Post-16 mathematics: Fine Art Maths Centre

This post represents Fine Art Maths Centre’s response to the recent Smith Review into post-16 mathematics.

I co-founded FAMC with Rich Cochrane at Central Saint Martins in 2014. Details of our activities can be found in the preamble to our Smith Review submission. We believe initiatives to increase post-16 mathematics participation are hampered by a conservative view of mathematics and the dominance of the quantitative skills lobby in England.

What follows  is taken from the FAMC blog:

“Participation should be guided by the principle that all students should study the mathematics they need for the future.” (Smith Review, §35)

The Smith Review, originally commissioned by George Osborne at the March Budget of 2016, was published on Thursday 20 July, the final day before parliamentary recess. Its headline remit was to review how to increase mathematics participation in England after GSCE, including considering the feasibility of making mathematics compulsory to 18.

There are a interrelated set of concerns here (paragraph numbers refer to the review):

• England is an international education outlier in having such a low percentage of students study mathematics to 18. Nearly three quarters of those achieving a good pass at GCSE drop maths at 16.
• Politicians and policy wonks are concerned that England’s low maths skills contribute to recent poor productivity and that there are new demands not being met, particularly around the quantitative skills needed to make the most of ‘big data’: “Higher levels of education and skills raise productivity directly by enabling individuals to accomplish difficult tasks and address complex problems. They also raise productivity indirectly by facilitating technological diffusion and innovation. Mathematics and quantitative skills are a vital component of this. Furthermore, analysis of student performance in international mathematics and science tests from 50 countries over 40 years shows that higher performance is significantly and positively related to growth in real output per capita.” (§80)
• Universities are concerned that courses which have some mathematical content (135,000 students enter courses with “medium” maths demands) are accepting students who have done no mathematics for two years.
• Worse: “International studies show that around 10 per cent of all university students in England have numeracy or literacy levels below GCSE level, indicating a major numeracy challenge, and suggest that this is often not resolved at the point of graduation.” (§103)
• In general, there is concern about the absence of statistics from the school curriculum with post-16 being the most likely place where it can be embedded. In relation to university study and workplace needs, the Smith Review concentrates on the ‘primary need’ for the ability to analyse and interpret data.

“By age 18, every young person should have secure numeracy – the ability to use and apply basic mathematical knowledge to make decisions and engage in society. Most should have gained, and retained securely, the fundamental mathematics needed to thrive in the modern workplace – for example, the ability to analyse, interpret and present quantitative and statistical information and reason with data.” ( §56)

 Smith decided that making mathematics compulsory was not currently achievable:

• 223 “There is not a case at this stage, however, for making it compulsory:
• the appropriate range of pathways is not available universally,
• teacher supply challenges are significant
• and it is unclear when sufficient specialist capacity will be in place for universal mathematics to become a realistic proposition.”

In sum, we don’t have the qualifications or teachers to achieve the target now. From Smith’s self-penned Foreword: “my clear conclusion is that we do not yet have the appropriate range of pathways available or the capacity to deliver the required volume and range of teaching.”  Instead there should be an ambition to have mathematics become universal by 2030, ‘by changing expectations and culture by ensuring a more appropriate range of pathways’.

Besides that headline, the review was mostly well received – particularly since the government has pledged £16million to address the review’s concerns about how funding reforms to Alevel (limiting each student to three funded Alevels) were affecting Core Maths and Further Mathematics take-up.

The review itself did little to explain why it felt Core Maths was ‘essential’, beyond being the only initiative aimed at increasing understanding of statistics and the application of mathematics. The limitations of Core Maths for increasing participation are clear – the qualification ignores students aiming at arts and humanities. The six qualifications currently available under this rubric are pitched to natural and social sciences: “Core maths offers the opportunity to apply mathematics and statistics to examples from economics, sociology, psychology, chemistry, geography, computing, and business and management.” (§116)

From the perspective of Fine Arts Maths Centre, too little attention was paid to the need to expand the range of pathways so that the mathematics offered is more relevant to those choosing options in the arts, humanities and design. Although the review repeatedly stated that it meant mathematics “in the broadest sense”, the only topics referenced here were statistics, data analysis and numeracy. If we are serious about identifying the mathematics that students will need for the future, we will need to be doing more than trying to argue that all students need better statistics skills.

Smith constructed a defence of current policy measures around quantitative skills but more fundamental questions need to be asked. Firstly, the problem is clearly that A levels are too narrow: students in England are specialising too soon and dropping mathematics is part of that problem. Secondly, if you are going to keep the current post-16 framework then you have to offer mathematics that is closer to the legitimate subject and career interests of students. Since students are exercising choices at 16, we need to develop pathways that cater better to those choices. Running a PR campaign around the benefits of mathematics, is not going to work if the maths is dreary and seemingly irrelevant.

At FAMC, we teach over sixty students a year (from an undergraduate and postgraduate cohort of 400), many of whom gave up mathematics the first chance they got. They come back to mathematics when they realise that mathematics is broader and more interesting than what they were taught pre-16 and when they have projects – ideas for artworks – where the technical impediments can be resolved with mathematical approaches. We run short course workshops in geometry (Euclidean, projective and non-Euclidean), topology, infinity and programming and logic along with new courses planned for 2017/18 featuring basic mechanics, data and algorithms. These topics could form the basis of an alternative post-16 qualification.

The mathematics students need for the future is not just statistics. There is a rich tradition of mathematics that can be much more appealing to art and design students. Our submission to the Smith review emphasised the importance of logic and studying axiomatic systems such as Euclidean geometry. We believe strongly that “A systematic study of geometry provides a foundation for thinking about and working with space that the disconnected fragments that remain on the GCSE syllabus do not provide.”

Core Maths could be expanded to offer a broader range of options and shouldn’t just be left in the hands of the quantitative lobby. We need to listen to what mathematics the students might think they need and look at what mathematics fits better with their future studies and careers, not simply tell them to learn their stats. From our submission: “Topics we believe are relevant for many creative practitioners and industries in the twenty-first century include geometry, programming, group theory and symmetry, abstract algebra more broadly, graph theory, probability and game theory, linear algebra, topology and set theory.”