What do social scientists need to know about science and maths? What should schools and universities be doing to make sure they have the necessary skills? This was at the heart of a recent meeting at the British Academy, where I found myself sharing a platform with colleagues from the CBI and ESRC, who are not my usual bedfellows as it were. The BA is leading a BIS-funded programme on Languages and Quantitative Skills (two separate strands), aiming to ‘strengthen skills and build capacity in these vital areas’ for the humanities and social sciences. This particular meeting was focussed on the quantitative skills’ aspect, with a morning devoted to the situation as we find it now in the UK, and the afternoon to what lessons might be learned from the international scene with talks from Korea, the USA and Canada. My role was to present the – rather dismal – scene within schools, taking data from the Royal Society’s four ‘State of the Nation’ reports, the last one of which I ‘launched’ last year, and then to participate in a long and thoughtful Q+A session, with fellow panellists John MacInnes (ESRC Strategic Advisor for the Teaching of Quantitative Skills) and Neil Carberry, Employment Director from the CBI, talking respectively about the situation in higher education and employment.

I think we all shared the view that our children and students are simply not gaining the skills they need. Only 59% of schoolchildren manage to get maths GCSE at A*-C, which means 41% don’t even obtain a C grade although these probably don’t go on to do degrees in social sciences. Furthermore, the vast majority of pupils don’t do any mathematics post-16, hence they are not well equipped to deal with the realities of large datasets, grasping the technical meaning of significance or distinguishing between correlation and causation and other such important realities that face social scientists day by day. The Wolf Report, published last year advocated that everyone should be doing some form of maths post-16, a view reinforced by the ACME reports on Mathematical Needs. This message seems to have been heard by Michael Gove: in a speech I hosted last summer at the Royal Society he said

I think we should set a new goal for the education system so that within a decade the vast majority of pupils are studying maths right through to the age of 18.

We will have to wait to see if anything actually transpires, but this (one hopes) is a changing scene.

Of course, in Scotland a far higher proportion of students carry on with maths past Standard grades, progressing on to Highers. In the BA talk I showed data demonstrating both these numbers and the way students combine maths with science subjects in their Highers choices. I was then challenged (by Roderick Floud, Provost of Gresham College) as to why, if the Royal Society felt the Scottish system had so much going for it we didn’t advocate moving towards a Baccalaureate system. I pointed out we had – but after a 24 hours flurry of media attention (during which I had the opportunity to speak on both Today and Radio Scotland early in the morning of the report launch; there was also some reporting in the print media) no further interest was shown. Clearly a more sustained ‘campaign’ would be required to make any significant inroads into either public or government opinion.

Government was represented at this meeting by David Willetts, albeit briefly. He lolloped into the meeting with his customary long strides, delivered a brief speech,answered a handful of questions and then lolloped out again. His speech was notable for its personal touch. Firstly he remarked on his own experiences as an Oxford PPE student, faced with a research paper including a regression analysis with which he had no familiarity. It wasn’t entirely clear how he coped with this – or indeed if he now feels comfortable with regression and other statistical methodology – but at least it meant his comments about the importance of quantitative skills in the social sciences were heartfelt. His second anecdote was at least as bothering. He said that as a junior (junior what was not made clear) in the Treasury he had once been presented with a report with all its prose complete. He was asked to insert the figures into the text, presumably implicitly being asked to find the figures that fitted with the policy being advanced. His comment that times were different now and that the Coalition believed in evidence-based policy was met with polite silence whilst he was in the room. The subdued snigger was only forthcoming after he had left.

I am myself supposed to be more quantitatively skilled than a mere PPE graduate. However, it has to be said that my own schooling provided me with no knowledge of statistics – by implication during the BA day regarded as the most important ‘branch’ of mathematics – and by the time I had left school I don’t suppose I had ever encountered a regression analysis either. It just didn’t feature in the A levels I took, which covered Pure Mathematics and Applied Mathematics. Maybe there was a Statistics course at the time, but my school did not offer it and anyhow I probably wouldn’t have appreciated its relevance for an aspiring physicist. So I had my own first moment of being asked to cope with statistical analysis at around age 18, and indeed in the context of the social sciences. During the year after A levels, which would now be termed a gap year – although that was a phrase unknown at the time – I went to work as a ‘statistical assistant’ at the National Children’s Bureau in London. This was my formal job title, despite the fact that I knew no statistics. The place was full of sociologists, and some medics, who were studying the so-called 1958 cohort of children. This longitudinal study encompasses all the children born in one week in March 1958 and who have been followed up 9 times since, most recently in 2008.

It is an amazing dataset, rich for study, with a massive associated output of papers (as far as I can see from the web the staggering total of 1716 papers have been published in connection with the study). This was, for instance, the cohort whose study first revealed the connection between low birthweight babies and smoking during pregnancy. My own role (working under Dr Eva Alberman, who was something of a pioneer herself) consisted of studying all the low birthweight babies, and tracking down records of those who had got ‘lost’, most usually because of neonatal death, as well as looking at the association between birthweight and subsequent IQ test data at age 7. At this point my memory tells me I had to do a student’s-t test, which of course I had never heard of before the request was made. Luckily I had those around me who could kindly fill me in, and show me how to deal with the punch cards – yes punch cards were the cutting edge of data analysis back then in the early 1970’s – to get an answer. So, given my own background, who am I to sneer at a PPE graduate who also had a moment of panic when faced with a statistical approach he hadn’t met before?

The moral of the story is of course what the BA Quantitative Skills programme is all about. Not everyone in the population will need to deal with something quite as specific as regression or test null hypotheses, but nearly everyone will have to face up to what it means when the newspapers scream ‘red meat increases the chance of death by 20%’ – a nonsensical Daily Mail headline alluded to at the meeting. People need to know what is going on when experts, and the deniers, try to explain what factors are contributing to climate change, sometimes (in the latter case at least, although one hopes not the former) using decidedly dodgy statistical analysis to back up their claims. So, let us hope that better numeracy for all, further exposure to maths post-16 for every student – appropriate according to their future envisaged degree/career trajectories – and a general enhancement in our quantitative skills ensues. It is shameful that England can boast fewer than 20% of post-16 students studying any form of mathematics, compared with nations such as Korea and Japan where as many as 95% do.

It’s strange that you should write about this today. I earn part of my living as a private tutor, teaching maths to failing German school kids. In a German Gymnasium maths is compulsory up to the final university qualification exams at about 18. Yesterday I was explaining to a 17 year old, who is definitively never going to study science, how to differentiate exponential functions. Afterwards I spent some time thinking about whether such kids really need to be introduced to the horrors of calculus even at an elementary level and if not what should a school maths course contain? One of my thoughts was that all school kids, whatever their aim in life, would benefit, in this day and age, from a well structured introductory course in statistics. I say this as a university educated mathematician who truly loathes statistics. But what else should a ‘useful’ general school course in maths contain?

Differentiating an exponential is something you do as a practitioner but which most people will never need to remember. However knowing what an exponential function is could be useful. Plenty of people talk about exponential growth, for example, without any clear idea what the term really means. Like you, I doubt sometimes why we torment students with details of applications of calculus that they will never make use of but also feel that a general knowledge of what calculus is about could somehow be important even to people who never use it directly – that it is about how functions behave over small intervals as you take things to the limit, that it enables you to find slopes and areas and that that can help you find maxima and minima, that those maxima and minima have certain properties etc.

I strongly agree that statistics is given too little emphasis but I think that there is something broader than that that is undertaught which is understanding of how to evaluate evidence more generally and quantitative evidence in particular. Teaching formulae and means of calculation for statistical measures, which seems often to be what statistics courses do, won’t, in itself, convey the feel for probabilistic reasoning and weighing of data that is what is really helpful. It is well known that comparing probabilities, assessing the statistical likelihood of patterns in data and drawing appropriate inferences doesn’t come at all naturally to anyone and it doesn’t come just by knowing how to do appropriate calculations. I wonder whether more use can’t be made, for example, of computer simulations to show how easy it is to be misled by the appearance of patterns in small samples and what sort of data comparisons are genuinely robust.

Your comment reminds me of a charming book my 5 year old daughter brought back from school this week called “Don’t count your chickens” where the little girl starts with two chickens, and then pesters her parents for “twice as many”. The book ends with her 16 chickens each laying an egg. It’s a great explanation of exponential growth!

Ian – I think this is exactly right. I guess the traditional thinking is that to really understand maths (and stats) – to really get inside it, as it were – you have to grind through a lot of the calculations. Most of our generation went through this and it is still very tempting to believe this is the only way. Maybe it still is; but it could be that with the advent of better computing possibilties and data displays we are finally entering an era where we can give a better ‘big picture’ understanding which is rigorous and useful but which does not require 100s of hours of manual calculations.

As for stats, I found it very difficult to even get off the ground in this subject because conceptually it was so different to other maths. Analysis is based ultimately on arithmetic and logic, and algebra, I guess, is based on patterns and their manipulations, but statistics? It always seemed to be a branch of philosophy to me – and a not very well-understood one at that! If we can find innovative and convincing ways to teach stats, then we are onto something interesting. Happy to talk more to you about this around College, if we get the chance!

Hi, Carl. When I learnt it, theory was taught in the classroom and application to data went on elsewhere. That was a natural response to resource constraints of the time. As a consequence, I could devise estimators for hypothetical situations, prove the theorems, write down the formulae and so on but never really got how this related to application until well after securing my qualifications and even after teaching the theory as a graduate student. Now we can, in principle, have students looking at large real and simulated datasets from the outset of teaching. I wonder if we always exploit this as fully as we can. Of course students need to learn theory in order to know what to do with the data but integrating data use with the hours of calculation not only motivates better but also enhances learning. Happy to talk too – maybe lunch sometime after Easter?

I think a major difference between you as a “statistical assistant” in your “gap year” and many students with GCSE maths is that I doubt you were scared of maths or stats. Many bioscience undergrads have very poor attitudes to maths and stats as I discovered in my survey last year of academic staff teaching maths for bioscientists. see pdf at http://www.bioscience.heacademy.ac.uk/ftp/reports/biomaths_landscape.pdf

A significant proportion of bioscience undergrads have a B grade or lower at GCSE maths which means that they can probably not rearrange a simple equations, are pretty weak at manipulating scientific notation and have no idea what logarithms are. So I definitely agree with the suggestion of introducing some study of maths and stats post-16!

The nettle that needs to be grasped by the education system is the distinction between pare maths (the current A level curriculum) and applied maths. Students pitching up at universities with A level maths are generally ill-prepared for handing and thinking about data, even though their pure maths skills may be good. I’d be in favour of “compulsion” about more applied maths teaching (i.e. “numeracy), but not pure maths for all beyond age 16. Nice though that might be, we simply don’t have the resources to support it, and it’s also not appropriate.

Pingback: Bioeconomy in action and Innovators of the Year | Professor Douglas Kell's blog

The Smith Report on school maths teaching goes way back to 2004

http://www.mathsinquiry.org.uk/report/MathsInquiryFinalReport.pdf

It recommended ” that there be a radical re-look at this issue and that much of the teaching and learning of Statistics and Data Handling would be better removed from the mathematics timetable and integrated with the teaching and learning of other disciplines (eg biology or geography). The time restored to the mathematics timetable should be used for acquiring greater mastery of core mathematical concepts and operations.”

I think that in order to develop quantitative skills, you need to embed more maths in other courses such as history (how much could you buy for a given salary? by how many percent did acquisitions extend territory?), social sciences (meta-analysis, survey design), biology, physics, chemistry … Show how maths can be used to solve real-world problems – the possibilities are endless.