This news changes research environment in the UK not only for mathematics but also for education research, and therefore deserves being mentioned here.
David Willetts accepted in full all recommendations of the Finch Report directed at adoption of the “gold model” (also known as the “Article Processing Charge” model, that is, “the author pays for publication” model) of open access to research publications. Some funds for publication will be provided by universities. A statement from HEFCE:
As a first step, we would like to make clear that institutions can use the funds provided through our research grant to contribute towards the costs of more accessible forms of publication, alongside funding from other sources.
In the coming months, the four UK HE funding bodies will develop proposals for implementing a requirement that research outputs submitted to a REF or similar exercise after 2014 shall be as widely accessible as may be reasonably achievable at the time. We will consult all our partners in research funding, and a wide range of other interested bodies, before finalising our plans.
And this is from RCUK:
[F]rom 1 April 2013 and until further notice, RCUK will solely pay for APCs through block grants to UK Higher Education Institutions, approved independent research organisations and Research Council Institutes.
27.1 per cent of teachers leading mathematics classes in the current academic year fail to hold a degree in the subject, up from 26 per cent 12 months earlier. Data for 2010 and 2011 can be found in Tables 13 of DfE documents SFR 6/2011 and SFR 06/2012.
The UK Arts and Humanities Research Council has agreed to fund a research network on mathematical cultures. Here, I describe this project and what we hope to learn from it.
Why study mathematical cultures? Why now?
Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematics. These may be the legacy of a dominant individual (e.g. the Newtonianism of 18th century British mathematics). Or, there may be social or economic reasons (such as the practical bent of early modern Dutch mathematics).
These local mathematical cultures are scientifically important because they can affect the direction of mathematical research. They also matter because of the cultural importance of mathematics. Mathematics enjoys enormous intellectual prestige, and has seen a growth of popular publishing, films about mathematicians, at least one novel and plays. However, this same intellectual prestige encourages a disengagement from mathematics. Ignorance of even rudimentary mathematics remains socially acceptable. Policy initiatives to encourage the study of mathematics usually emphasise the economic utility of mathematics (for example the 2006 STEM Programme Report). Appeals of this sort rarely succeed with students unless there is a specific promise of employment or higher remuneration.
What these political anxieties call for is a re-presentation of mathematics as a human activity, which means, among other things, that it is part of culture. The tools and knowledge necessary for this have been developing in recent years. Historians of mathematics have begun to consider mathematics in its social, political and cultural contexts. There is now an established sociology of science and technology, published in journals such as Science as Culture and the Journal of Humanistic Mathematics. Mathematics educationalists have begun to draw on some of these developments (particularly historical research).
The Department for Education announced that
A new statutory test of English grammar, punctuation and spelling will be introduced for children at the end of Key Stage 2 from May 2013.
Some sample questions are published here. An example:
Insert a comma and a semi-colon in the sentence below to clarify the meaning of the sentence: David eats cake whenever he has the chance I prefer apples oranges and bananas.
I am not in position to judge whether 11 years is an appropriate age for such tests. However, I share the view that grammar expresses the logical structure of language and therefore should be of concern for mathematicians. This point of view is fully developed in the submission made by the British Logic Colloquium to the National Curriculum Review:
Grammar is a precondition of logic in any language, the foundation of systematic reasoning. This connection is obvious at later stages of education, especially in mathematics, computer science and law, but also in every discipline or profession that involves clearly defined rules, such as natural science and finance.
The ability to understand and use principles of grammar to analyse the meaning of complex texts and express thought precisely in speech and writing is one of the most important skills for students to acquire in their school education. Mastery of grammar helps us navigate the increasingly complex information world in which we all live in the 21st century.
Every dialect has its own grammar. What students need to acquire is sufficient grasp of general concepts and principles of grammar to enable them to understand how sentences of English work, how their parts fit together to express the meaning they do. We have found in practice that students who have never been explicitly taught formal grammar are at a disadvantage when they have to assess reasoning to exact standards, because they lack the intellectual resources to reflect critically on the language in which it is stated.
We leave it to specialists to decide the optimal scope and methods for English grammar teaching in schools. The aim of this statement is to raise the profile of the issue.
From the speech by Nick Gibb, State Minister for Schools, at the annual meeting of ACME, 10 July 2012:
[T]he draft programme aims to ensure pupils are fluent in the fundamentals. Asking children to select and use appropriate written algorithms and to become fluent in mental arithmetic, underpinned by sound mathematical concepts: whilst also aiming to develop their competency in reasoning and problem solving.
More specifically, it responds to the concerns of teachers and employers by setting higher expectations of children to perform more challenging calculations with fractions, decimals, percentages and larger numbers. […]
As it stands, the draft programme is very demanding but no more demanding than the curriculum in some high-performing countries. There is a focus on issues such as multiplication tables, long multiplication, long division and fractions.
Last month, the Carnegie Mellon University in the US published research by Robert Siegler that correlated fifth grade pupils’ proficiency in long division, and understanding of fractions, with improved high school attainment in algebra and overall achievement in maths, even after controlling for pupil IQ, parents’ education and income.
Related posts in this Blog: an alternative curriculum and Robert Siegler’s paper.
Pupils will be given national rankings according to their exact scores in the new O level-style exams being planned by Michael Gove, TES has learned. Sources close to the education secretary said that he intends to introduce the controversial idea, proposed last year for A-level students, as part of his overhaul of the exams system for 16-year- olds.
Certificates for the qualifications replacing GCSEs in English, maths and science would go beyond a simple grade. They would include the candidate’s ranking and a graph showing where they placed in the overall distribution of scores. [Read the rest of the article in TES.]
The Telegraph adds (with reference to TES) that
Each pupil’s score would be set against marks achieved by all other candidates nationally, with teenagers being given a percentile ranking from one to 100.
A new study published today in BioMed Central’s open access journal Behavioral and Brain Functions [Devine A, Fawcett K, Szűcs D, Dowker A (2012), Gender differences in mathematics anxiety and the relation to mathematics performance while controlling for test anxiety. Behavioral and Brain Functions (in press; still was not online at time of writing).] reports that a number of school-age children suffer from mathematics anxiety and, although both genders’ performance is likely to be affected as a result, girls’ maths performance is more likely to suffer than boys’.
A word problem from the Khan Academy
Last year, I was asked by my American colleagues to give my assessment of mathematical material on the Khan Academy website. Among other things I looked for the so-called “word problems” and clicked on a link leading to what was called there an “average word problems” but happened to be a “word problem about averages”. It appears that the problem there changed since last year. I reproduce here the old one, it is more of interest for discussion of “word problems”.
Gulnar has an average score of \( 87\) after \( 6\) tests. What does Gulnar need to get on the next test to finish with an average of \( 78\) on all \( 7\) tests?
The Sutton Trust (see their Press Release) published today a report by Alan Smithers and Pamela Robinson, Educating the Highly Able. From the Executive Summary of the report:
Policy and provision for the highly able in England is in a mess. […]
When compared to other countries the consequences are stark. In the 2009 PISA tests only just over half as many achieved the highest level in maths as the average of 3.1% for OECD countries. England’s 1.7 per cent has to be seen against the 8.7 per cent in Flemish Belgium and 7.8 per cent in Switzerland. On a world scale, the picture is even more concerning – 26.6 per cent achieved the highest level in Shanghai, 15.6 per cent in Singapore and 10.8 per cent in Hong Kong. In reading, where the test seems to favour English-speaking countries, England is at the OECD average, but only a third get to the highest level compared with New Zealand and only half compared with Australia. The few top performers in England are in independent and grammar schools and almost no pupils in the general run of maintained reach the highest levels.
The root of the problem is that “gifted and talented‟ is too broad a construct to be the basis of sensible policy. As it has morphed from “intelligence‟ to “gifted‟ to “gifted and talented‟, it has become ever more diffuse. It is not just the conflating of “gifted‟ and “talented‟; it is that “gifts‟ and “talents‟ are often specific. A gift for mathematics and a gift for creative writing are rarely found in the same person. Few top footballers are also top artists. Continue reading
Department for Business, Innovation & Skills (BIS) published Government Response on Consultation “Students at the Heart of the System“. Two points relevant to mathematics:
(A) Unconstrained recruitment of students with AAB+/ABB+ is to stay:
2.2.52 HEFCE’s decision that institutions will retain a student number limit equal to at least 20% of their 2011-12 numbers also means that for the institutions that currently recruit a very high proportion of AAB+ students, there will still be a core to make contextual data offers, and they will still be able to expand if they choose to. HEFCE will look at how best to achieve a similar outcome for 13/14, with the introduction of ABB+. […]
[p. 33] However we are clear that our tariff policy (allowing unconstrained recruitment of students with AAB+ and equivalent grades for 2012/13 and ABB+ from 2013/14) should not impact negatively on fair access to higher education by taking away places from people from disadvantaged backgrounds. […]
(B) But mathematics is excluded from “contestable margin”:
1.4 […] [F]rom 2013/14 the tariff policy should be further liberalised to apply to students with ABB+ grades, taking one in three entrants out of number controls. We also announced that a further 5,000 places should be made available through the contestable margin. […]
2.2.53. We also welcome the way in which HEFCE has implemented our core and margin policy. In particular we welcome the fact that: […]
Student numbers in chemistry, engineering, mathematics, physics and modern foreign languages will be excluded from the calculation to create the margin.
Regarding (A), BIS recognises that
2.2.42. Many respondents expressed the view that AAB+ grades are harder to achieve in STEM subjects and warned of the potential consequences for the supply of STEM graduates. They were concerned that unconstrained recruitment would lead to students choosing to study subjects in which they are most likely to achieve AAB+ grades, and to institutions favouring those courses where they can attract large numbers of high-achieving students.