Senior Research Fellow
School of Computing Science, University of Glasgow
TL;DR: Maths has had an unprecedented impact on daily life in recent months; we need to rethink mathematics education so that this leads to greater mathematical literacy rather than increased mistrust in the subject.
It’s been a strange time to be a mathematician.
In March, social media was suddenly flooded with hundreds of variations on this diagram, the likes of which used to be seen primarily in undergraduate calculus lectures, and discussions about exponential functions began to dominate the headlines. One thing we can be sure of in the “new normal” is that, after months during which mathematical models helped to decide how often we could leave our homes, teachers of these particular mathematical concepts will never again struggle to find examples of their impact outside the classroom.
What these last few months have highlighted for me, though, is just how poorly even simple mathematical concepts are presented in the media, with potentially dangerous consequences. One recurring issue relates to the presentation of percentages – something in which, at least in theory, should be well within the comfort zone of most high-school pupils. I have lost count of the number of recent headlines that – perhaps in the name of journalistic brevity – announce a percentage without giving any indication of the group to which this statistic relates. When the percentage in question relates, for example, to the number of people who have been infected with COVID-19 but not shown any symptoms, the statement has very different implications if it actually relates only to the (relatively small) group who have tested positive for the disease rather than – as one might reasonably assume from the headline – the population as a whole.
My hope is that, as well as highlighting a widespread lack of mathematical fluency, this year’s events – and the starring role that statistics and mathematical models have played in our daily lives – could create new appetite across the population to learn more about the underlying concepts. Numerous brilliant mathematical communicators have risen to this short-term challenge with articles and documentaries, but across the whole profession we need to work to maintain this interest – even while we scratch our heads about how our tried-and-tested public engagement activities can be reimagined for virtual environments such as this year’s online versions of the Edinburgh and Glasgow Science Festivals.
Alongside this optimism, though, I also fear that there is a danger – especially as maths is a subject that people love to hate – that mathematics will become a scapegoat for political decisions that are unpopular or that, with perfect hindsight, turn out to have been less than optimal. We have already seen numerous examples of pandemic-related decisions being attributed solely to “the science” when political and economic factors undoubtedly played a role, while in the last few weeks the UK government has attempted to pin the blame for the A Level results fiasco on a “mutant algorithm”; there is concern more generally that the pandemic may contribute to the ongoing erosion of public trust in scientific experts.
Of course, it is true that mathematical models – whether it is those used to model COVID-19 or to decide who is approved for a mortgage – are not perfect: they are by definition an informed guess, not a crystal ball, and are limited both by the available data and the significant simplifying assumptions usually needed to make the calculations feasible. And there should be no problem in using an imperfect model, so long as those interpreting the results understand the limitations of the model – whether these include the fact that small errors or biases in the input data could be amplified, or that the model is only valid when specific conditions are satisfied. The problem is therefore not with the use of models to inform decision-making, but with a lack of education around their use; this can partly be attributed to the speed with which automated decision-making has been adopted across many facets of our lives, leaving educators struggling to catch up.
Personally, however, I think that these changes in how mathematics influences our lives require a more radical rethink on the role of mathematics education. Just as the set of skills needed to design and build a safe car is completely different from that needed to drive the same car safely, we need to distinguish between the skills needed by the minority – currently the intended audience for many mathematical curricula – who will go on to be the creators of new mathematical concepts, models and algorithms, and the majority who need to be informed users of mathematics without necessarily understanding all the theory underpinning the tools they use. For those not planning to pursue a career involving mathematics, is it really essential to become proficient at carrying out a few specific kinds of calculations – many of which can be outsourced to a smartphone – or would it be better to spend the time getting a flavour of some more advanced mathematics, learning about what can (and, importantly, cannot) be done, without necessarily understanding all the details of how? And for all students, we need to challenge the perception that maths is the subject of choice for those who don’t like writing: the ability to explain mathematical concepts clearly, and justify results, should be rewarded at least as much as the ability to calculate the correct answer – after all, in the real world, there is often no single “right” answer.
If we can do this successfully, then there is hope that the pandemic will leave us with a generation equipped to use mathematical tools to inform decisions in a responsible way, rather than a generation more mistrustful of the subject than ever.