticise the current programme at this early stage because we have no evidence of its impact, other than on the grounds that the number of beneficiaries will be comparatively small.

It may eventually be demonstrated that the positive impact on students is so marked that the programme is good value for money despite the heavy outlay. One might begin with the core purpose of creating and sustaining a national network designed to support all students in state-maintained schools and colleges with the potential capacity to achieve, say, at least grades AAB in three of the target A level subjects plus a STEP paper grade of 1 very good or S outstanding.

Such support would be available from Year 9 at the latest and ideally from Year 7. From Years 7 to 9 it would be light touch and provided to a relatively broad cohort, in recognition of the difficulty of predicting future performance at such an early stage. But, from Year 10, it would be concentrated on a smaller group of future high achievers. This would include existing high attainers, but would also give priority and additional intensive support to learners whose potential is significant, but is unfulfilled as a consequence of socio-economic disadvantage. They would be drawn into a powerful coalition, prepared to sink their differences in pursuit of this common cause.

Those receiving Government funding might have it made conditional on their constructive involvement. The network would aim to reach every state-maintained secondary school and post institution, and to draw directly on the expertise within the widest range of institutions which have it to offer, including specialist academies, outstanding schools with an old-style maths specialism, national teaching schools, independent schools and post institutions. In addition, a small core of schools and colleges — some academies and free schools, some not, some independent — might be identified as post centres of excellence and funded to admit the most promising students from disadvantaged backgrounds.

The Government would ensure that all appropriate policy connections were made — whether with wider support for maths education, academically able pupils, fair access to higher education and so on — to ensure that all are mutually supportive and that benefit from the whole is greater than the sum of its parts. And of course the whole caboodle would be rigorously evaluated, both formatively and summatively. Success would be judged against achievement of a few rigorous performance measures. As we approach the Budget, there are many signs that we have emerging consensus on the importance of investment in human capital.

Witness, for example:. But, with the honourable exception of the CBI which is not as explicit as it might be on the point none of these recognise the substantial benefits that would accrue from more targeted investment in our school-age high achievers. To give the Government credit, the maths free schools programme shows that they are alive to these arguments, even if only in a relatively narrow STEM-related context. But it is worth pausing to consider whether a network eventually built around a small set of selective post institutions is the optimal approach.

There are lessons to be learned from the careful study of similar provision in jurisdictions like Hong Kong, Singapore, South Korea, Taiwan and Israel, all of them featured in earlier posts on this blog. An evaluation of the maths free schools pathfinder project might usefully incorporate that comparative dimension, while also reflecting the current predilection for randomised control trials. It follows up a commitment I made to revisit the topic in The Gifted Phoenix Manifesto for Gifted Education which relies significantly on the economic case for investment in gifted education:.

They deserve to be paramount in our current financial predicament. Photo Credit: Leo Reynolds via Compfight cc. Discussion of the Manifesto shows that this view is not unanimous amongst the global gifted education community. Some believe that the economic arguments detract somehow from the educational case for meeting the needs of gifted learners, and results in them being perceived as nothing more than a convenient tool to generate economic growth.

Some are also wary of the economic arguments for education per se, because they are perceived to distort and over-ride the case for education as an end in itself, worth pursuing for its intrinsic benefit alone. I believe neither of these things. I firmly uphold the educational case for supporting gifted learners and fully recognise the intrinsic benefits of education, but I believe that each can be complemented and enhanced by the economic case rather than being threatened or undermined by it. Advocates for gifted education are of course free to use these arguments or to ignore them, entirely as they wish.

I feel it incumbent on me to warn readers that this is a long and complex piece. The meat in the sandwich is academic research — barely digestible at the best of times — but I have tried to make the bread on each side as nourishing as possible. You should be able to get a good sense of the basic argument by consuming the bread alone. I want to begin by unpacking the basic premiss I advanced in the Manifesto. The case I am advancing has eight distinct steps and runs as follows:.

I wanted to see whether I could find any research evidence to support this premiss since I last discussed the economics of gifted education in June There is some evidence and I have drawn together a selection of material that goes some way towards supporting my argument.

But I can find no similar statement of the complete argument. There are bits and pieces here and there, but no perceptible effort to draw the different strands together. Nor can I find any work that systematically analyses the costs and benefits of a national investment in gifted education , so serving as an exemplar of the Gifted Phoenix premiss. The economics of gifted education is nascent merely, but still I find this profoundly disappointing.


Gifted educators could make a much more convincing case to policy makers with such evidence at their fingertips. Maybe there is such work and I have failed to find it. Perhaps it is written in languages other than English, possibly to persuade those who have invested so heavily in gifted education in some of the countries I have featured on this blog.

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Flickerings of Interest Since June and my own involvement. I flatter myself that I know something about gifted education but I am certainly not an economist. So I have some basic grounding but I am very rusty indeed. I recall using it in discussion from around or thereabouts. If you Google the term most of the references are to my work, especially the two posts dating from June that appear on this Blog:. It says Clinkenbeard:. The article refers to a paper presented at the World Council Conference in , but I can find no record of that online.

Further searches on Google Scholar reveal no subsequent publications from Clinkenbeard in this field. After I wrote my posts, there were signs of interest elsewhere. The IRATDE considered devoting an edition of its online journal to the topic and I was even offered the chance to serve as joint editor. Unfortunately the call for manuscripts elicited little interest amongst the academic gifted education community. So I approached Eric Hanushek for some advice about how best to tap in to economics of education networks.

There will be more from Hanushek later in this post. I heard that Hanushek had been invited to speak, but presumably he turned down the opportunity. So did I. Moreover, the research I had undertaken to write a post on gifted education in Saudi Arabia led me to conclude that it was definitely not a place I wished to visit. Unfortunately, this sits behind a paywall and, equally unfortunately, the contents list on Amazon is rather oblique, mentioning only:.

This meeting aimed at discussing the role of creativity in developing business, in addition to the economics of education. This meeting motivated us to talk about the importance of gifted education, and to start working on a special issue of Gifted and Talented International GTI concerned with the Economics of Gifted Education.

Based on the outcomes of this discussion, the Editor-in-Chief has invited one of the top leaders in the field of economics of education to write the theoretical framework that will be the target paper. Consequently, a number of scholars will be invited to write their critiques and response articles. I will work with the editorial board to develop candidate themes for a number of special issues. We are open to ideas from the members of our community.

Does this mean that the promised edition featuring the economics of gifted education will not materialise? This is not simply an arid theoretical matter. Human capital arguments have long been part of the political rhetoric, though they seem to fade in and out of fashion and are often applied in very specific contexts and settings. In the UK as I write, parts of the Government are beginning to make the case.

There is overt support for human capital arguments:. Unfortunately, the Growth Commission has a relatively narrow view of human capital investment. But their proposed solutions — while focused on the necessity of improving the quality of human capital — are entirely generic, insufficiently differentiated to support potential high achievers.

Their recipe for success consists of across-the-board solutions such as more semi-autonomous academy schools and improvements to teacher quality. No sign here of any conception of the smart fraction or the excellence gap! English Education Ministers are also seized of the importance of human capital investment and sometime even couch this in differentiated terms.

Witness this recent speech from Elizabeth Truss :. But we do know that they will demand people with even greater powers of thought, innovation and skill. As the middle is squeezed from the hourglass economy, it will no longer be enough to be able to process — instead much more flexibility and greater cognitive skills will be required. And along with this ability to think, the demand for specialist skills is rising, particularly for quantitative and mathematical skills and for effective communication skills — ideally in more than one language.

The Government is advancing a series of actions to tackle this need — some system-wide and some focused specifically on mathematics — but they too stop short of systematic and concentrated effort to increase the supply of high-achieving learners through interventions targeted specifically at them. The flow of the argument causes me to introduce at this point some recent work by John Jerrim. He richly deserves his position at the top of the bill since he is probably the nearest thing we have to an economist of gifted education in England today.

This is a particularly prominent policy issue, as having a pool of very highly skilled individuals is vital for technological innovation and long-run economic growth. The subsequent table gives test scores at the 90 th percentile for a selection of other countries too expressed in terms of standard deviations above the mean. So there is a tendency for the gap between the highest achieving pupils in England and the highest achieving children in the high-performing Asian countries to increase between the end of primary school and the end of secondary school.

Evidence presented in this paper has suggested that the gap between the highest achieving children in England and the highest achieving children in East Asia widens between ages 10 and 16 at least in mathematics. This is something that needs to be corrected as highly skilled individuals are likely to be important for the continuing success of certain major British industries e. The paper explores whether the East Asian predilection for private tuition helps explain the difference. Consequently, the state may need to intervene. Gifted and talented schemes, a shift of school and pupil incentives away from reaching floor targets e.

Indeed, it is important for academics and policymakers to recognise that East Asian children vastly out-perform their English peers even when they have been through the English schooling system. This is perhaps the clearest indication that it is actually what happens outside of school that is driving these countries superior PISA and TIMSS math test performance.

It is worth emphasising that a well-designed gifted education programme and effort to bring about cultural change need not be mutually exclusive. A gifted programme can be designed to improve the motivation, aspirations and attitudes of the learners who participate and their immediate families as well as improving their achievement. Indeed, given the range and size of out-of-school effects on socio-economic achievement gaps, that is arguably an essential component of any effort to narrow the excellence gap. I proceeded to give a brief account of the development of smart fraction theory, which has its origins in the correlation between national average IQ and per capita GDP.

The authors applied the term to differences between the achievement of advantaged and disadvantaged students performing at the highest levels, in this case on NAEP reading and maths assessments for Grades 4 and 8 respectively. They considered the impact of gender, ethnicity, socio-economic background and English language proficiency, recognising the complex interaction between these factors.

They also concluded that federal involvement in reducing the excellence gap was negligible. The Javits Scheme — then in operation — did not bring about any substantive improvements. Part Two of this post examined the evidence for a corresponding excellence gap in England, while Part Three discussed the relationship between the excellence gap and fair access to higher education in the UK.

So far as is possible in this paywall-restricted context, I want to explore how these different strands of thinking have evolved since In order to make the post manageable I have confined myself principally to the writings of the four key protagonists we have already encountered, namely messrs Hanushek, Jerrim, Plucker and Rindermann as well as their various co-authors. I have been fortunate to find all the papers referenced below freely available online.

I sincerely hope that they will remain so, because they deserve to be widely read. As you proceed through the remainder of this post, imagine a dartboard. I will try to show where these leading thinkers have brought forward material that is relevant to the argument I have advanced above. Each paper contributes a score on the board by inserting a dart in one or more segments. Extending the metaphor, imagine that a bullseye is a full economic justification for the investment in gifted education.

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