The introduction of post-16 maths is in the news again with a report from the House of Lords committee on Higher Education in STEM and many of the headlines from the Guardian, Independent and Times Higher have picked up on the recommendations regarding maths study post-16.

I have written a few thoughts here on my first impressions but would very much welcome comments.

Though I was pleased to see that some of my work showing that only GCSE maths is required for undergraduate biosciences was cited, the conclusion from this was that more students should take maths A level and this is a little worrying.

The lack, or low level, of maths requirements for admission to HEIs, particularly for programmes in STEM subjects, acts as a disincentive for students to take maths and high level maths at A level. We urge HEIs to introduce more demanding maths requirements at entry for STEM courses.

At the moment I couldn’t say that a new bioscience undergraduate must have done AS and A2 maths as they currently exist. I’m not alone in this as comments on Stephen Curry’s blog last year and the related Times Higher article will testify. It certainly helps if they have done it but much of the content of A2 maths really isn’t that relevant for the biosciences. Furthermore, Jane Harris in her recent report “Rational Numbers: investigating compulsion for mathematics study to 18” pointed out that those with only a B or C at GCSE are often not allowed to go on to do A level maths as they are unlikely to be successful.

Therefore we will need a different sort of A level maths, one that is suited to those who don’t necessarily identify themselves as mathematicians but still need to apply maths in a rigorous way. In another part of the report this idea that different students will require different sorts of mathematics was recognised:

all students should study some form of maths post-16, the particular area of maths depending on the needs of the student. For example, prospective engineering students would require mechanics as part of their post-16 maths, whereas prospective biology students would benefit from studying statistics.

The challenge is going to be to work out how to design maths A levels so that there is a degree of flexibility whilst keeping all the options equally rigorous and respected. Statistics is often viewed as an easy option but it doesn’t need to be (and quite often it isn’t!). Besides, biologists do need more maths than just statistics. In my experience students can often do some fiendishly-difficult calculus techniques but have no idea how to apply it to the real world. The ability to apply maths and problem solve is very much harder than being able to do fancy calculus techniques. It’s also very much harder to teach and to assess. Our currently accepted norm for what is “advanced maths” needs to be turned on its head.

The demands of modern-day biology are very different from what a mathematician might put in an advanced maths course. So biologists need to get involved in the design of maths A levels. The government recognises the role that HEI should play, it just doesn’t really say how it’s actually going to happen given all the other demands on academics.

We support the Government’s efforts to involve HEIs in setting the curriculum and we urge HEIs to engage fully and make every effort to smooth the transition from school to HE, particularly in maths. In order to inform this process, we urge that HEIs work together to establish where the skills gaps are and which areas of the maths syllabus are essential for STEM undergraduate study. We would expect this work to be completed by July 2014.

Finally it is interesting that in the USA in a recent report the recommendation was to:

Launch a national experiment in postsecondary mathematics education to address the mathematics-preparation gap.

This report recognised that in the USA a significant proportion of students are unprepared mathematically for STEM degrees and that much of the mathematics teaching was uninspiring and ineffective for a substantial group of students. A number of exciting initiatives were identified and there was a drive towards finding new ways of teaching in this area. It recognised that education research in teaching mathematics for non-mathematicians is less well-developed than science education generally and more work needs to be done. Furthermore they wanted new mathematics curricula designed and taught by faculty from math-intensive disciplines others than mathematics given as bridging courses or first year remedial courses. All in all they were looking at at an annual cost of $20 million per year for five years, sigh…

Well I am not sure I agree with the proposal to tailor AS (or A2) maths to any particular group since it would require students to make yet more choices at a time when they may be uncertain about where their interests and abilities lie. Starting on an AS Biomaths (whatever its called) would the lock students into a particular path – what happens if they then discover the delights of engineering or even maths itself. They would not be able to make the change …

I think there’s not much wrong with having the sensible maths syllabuses that we have now that present a coherent body of knowledge for its own sake and as a training for the mind. With a sound understanding of ALGEBRA, everything else (like its application to biosciences) will fall into place – without it, it will not. That’s not to say that what happens in schools is perfect – in fact the better students are not challenged and get their A’s or even A*’s without much real understanding. So, much as I hate to agree with a Tory minister, the AS and A levels need toughening up to discriminate at the upper end. But that’s all.

The universities need to play their part too, not by telling teachers what to do or how to do it, but by simply changing their admissions policies. That is to say, the Russell group could say that in two years time, ALL STEM subjects and most Social Sciences will require at least a B at AS in Maths. Schools, students and parents would then respond and stop offering and doing subjects like e.g. law, psychology etc at A level which nobody (not even the lawyers and psychologists) actually want! Lesser universities, such as my own, would then follow suit, thinking of this requirement as an indicator of quality … whatever that might mean! Good students would think “Oh they aren’t asking for an AS in maths so they must be second rate!”. and we’d start losing applications I think. So if the Russell group make this change, we’d follow and so would most others …

(That’s enough ranting Martin – get back in your box!)

Martin Greenhow

Maths Dept, Brunel University

Reblogged this on In the Dark and commented:

Interesting view from a Biosciences perspective about the recent recommendations to increase the number of students taking Mathematics at A-level.

I’ve always had a problem with the way Statistics is taught at A-level, which is largely as a collection of recipes without much understanding of the underlying principles; would more emphasis on probability theory be a better way to go?

The Royal Statistical Society recently published a review of stats teaching in schools (The Future of Statistics in our Schools) and their main recommendation was to get students doing the whole cycle of problem posing, data collection, data representation and then analysis. It think that’s a good idea as it must be a lot more motivating and much more fun. The link is:

I think including relative and absolute risk would be a good idea given how often they appear in newspapers and magazines.