On Wednesday 02 July the Nuffield Foundation published report Mathematics after 16: the state of play, challenges and ways ahead. It argues that reforms to GCSEs and A levels risk undermining the government’s goal of universal participation in post-16 mathematics education, particularly if new ‘Core Maths’ qualifications are not backed by universities. The report brings together a wide range of evidence and warns that plans to make GCSE Maths more demanding, detach AS from A levels, and replace the modular structure in favour of terminal exams could actually discourage students from continuing to study the subject beyond the age of 16.
The report is available to download from the Nuffield Foundation website.
The government response to consultation for key stage 4 English and mathematics on December 2nd 2013 can be found here; pdf.
DfE are now consulting on the draft Order and Regulations that will give effect to the new programmes of study for English and mathematics at key stage 4 from September 2015 and to extend the disapplication of the key stage 4 science programme of study for a further school year (2015/16).
Reformed GCSE subject content includes three types of content: standard, underlined and bold. In the words of he document,
The expectation is that:
- All students will develop confidence and competence with the content identified by standard type
- All students will be assessed on the content identified by the standard and the underlined [here, for technical reasons, emphasised -- AB] type; more highly attaining students will develop confidence and competence with all of this content
- Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.
The distinction between standard, underlined and bold type applies to the content statements only, not to the assessment objectives or to the mathematical formulae in the appendix.
What follows is the list of items in the Mathematics GCSE subject content and assessment objectives which contain bold type, higher content.I think this short lists clearly marks the boundaries of GCSE — AB
From the Department for Education:
Following the GCSE subject content consultation that closed on 20 August 2013, the Secretary of State has today published revised subject content for English language, English literature and mathematics, as well as the Government’s response to the consultation. The Secretary of State has also made a Written Ministerial Statement, which can be read here.
Ofqual has also published reforms to the design requirements for new GCSEs, including on arrangements for controlled assessment, tiering and new grading. Its summary of these reforms can be found here.
The Rt Hon. David Willetts MP has just published a pamphlet with the Social Market Foundation called Robbins Revisited: Bigger and Better Higher Education. Here are quotes where he mentions mathematics.
Women are still under-represented in sciences (maths and physics) and the applied sciences (computing, engineering, technology and architecture), but the margin has narrowed from the 1960s when only three per cent of students studying “applied science” were women. (p.26)
We want scientists with an awareness of historical context; historians with the maths to handle statistics; mathematicians who can speak another language. (p.50)
Nonetheless, there is an important distinction to be made between the need for breadth in general, and the need for maths skills in particular. In an interview with The Listener in 1967 Robbins was asked why the numbers opting for applied and pure sciences had fallen below expectations. He blamed what he called “the terror of mathematics”, caused by poor teaching and a preoccupation in university maths departments with producing “aces”.
This issue has not gone away. Last year the Lords Science and Technology Committee expressed its shock that many Science, Technology, Engineering and Mathematics (STEM) undergraduates lacked the mathematical skills required to cope with their course at university. The National Audit Office has warned that this is an issue for student retention (pp. 50-51)
Maths is a core part of science and engineering subjects – but it comes into many others. As Liz Truss argues with great passion, it is the universal analytical tool which matters more and more in today’s higher education. It matters to the politics student who has to grapple with difficult statistical data, or the nursing student performing a drug calculation. And after leaving university many graduates will find themselves faced with numerical reasoning tests when competing for jobs. Yet only 16 per cent of undergraduates studying subjects other than maths have an A-level in maths under their belt. Often they will have forgotten much of what they once knew, and even if they haven’t, their confidence in their own abilities may be low. (p.51)
This is why Michael Gove’s moves to ensure that everyone continues some level of mathematical study until the age of 18 are so important. Another important initiative is “sigma”, a Hefce funded project. It is establishing approachable maths support services at institutions across the country. Thanks to their work, politics students suddenly confronted with a regression analysis have someone to turn to. STEM (Science, Technology, Engineering and Mathematics) undergraduates too are receiving expert support to bring their maths skills up to speed. (p.52-52)
A report from Demos, published today. From Executive Summary:
This report strongly argues that the current model of accountability is profoundly toxic and is failing to achieve its stated goal of improving education. It sets out an alternative
regime, which would allow all children to achieve their potential, while ensuring the quality of education in schools is of a high standard. [...]
An Institute of Education working paper by John Jerrim and Alvaro Choi The mathematics skills of school children: How does England compare to the high performing East Asian jurisdictions? generated a number of responses in the media: The Telegraph (from where the title of this post was borrowed), The Guardian, BBC, The Independent.
A quote from the paper, p. 19:
[A]lthough we maintain that policymakers should focus on the earlier stages of young people’s educational career, some important changes are needed to improve aspects of mathematics provision during secondary school. The most pressing issue is to ensure that the curriculum stretches the best young mathematicians enough, and that they are motivated (and incentivised) to fully develop their already accumulated academic skill. 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.g. financial services) and to foster the technological innovation needed for long-run economic growth (Bean and Brown 2005, Toner 2011). One possible explanation for this finding is the widespread use of private tuition by East Asian families for both remedial and enrichment purposes (Ono, 2007; Sohn et al., 2010). This helps to boost the performance of all pupils, including those already performing well at school. In comparison, private tutoring in England is mainly undertaken by a relatively small selection of children from affluent backgrounds, often for remedial purposes. While a large proportion of East Asian families are willing to personally finance such activities through the private sector, the same is unlikely to hold true in the foreseeable future within England. Consequently, the state may need to intervene.
National Curriculum Consultation, KS 1-3, announced today. Closing date: Tuesday 16 April 2013
Published for information only:
From other news:
The Education Secretary has dropped proposals to replace existing exams with new English Baccalaureate Certificates as part of a compromise deal between the Coalition parties, it emerged.
A move to axe competition between exam boards – forcing each body to bid for a “franchise” to run one subject – has also been abandoned amid fears it will fall foul of EU procurement laws.
Curriculum, exam and accountability reform: Michael Gove’s Oral Statement in the Parliament.
Michael Gove’s speech, “The Progressive Betrayal” to the Social Market Foundation – 5th February 2013. Some random quotes related to mathematics:
This approach [...] was called progressive because it moved away from a set hierarchy of knowledge – literary canons, mathematical proofs, scientific laws, musical exercises and artistic traditions towards a new emphasis on “learning to learn”.
The EBacc squeezed out creativity, some claimed. So does that mean scientists from Rutherford to Dawkins are arid and uncreative mechanics? Mathematicians from Pythagoras to Turing are enemies of creativity?
[...] unless you have knowledge – historical, cultural, scientific, mathematic[al] – all you will find on Google is babble.
So our new curriculum affirms – at every point – the critical importance of knowledge acquisition. [...] There is new and detailed content on the mathematical processes every child should master – including early memorisation of tables, written methods of long division and calculations with fractions – which was either absent or obscure before.