Mathematics and moral agency
I don’t usually mix maths with morality, but two events collided last week to force the issue. On Tuesday, I awoke to the horrific news of events in Manchester. Early indications were a terror attack; 22 dead, scores injured, all innocent. On the train ride into the office, I found myself probing the deeper meaning to my work. I represent a company whose core mission is to ‘raise standards in mathematics’. As it happens, I was due to chair a meeting that very day on the meaning behind our mission.
As I prepared for the meeting, the news still fresh in my mind, I desperately sought to join the dots — does raising standards in maths make the world a safer place? Would a stronger mathematics education help prevent such acts of lunacy? Is the deeper purpose of mathematics that it shapes our morality?
I had more questions than answers.
Somewhere, Ted Kaczynski was chuckling away. The mathematician turned Unabomber is evidence enough that a solid foundation in maths is no absolute pathway to morality (just search ‘evil mathematicians’ for more examples). Maths does not imply morality. So what’s left for maths educators? Perhaps it’s to ensure students are fully equipped to understand the moral implications of their choices, even if we can’t guarantee they’ll make the right ones.
Any individual who is capable of formulating or following general moral principles and rules, and who has an autonomous will so that he can decide ultimately what acts he should perform and not perform…Accordingly they are responsible for their acts and are the subject of blame or praise.
By this definition, moral agency relies on the ability to think for oneself. This may explain why mathematics has enjoyed a longstanding association with issues of morality. Let’s start with Socrates, for whom ‘the unexamined life is not worth living’. Damning words for those among us who do not critically reflect. The Socratic method implores us to assume nothing and arrive at truths through relentless questioning. It’s good news for mathematicians, who learn their craft in much the same way. Plato placed maths in even higher regard, singling out arithmetic and geometry as two disciplines essential to developing knowledge of goodness.
The arguments continue to the present day. Robert Heslep offers a slew of ways in which maths supports moral development. Mathematics endows us with the basic elements of rational thought, such as deductive thinking, on which all moral judgements rest. It teaches us to create abstractions, allowing us to reflect on moral problems outside of their immediate context. The quantitative skills of maths let us understand how moral judgements play out in social and economic terms.
How about mathematics as the stalwart of our democracy? Thomas Falkenberg argues that because maths is constrained only by absolute truths, it fosters a democratic approach to learning that creates equality between problem solvers. For Falkenberg, maths is no less than a ‘moral adventure’.
The argument is appealing — maths sharpens our thinking skills which, in turn, allow us to engage moral concepts. It’s a far cry from the heartless, dehumanised, decontextualized form of school maths. Students acquire knowledge through the distinctly undemocratic pedagogy of knowledge transmission. They tackle closed problems with a clear right/wrong answer, engendering a binary view of the world. They are instructed to study maths for the sake of boosting their employment prospects; a squarely economic perspective that strips the subject of its moral compass.
School mathematics has moral choices built in; perhaps the highest charge for maths educators is to make sure they are the right ones.
G H Hardy would recoil at such a suggestion. He was the most unapologetic of mathematicians, describing his subject as the one true science that is removed from real-world drivers. According to Hardy, mathematicians study their subject for its own sake, not for its utility or morality. Perhaps maths educators should cast aside questions of moral agency.
I stand with Hardy, for the most part. Tying the content and form of maths so closely to our moral agency seems far-fetched. There are too many factors that shape our moral choices. Propaganda remains the most potent weapon for neural manipulation. It is effective because it creates a chasm between our intellectual and emotional selves. It makes smart, rational people do the most horrendous things. Changing the maths curriculum may strengthen the cognitive wiring of our brain, granting us deeper facility to think for ourselves. But the ease with which our intellect and emotion are decoupled suggests that maths educators are, to some degree, helpless in their moral objectives.
If moral agency truly is a goal of maths educators, nothing short of a revamped curriculum will do. It would have to marry the cognitive aspects of maths with students’ social and emotional development. The content and form of maths would have to be shaped around real-world ethics and problems would be solved within the context of our moral choices. It may then leave us to question whether it is mathematics at all.
The conclusion is sobering, but it does give the educator in me some clarity. Moral problems have solutions quite separate to the goal of raising standards in maths. Better to be aware of that limitation than to be complacement in assuming maths education has all the answers. Sometimes, it doesn’t even have the right problems.
I am a research mathematician turned educator working at the nexus of mathematics, education and innovation.
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