Mathematics at the Transition to University: A Multi-Stage Problem?

AS Director of the National HE STEM Programme I am immensely proud of all areas of its work, but one that I continue to take particular personal and professional interest in is the teaching and learning of mathematics at the transition to university. This naturally reflects my background within the Higher Education Academy Maths, Stats & OR Network, but more so the fact that I also teach both foundation and First Year mathematics university courses.

Mathematics and statistics form an important component of many degree programmes. There exists, however, a well-documented problem with the mathematical preparedness and skills of undergraduate students as they commence their university studies, and not just within the Science, Technology, Engineering and Mathematics (STEM) disciplines. The evidence for this problem goes back over 15 years, yet recent reports continue to provide robust evidence of ongoing concerns. But is this problem the same as that documented 15 years ago?

The report, ‘Measuring the Mathematics Problem’ (2000), recognised the existence of a mathematics problem within the disciplines of mathematics, engineering and physics, and highlighted two contributing factors in particular: ‘insufficient candidates with satisfactory A-level Mathematics grades for the number of degree places available’ and ‘the freedom of A-level students to choose Statistics as an alternative to Mechanics’.

Since 2000 we have seen a substantial increase in the number of students studying mathematics at A-level. For 2011 completers, mathematics is now second in the top ten list of most popular A levels, although there is a need to remain cautious as there is evidence that students at private schools are twice more likely than their peers in comprehensive schools to study mathematics at this level. While there has been growth in mathematics A-levels, there has also been growth within the HE sector. In recent times growth within the STEM disciplines has, on the whole, greatly exceeded the sector average. Studying the average tariff data for 2009/10 and 2011/12, presented in the Guardian university rankings, and which indicates the average number of UCAS points students possess on entry to only mathematical sciences degree programmes, reveals some interesting patterns. Averaging these across all institutions who provided data shows that the average UCAS tariff for the mathematical sciences increased by 10 points to 386 points in 2011/2012. While not conclusive, it reflects a general trend of an increase in the qualifications of incoming students being accepted for university entry to study mathematics, although it is certainly not a universal pattern for all the HEIs for which data was available.

There has been growth in both A-levels and university courses within mathematics and disciplines that contain a significant mathematical component, and it is evident that there are now more learners who have higher pre-entry qualifications in mathematics than previously. Despite this, the mathematics problem continues to exist, suggesting it is no longer due to an insufficient number of A-level candidates with the necessary grades. The Institute of Physics, one of the Partners of the National HE STEM Programme, recently produced a report entitled ’Mind the Gap: Mathematics and the Transition from A-levels to Physics and Engineering Degrees’ which indicates many physics and engineering academic members of staff feel new undergraduates within their disciplines are underprepared as they commence their university studies due to a lack of fluency in mathematics. In addition, the report also highlights the concerns that students themselves are now beginning to articulate in relation to their mathematical skills prior to university entry. This is despite the evidence that they are typically arriving at university with increased mathematical grades, and provides further evidence of issues with pre-university qualifications rather than the individual students themselves.

The ‘Measuring the Mathematics Problem’ report recommended that “Prompt and effective support should be available to students whose mathematical background is found wanting”, and while it is evident that the mathematics problem has not been solved, significant progress has been made. An ample supply of free, good quality resources are available to help any students serious about remedying their shortcomings, and to help academic and support staff who aspire to assist students who struggle at the school-university interface, and a significant proportion of universities have invested substantially to put palliative mechanisms in place, for example mathematics support centres. It is also the case that there are, or have been, several high profile, well-resourced national projects designed to increase the supply of mathematically qualified school leavers, and to improve teaching quality and continuing professional development of mathematics teachers.

So where should we now focus our efforts to address this problem given the progress we have made to date? A key finding of the Institute of Physics report is that that many of the academics surveyed believe that current mathematics and physics provision at A-level leads to students learning by rote rather than through their own independent techniques. A 2008 report entitled Newton’s Mechanics – Who Needs It? Highlighted similar concerns and linked this to a decline in the ability of undergraduate students to model and solve problems at the transition to university. Our efforts should now be to address the lack of fluency amongst incoming undergraduate cohorts in the application of mathematical techniques to unfamiliar exercises, problems or scenarios. The current A-level system does not allow students sufficient opportunity to apply their mathematical skills, particularly if they choose not to study modules of mechanics. It is interesting to note that those students who responded to the Institute of Physics survey and had studied components of further mathematics prior to university entry felt better prepared mathematically for their studies and indicated they felt they required less support. Our interventions, particularly during the first year of university study, need to focus upon allowing students to model scenarios, solve problems, and generally have extended opportunities to engage with the application of mathematics to disciplinary contexts. These are in addition to ensuring ready access to the existing support measures we have developed remains available.  

There is also now clear evidence that the number of disciplines impacted by the mathematics problem has broadened, from its initial impact upon the disciplines of mathematics, engineering and physics, with issues now being seen within chemistry, and the biological, health and social sciences. A different contributing factor is responsible which was highlighted in a recent report by the Advisory Committee on Mathematics Education (ACME) that found around 210,000 students out of the 330,000 that are studying courses that require mathematical knowledge beyond GCSE do not have the required skills, leading to challenges for both the universities and students involved. Here the issue is that students on a wider range of higher education courses are either not aware that the further study of mathematics would be highly beneficial to them or universities are not requesting they study it. As a consequence, students are arriving at universities without having studied the necessary mathematical courses, and for many, they may not have studied any mathematics for two or three years prior to university entry. This is something we can collectively influence and address through our university admissions processes.

The fact that a mathematics problem continues to exist many years on may imply a gloomy picture, but the response of higher education to it does not. Measures have been put in place nationally to ensure that all students embarking upon undergraduate programmes with a strong mathematical content have access to resources that will ease their transition into higher education. Universities are adopting a number of approaches to tackling transitional problems, for example by the provision of summer schools, bridging mathematics courses and through mathematics support centres which many universities have now established. Universities now also have access to a range of quality resources that have been produced directly to support students: the FDTL4 project Mathematics Support at the Transition to University has developed mathtutor, the FDTL4 project Helping Engineers Learn Mathematics (HELM) produced workbooks, and the mathcentre project has produced numerous resources as well as an online resource bank. In addition, through the work of the National HE STEM Programme and the sigma centre of excellence in mathematics and statistics support, a national mathematics support network has been established for higher education staff working to address the student mathematical transition to higher education. The Programme also has several other projects active in addressing the issues described. For example, at the University of Leeds a project focused upon enhancing students mathematical modelling and problem solving skills at the university transition now involves seven departments within four HEIs who have all made changes to the way their programmes of study are delivered to ensure these vital mathematical skills are effectively developed.

To address the mathematics problem prior to university entry clearly requires adjustment to the pre-university curriculum. Members of the Programme Team, and by this I include those from the HE sector who are participating in its activities, would be willing to contribute to the redesign of the existing GCSE and A-level curriculum and there is a very natural role for higher education here if government so chooses. Until then, we must continue to support students develop and enhance their mathematical skills upon university entry; I am delighted we are working with the sector to do just that.