Figures of merit
Competence in mathematics is desirable for everyone but vital for scientists, yet there is a widespread, deep-rooted fear of the subject. Stephen Curry insists that this can be overcome by making maths an integral part of science education
Most people are quite happy to pronounce themselves useless at maths. A lack of numerical skill is confessed with a nonchalance that would never apply to literacy. Our divergent attitudes to words and numbers are well known and deep-rooted: the source can probably be found somewhere at the bottom of the fissure between the sciences and humanities explored by C.P. Snow in his famous "two cultures" lecture.
However, I have been surprised to learn that the widespread antipathy to maths is often shared by scientists, especially in the biosciences. Recently, while working on a video project, I talked to six life scientists from different backgrounds about how their careers got started. Unprompted, four of the six admitted to early difficulties with the subject: they were variously "challenged by maths", "mathematics-phobic" or "a terrible mathematician". A Nobel laureate I spoke to described himself as "hopeless at maths".
Clearly the subject has an image problem, even among scientists. The difficulty is not insurmountable, since each of my interviewees has forged a successful career in the biosciences, but it is perturbing the scientific and educational landscape.
As a physicist who has always been relatively comfortable with maths and migrated into biochemistry early in his career, I have seen the value of bringing a mathematical approach to my teaching and research, and been frustrated by students' resistance to the subject.
I think I can understand that resistance. The abstractive power of the discipline, so delightful to mathematicians, leaves many students cold and bemused. They see the formulae as detached from reality, a jumble of indecipherable symbols written in an alien language that is easy to dismiss as irrelevant. But to me and many other scientists, competence in maths is like having a sixth sense - you see things differently. Not having that facility is similar to watching an elephant walk across the African plain without realising that the great beast has a skeleton through which its muscles articulate motion. Maths is the backbone of nature, but too few of our students see it as a necessary component.
As a professor of structural biology, I have long taken a hard line in my department and argued that A-level maths should be an entry requirement for our degree programmes, to ensure we take in "properly trained" students. I tried again at a recent staff meeting to make the case that GCSE maths is a wholly inadequate preparation for university science in the 21st century. It fits its purpose well enough - to equip 16-year-olds with basic numeracy - but the GCSE syllabus provides little grounding for budding scientists. It omits too many basic and necessary concepts: logarithms, exponentials and simple calculus, to name just a few.
I did not carry the day but, having got the bit between my teeth, raised the issue on my blog where it triggered a huge response. I was overwhelmed. Maths, it turns out, is one of those serious and unavoidable subjects, like death or taxes: it touches everyone, and a surprising number care deeply about it, even if their initial experiences with the subject were negative. The lively discussion that ensued in blog comments and emails was extremely illuminating, with many shades of opinion and experience. It has propelled me along a steep learning curve and changed my view of the maths problem.
Part of the current focus on maths in the life sciences derives from the perception that biology and biochemistry are becoming increasingly quantitative sciences. This perception is not universally shared: there is a long history of mathematics being crucial to discoveries outside its natural home in physics - William Harvey's insights into blood circulation, Gregor Mendel's genetics and Alan Hodgkin and Andrew Huxley's examination of the mechanism of the transmission of electrical signals in brain cells, for example, all relied on keen attention to numbers and the formulae that bind them together with meaning.
Nevertheless, it is still arguable that the rise of more sophisticated instrumentation and the massive increase in the amount of data now being gathered in the life sciences - from genome sequencing, microarrays, proteomics and suchlike - have brought a new level of quantitative detail and are driving a less reductionist and more systemic view of biology, where mathematical analyses are more in demand than ever.
But although the need for maths may be visible to university researchers, it has not filtered down to schools, where the subject is rarely seen as a necessary complement to biology or chemistry. The uptake of maths at ages 16-18 in the UK is disappointing - only 25 per cent of A-level students are taking the subject, according to a recent Nuffield Foundation report. This is the lowest level of uptake among members of the Organisation for Economic Cooperation and Development. Among our scientifically inclined students the picture is not much better, since only 40 per cent of A-level biology students in the UK combine this subject with an A level in maths.
This lack of connection is troublesome. The enormous variation in the mathematical ability of students taking science degrees - entry grades can vary from a C at GCSE to an A at A level - is a particular challenge for universities. Some institutions offer intensive maths courses to bring the weaker students up to speed, but this has to be done carefully: importing maths teaching from mathematics departments can be problematic if the training is not sufficiently sympathetic to the needs of life scientists.
Elsewhere, there may be a tendency for lecturers to be accommodating and strip out the more complex mathematical topics from the curriculum. In my own teaching, for example, I have felt obliged to streamline my treatment of the Fourier theory that underpins protein crystallography in order to cater for those students without A-level maths who are not equipped to absorb the algebraic details.
Staff who lack any formal training in mathematics beyond the age of 16 face a different challenge and may struggle to impart the numerical aspects of the curriculum with confidence. Their approach can be apologetic (not wanting to frighten students off), or mechanical (teaching methods or recipes for mathematical analyses without imparting any comprehension of the underlying theory). None of these accommodationist approaches represents a healthy approach to education.
It is commonly supposed among university teachers that the root of students' problems with maths is to be found in our schools, but I think we need to acknowledge the feedback in the interaction between schools and universities that maintains mathematical weaknesses. The longstanding shortage of maths teachers in the UK means that non-maths graduates are often co-opted to teach the subject in secondary schools, even up to A level. Such teachers - many of them having taken university science degrees where maths was not taught as an essential core - are less likely to have the necessary command of the subject to reach beyond the national curriculum and inspire students to see and feel the power of the subject to illuminate science. Couple that with the massive pressures on schools imposed by league tables, which induce a tendency to coach for the exam, and it is no surprise that so many students go off the subject.
The problem of the lack of maths among candidates for university degrees in the life sciences is exacerbated by the limitations of the A-level system, which restricts choices to three or four subjects. Applicants for life science degrees are well advised to take chemistry and biology at A level to demonstrate a well-grounded interest in the area, but feel they can avoid maths. Some do so out of school-bred antipathy towards the subject, although for others it is simply a matter of devoting themselves to topics they find more interesting. Whatever the reason, many students arriving at university for life science degrees are shocked to find the demands placed on their numeracy.
What is the solution? In light of the conversations stimulated by my blog, I have become convinced that an insistence on A-level maths for university entrance is not the answer. There are three main reasons for this conclusion.
First, to do so would exclude many able students who, with appropriate support to overcome any residual fear of the subject, would be more than able to cope with the mathematical content of degrees in biology or biochemistry.
Second, an A-level maths requirement would particularly affect students from low-income backgrounds who are less likely to have been taught maths by teachers with degrees in the subject. At a time when such students are already thinking twice about university education because of rising tuition fees, we should not be adding to the list of disincentives.
And third, the possession of an A level in maths is in practice a poor guide to a student's ability to be able to apply mathematical training in a bioscience laboratory. Many lecturers who commented on my blog noted that students with A-level maths have difficulty with even the simple calculations needed to prepare buffer solutions at a defined salt concentration. And at Imperial College London, we detect no difference in the final degree scores of those with A-level maths and those without. This may partly reflect accommodation in our curriculum, but it probably also reinforces the first point - that talented students can master the maths needed for their degrees.
I haven't abandoned hope of getting more nascent scientists to stick with maths all the way through school, but in the short term, at least, the solution to our difficulties lies elsewhere.
An AS-level "maths for chemists and biologists" might be a worthy intermediate goal to help students prepare for university while still allowing them some scope to pursue other interests at A level. However, it would be preferable to include more maths in the A-level curricula for biology and chemistry, so that students get a stronger sense that the subject is integral to science.
Equally but more pressingly, we need to do more to embed mathematics in the life sciences curricula at university. The key to winning a high level of engagement from students is to ensure that maths is taught within the context of the life sciences. A striking number of respondents to my blog reported that, despite having become disenchanted with the subject at school, they were willing to make the effort to face down their numerical demons once they were able to connect maths with their science studies at university.
Those experiences give me hope that we will be able to seed our science programmes with maths and propagate an appreciation of the subject, not just among undergraduates and future scientists, but also among the next generation of science schoolteachers.
Things are already moving in that direction. In the US, the BIO 2010 project is aiming to stitch maths teaching into the fabric of university bioscience programmes as part of a broader overhaul of teaching. In this country, Jenny Koenig, dean of Lucy Cavendish College, Cambridge, has just completed a survey for the UK Centre for Bioscience that analyses the maths component of undergraduate and postgraduate training in the life sciences (see box, far left). Her conclusions also point to the need for better integration of maths within our curricula and provide a valuable framework for the sector to get its numerical house in order.
The challenges are not trivial. Koenig warns that progress will require enthusiastic support from our academic leaders and incentives for those on the ground who are charged with re-engineering the teaching of maths on science degrees. I agree.
But if we can help students meet the challenge and build the confidence needed to overcome the fear of maths, we will guide them to the discovery that the mathematical substructure of biology and biochemistry is the most natural thing in the world.
Maths myths: 'A dark art sent to terrorise biologists'
Bioscience students too often lack basic mathematical skills, according to a UK-wide survey of academic staff.
Jenny Koenig, dean of Lucy Cavendish College, Cambridge, surveyed 40 universities across the country to investigate the teaching of maths on bioscience degrees.
More than 80 per cent say that new students are not sufficiently well prepared in maths when they start their undergraduate bioscience courses.
The study, commissioned by the UK Centre for Bioscience, found that entry requirements for bioscience degrees vary widely.
Most undergraduate programmes (92 per cent) require a GCSE in maths, rather than AS or A2 level.
While almost 40 per cent of institutions accept students with a GCSE maths grade of A* to C, 40 per cent say their students predominantly have a B or C, and 16 per cent accept students with less than a C.
A "fear of maths" among students is commonly reported.
"There is a culture among students...in which it is acceptable (almost fashionable) to treat maths as some kind of mystical dark art, sent to terrorise biologists," one respondent says.
The most commonly taught mathematical topic in undergraduate bioscience is statistics, along with algebra, calculating concentrations and dilutions, and exponential equations and logarithms.
However, survey respondents say that the need for maths could come as a surprise to students.
Only about a quarter of undergraduate degree courses give bioscientists the option of extending their mathematical knowledge beyond the equivalent of AS-level maths.
This means that bioscience graduates are largely unprepared for further study involving quantitative approaches, says the study.
Stephen Curry is professor of structural biology at Imperial College London. His blog Reciprocal Space is at http://occamstypewriter.org/scurry/