Understanding post-16 maths participation: A pipeline, a set of pathways or an expanding portfolio?

Jennifer Norris, Research Associate 

Improving learners’ access to maths after the age of 16 in England has long been a goal of successive governments. It’s also something that researchers in the Observatory have been investigating for a number of years. From the recent Mathematics Pipeline report that focused on under-represented groups on track to study maths at university-level, to the 2011 Mathematics Pathways project that evaluated new pilot qualifications in mathematics at GCSE and A-level. 

But why do we talk about pipelines and pathways? Metaphor theorists argue that using metaphors is our default mode as humans to explain and understand complex ideas by relating them to our physical experience. The problem with metaphors is they always provide a partial picture, so they inevitably highlight some aspects of the idea while hiding others. So, when we talk about maths pipelines and pathways it’s important to understand what gets highlighted, and what might be missing. 

I analysed National Pupil Database data for A level students (i.e. students with at least one A level qualification) using pipeline, pathways, and portfolio metaphors as models, and came out with some strikingly different numbers for how many students count as studying post-16 maths.  

The maths pipeline 

The pipeline metaphor implies clear boundaries demarcating who is in and out of maths education. It views participation as the collective motion of students flowing through the education system where students, a valuable resource, are retained inside the pipe for as long as possible. The pipeline image is useful for discussing social inequalities because it draws attention to the kinds of students that disproportionately leak from the pipeline. The end point of the pipe is to supply high-level mathematical skills, so in the 16-18 phase of education we are only really interested in students taking A level Maths, since this is typically an entry requirement for university maths.  

Among students with at least one A level, 32% took A level mathematics and therefore were within the maths pipeline. 

Maths pathways 

Rather than being in or out of a single pipeline, in this metaphor we imagine students being on or off one of many possible pathways. In post-16 education the paths are different qualifications like A and AS level, Core Maths, and GCSE resits. Students travel along these paths, so participation is individual motion. This metaphor highlights student choice, which means it also draws attention to the question of whether there are appropriate qualification routes available to each student.  

41% of A level students took a maths qualification (A level, AS level, Core Maths, or GCSE) and so were on a maths pathway. 

Maths portfolios 

The idea of a maths portfolio is still in its early stages. We’re imagining a bag or folder that students carry with them. As they go along, they collect mathematical objects of many types: concepts, skills, attitudes, beliefs, motivations, and more. In metaphor terms, this means that the student is (or has) a container, while maths education is any source of maths resources, both inside and outside of the maths classroom.  

In 16-18 education, many students choose A level subjects that include assessment of quantitative skills, such as Business, Economics, Geography, Psychology, Biology, and Chemistry. We can view these subjects as sources of maths resources that students can use to grow their individual maths portfolio, whether or not they are taking a standalone maths qualification.  

84% of A level students took at least one of the quantitative A levels, meaning that they expanded their maths portfolio.  

Metaphors matter 

It matters how we define what counts as participating in post-16 maths because it determines whether we count 84% of A level students as studying maths, or only 32%. This in turn affects what we decide to do next to solve the post-16 “maths gap”. Do we need more students taking A level Maths, or more alternative qualifications like Core Maths, or greater recognition of the quantitative skills developed within other A level subjects? Or perhaps a combination of all three! 

What metaphor would you use? 

Author information

Jenny is a research associate at the Observatory for Mathematical Education. Alongside her work for the Observatory, Jenny is an ESRC funded doctoral student in the School of Education. 

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