Do we have a numerate workforce? I’m afraid it is far too obvious the answer is no. I’m not just talking about the relatively low numbers of students taking maths A level, as detailed here in the recent Royal Society report on the transition to HE, but a much lower level of general numeracy allowing people to use the calculations they need to make their way through life: making sense of interest rates and mortgage repayments; working out how far their pay will stretch when it comes to thinking about a summer holiday; or, for a builder or dress designer, working out how much material they need to complete a job. Not exactly rocket science, not needing calculus or complex numbers, just confidence to manipulate a few figures and possibly the odd formula.
A few months ago, my fellow OT blogger Stephen Curry wrote a plea for maths A level to be seen as a necessary prerequisite for entry to biological HE courses, and followed this up with an opinion piece in the THE. Both these pieces stimulated a huge amount of discussion, predominantly supporting the idea. These ideas are relevant to the more skilled part of our population, those who are going on to science in higher education. For the population at large the problems are different and even more fundamental. This week saw the publication of a report (downloadable from here) on maths education more broadly by a group led by Carol Vorderman and commissioned by Michael Gove and David Cameron when in opposition, but likely to be all the more influential now that they are in Government. It is a report which is well worth reading in full, because it is full of sensible suggestions about how to make all our school-children functionally numerate and what could be done to break the current vicious circle our maths education finds itself in. Its messages are closely aligned with other recent reports including the Royal Society one I allude to above, and one launched in June by ACME (the Advisory Council on Maths Education).
The key recommendations from the Vorderman report are clear, and the one that the media homed in on is one of the most important: with the school leaving age being raised, everyone should continue with some form of maths education until they leave school. What form that should take will depend on ability and future aspirations, it most certainly cannot be one-size-fits-all (as unfortunately the current GCSE essentially is). Currently, as cited in the Vorderman report, we have a cohort of school children more than half of whom cannot correctly work out what the sum 1/2 + 1/4 equals. The most common mistake is an answer of 2/6, showing a complete lack of understanding of what fractions are all about. I would hazard a guess that give a child an apple cut up appropriately, and a far higher proportion would instantly grasp what the correct answer was, so it is to a large extent an ability to deal with the abstraction of an equation that is missing.
That these children leave school with skills so woeful that they will be let down by them in almost any job is not going to help this country out of the economic straits it’s in. There is an interesting commentary in the Vorderman report giving information provided by the Fashion Retail Academy, not – you might think – an obvious place for lack of maths skills to be a problem. But inevitably it is. Ranging from working out the necessary square metre space in stores to calculations of percentages in profits and sales reductions, anyone in the retail industry will face the same problems. School-leavers may fancy a career in fashion is all about clothes so who cares about the maths, but they’d be very, very wrong.
To take another part of the landscape, if someone wants to train to be a primary school teacher, all they need is a grade C at Maths GCSE (which can in fact be obtained even from the lower tier exams). After that, they might get a tiny bit of training in teaching arithmetic in their ITT (initial teacher training), but there isn’t room for much in that crowded curriculum, so essentially their numeracy skills will remain – optimistically – at that GCSE level. In many cases they may forget much of what they knew, and they are likely to lack confidence (not unreasonably) that they have a firm enough grasp of the concepts they need to teach maths/arithmetic even to young children, perhaps particularly to young children. But teach it they must. Somehow they are supposed to know enough to put the next generation of school children’s understanding onto a firm footing. Inevitably many of them find this dreadfully hard, but too often there is no one to turn to for advice. Putting a specialist maths teacher into every primary school would help; ensuring a higher degree of confidence in their own abilities in every teacher’s mind would be even better. If post-16 maths education (with different strands for different end-points) were mandatory to help students retain what they have already learnt through more practice with basic number-handling skills or stretching them a bit further, then for the primary school teachers of tomorrow just as much as for those going on into degrees in history, business and other non-STEM subjects, there would be clear benefits. This might also go some way to solve Stephen’s identified problem of biologists entering university with inadequate maths skills.
However, for all its sensible suggestions it may, as previous similar reports have done, end up simply gathering dust on the shelf. Mike Baker, the BBC’s Education specialist reporter said on his blog
However we have been here before. Sir Mike Tomlinson warned years ago that GCSE maths and English failed to provide functional numeracy and literacy. The subsequent reforms for Diplomas, and the associated requirement that all pupils needed to pass at Functional Skills to gain the Diploma, would have sorted out this problem. But the current government has allowed the Diplomas to wither on the vine.
Nevertheless, there is an opportunity for something radical to be done which could solve a number of problems: for STEM departments in HE where we aren’t impressed by the skills incoming students have; adequate support of those schoolchildren who find maths difficult and for whom the current system is letting them down as they enter the workforce; and those of employers who are frustrated that their workforce are so ill-prepared for the tasks they need to complete. The one thing that perhaps makes me marginally optimistic is the comment Michael Gove made to me before his recent speech at the Royal Society. He said that, as he had been educated in Aberdeen and gone through the Scottish Highers system, he appreciated the fact that he had taken maths at Higher level and felt the breadth of education he had obtained was very important. Indeed, the very fact he had come to the Royal Society to talk about education in STEM subjects was in itself a very positive message. But I, as no doubt many of you, will be watching this space to see what actually transpires.
Thanks for the interesting post. Speaking from my field, some forms of biology don’t use a huge amount of maths, but I have noticed that a few of the undergraduates passing through our institute over the years are struggling to work out even very simple dilutions (“How much 5% BSA do you add if you want a final concentration of 1% BSA in 500 microliters of solution?”, for example.). And these people are in their second or third year of a science degree. I have to admit that I don’t have an easily intuitive grasp of maths, but I’ve certainly worked hard and trained myself until the relevant formulae are like second nature – which in some ways is good if you need to teach someone else. (Some of my scarily adept math friends instantly see the solutions but don’t know how to work it out from first principles).
It’s great to see that this is being taken seriously.
Thanks Athene – very thought provoking. I remember my struggles with maths all too well, and am reliving them now with Crox Minor (now year 9, beginning to think of her GCSE options) and Crox Minima (going up to High School next month.)
Two points – first, a lot of it is down to teaching. When Crox Minima was at her last primary school her teacher was a most unsympathetic character who wasn’t very good at explaining things. The result was that Crox Minima was quickly lost and had the frailest grasp of the concepts. Sitting with her ‘helping’ her with homework – well, the tears, the tantrums, the rage, the stormings-out-of-the-room, the lying-on-the-floor-screaming — and that was just me. It doesn’t help that maths teachers seem to use methods in arithmetic that seem very odd and certainly more laborious than those I was taught. But then Crox Minima changed primary school, found a better teacher, and simply ‘got’ it. I knew this when she came home and said “I LOVE maths!” and, even more surprisingly, begged me to give her algebra problems to solve. My response was “who are you and what have you done with Crox Minima?”
Second, my sister, a fortysomething married lady with 2 kids, was always terrible at maths at school, and always put down by the teacher. But she recently got an adult-education qualification at our local institute in Cromer called ‘Maths for Life’ or words to that effect, which teaches basic numeracy to adults through real life examples, such as calculating the change you’ll get on a shopping bill, working out how much wallpaper you’ll need for a given room, and so on. None of that geometry and trig and calculus which seems so abstract, and which is certainly inapplicable in daily life. Sure, I found calculus useful in first year biochemistry for working out enzyme kinetics – but that’s it.
Cromercrox, yes a lot of it is down to teaching, which is why if the primary school teachers themselves lack confidence they will never set things off in the right direction. ‘Not being good at explaining things’ may amount to ‘not having a good grasp of things’, which is why we have such an unsatisfactory vicious circle going on at the moment. We need more specialist teachers in primary schools (this goes for science as well as maths, only about 3% of primary school teachers currently have a STEM degree) and we need all teachers to have a good grasp of the fundamentals and the support they need to get to that point. Methodologies have certainly changed and I find it worrying that I can read the Vorderman report and not know what the methods she refers to mean: number bonds are a case in point. Not a phrase I knew before this week, but someone (with school age kids) has kindly explained it to me.
Jenny, yes there are few degrees of any kind when some basic maths isn’t required. Humanities subjects increasingly use statistics, for instance in history to make sense of demographics (see a much earlier post of mine related to this ) and of course subjects like business studies rely on handling numbers. As I said, it isn’t complex numbers or calculus these sorts of degrees need, but in biology – as Stephen discussed in his earlier post – differential equations can be crucial almost as much as in physics or chemistry, and certainly working out molarity etc ought to be taken as trivial not needing hours of thought. With or without a calculator, you need to understand the principles before you can do anything else.
‘Not being good at explaining things’ may amount to ‘not having a good grasp of things’, which is why we have such an unsatisfactory vicious circle going on at the moment.
Never a truer word like wot she is spoke.
Very nice post.
Like Jenny, I am not a fan of math, but my husband and my son are.
You have addition of fractions as a good example. When I was teaching my son fractions when he was 6, I had to figure out a way to explain why even learn fractions. How do fractions help explain the world better when compared to whole numbers? It was a great experience for me because that was the first time in my life that I asked those questions. Math was taught to me by people who didn’t care much about it. I had realized early that I am not mathematically wired. I did learn some calculus and stuff, but to me they were useless pieces of information that I didn’t care about at all and I worked extra hard and got OK grades and that was that. Those years of math did not transform the way I thought of things, like biology did. When you learned how things worked in your body, it completely changed the way you looked at it and it was so exciting. If someone had explained in some way how these calculations and all the complicated math helped me see the world, I would have looked at math very differently. Thankfully, my son is learning math in a more involved way and having inherited mathophilic genes (and silenced mathophobic genes) he seems to be enjoying it.
There is this online game called First-in-math, where there are all kinds of problems that increase the speed of your calculations. It begin with simple concepts and takes it to complex equations. It is in the form of a game and you can see the progress you make. There are sections on time, money, weights, geometry, logic, probability and problems that help you sense patterns and problems that increase the speed at which you can solve simple calculations.You earn stickers and you can compete with your friends in class and your school and other schools in the district, state and country. I wish I had access to something like this when I was growing up, would’ve definitely changed my attitude to math.
Such programs have helped children in low income neighborhoods and increased their ability in math considerably. It is not that expensive, a license for a year of play is only $8-10 and if you buy the license for a large group it is cheaper. Because it is in a game format, kids (esp girls) are not intimidated by it and once they learn some basic skills, school math becomes so much easier and when they realize how good they are at it, they are ready for more challenging stuff.
I wish such programs would become part of the curriculum in all countries in the world. That would be so wonderful! And with such widespread use of the Internet, I cannot understand why such things are not happening. So anybody interested in spreading a love for math could google first-in-math and persuade their children’s schools to purchase the license or better still have your friends in the PTA sponsor it for the school. Once the school sees what it can do, they will buy it themselves.
Hi Athene – interesting stuff – I had seen a few sporadic reports on this report when it came out.
For the record, though I started out by calling for student entrants to university life sciences courses to have A level maths in my original post, the resulting discussion — where many disagreed with me — led me to modify my view so that, by the time I came to write up the discussion in the THE I recognised that more context-based training, rather than an A level per se was what was required.
But, as you say, clearly our Maths problems are deeper and wider than the particular issue of how to prepare students for university entry. I do hope that the increase in the school-leaving age will create an opportunity that government will take to bolster maths education for all. And teacher-training, or teacher experience, is a key element of the solution. I guess I shouldn’t have been but I was shocked to learn that a C grade in GCSE maths is considered a good enough qualification for a primary school teacher. It’s clear that more effort needs to be put in at this level to make sure that children do not become disenchanted at such an early stage with the subject. More maths specialists would go some way to ameliorating that.
In a way this issue may relate to yours and Jenny’s foregoing discussion of science careers. If teaching were viewed more sympathetically as an honourable and extremely valuable role by postdocs looking to exit the scientific life, they could surely bring a great deal of mathematical fluency (not to mention so many other attributes) to the job.
Stephen, I stand corrected about the THE article – I did read it but it’s the OT post that stuck in my mind.
I think you’re absolutely right about the desirability of teaching being seen as an honourable thing to do for an experienced postdoc. From what I gather, teachers who enter the profession, not just as raw graduates but with some years of work under their belt, often find it easier to keep control/assert their authority on classes. As a result they are more likely to keep going rather than feel the stresses are just too great and drop out (of course this applies more to secondary teachers than primary ones).
Thank you for this post, Athene.
I’m a maths teacher in a secondary school (ages 11 -18) and I found your say, as well as the comments very useful.
Absolutely, a teacher who cares about what they do is the sine qua non for any subject.
The mathematics taught in schools is not just a means to an end, it does not only teach things that are useful in real life. There is another purpose, which is not negligeable: it is a way of exercising the brain – something that everybody needs at least until they are 18 🙂
(As well as providing children with thinking tools that are broadly covered by the phrase ‘problem solving’)
I think that, for younger ages (and lower abilities) there should be a greater degree of practising involved. Understanding is necessary but not sufficient – in fact this is valid for any level of maths in school.
Thirdly, many bright students are not stretched by the GCSE Higher syllabus, which is very limited. (One thing that I think should be included is Euclidian geometry and proof, for example).
As a retired math teacher, I believe that there are two fundamental circumstances that sabotage a child’s math understanding. The first is being in a family whose members had trouble wih math and treat math failure as a hereditary trait. The second is sitting through math classes taught by people who think that math is a necessary evil that can be mastered only by hugh amounts of practice and memorization.
Math can be made interesting by showing its applications and treating math “problems” as challenging puzzles. No other subject has “problems”.
After I retired, I published the Basic Math Quick Reference Handbook for people who didn’t have the time or interest to read a lot or practice solving math problems. As it turns out, its biggest fans are elementary school teachers.
It’s not right to have teachers who have to brush up on a subject the day before it is taught, but sometimes it’s necessary.