Yesterday: to Essex University with a group of upper school students to try to enthuse them for the academic life… In the afternoon, we had a seminar with one of the young lecturers from the University’s Mathematics Department. I must admit that Maths never lit my own candle (possibly the result of a fixed maths-mindset at home, where the family was firmly on the arts side…?) so I confess my reservations about how engaging this would be…
But for ninety minutes, our pupils’ attention was held by a young guy with nothing more than a clear passion for his subject, a few fairly basic PowerPoint slides and a handful of challenging mathematical puzzles. Having done previous outreach work, he clearly knew his audience, and related well to them, pitching his opener at a challenging but accessible level and ratcheting it up from there. Even as an erstwhile maths unbeliever, I found it very stimulating, not least the way he demonstrated how problems can be difficult for ‘even’ maths to solve, once variables starts to increase in number. (I was left thinking about classroom applications of this: Causal Density and the impossibility of predicting the specifics of how any given lesson will develop…) But for all that he enthused about the clarity of maths, for me the success of the session was down to the distinctly unquantifiable, untechnical element of his infectious enthusiasm.
A discussion over today’s lunch-table ranged far and wide from this starting-point. At one point (the circumstances are unimportant, but they related to education) the observation was made, “If you don’t measure things, you won’t know how to improve them!”
Is this valid or not? It would certainly seem to be the case that without knowing what you’ve got, then it’s hard to appreciate it – and I suppose ‘improve’ it, always assuming it needs improving. If the aim is indeed to increase the quantity of what you’ve got, then knowing where you’re starting from would seem to make sense. And – most important in these accountable days – if you don’t measure, it’s hard to ‘prove’ there has been an improvement at all…
But this is where my habitual reservations kicked in: an increase is one thing – but an improvement is quite another. One objective, the other subjective; more is not always better. One needs to know what needs to be measured – and that it is being measured in a suitable way. Quantity is often not the only relevant factor – but quality is much harder to objectify. For all that the young lecturer promoted Maths on its objectivity, the significant thing that made his lecture succeed was inherently un-measurable in any really meaningful way.
There risks being a blind-spot in those who love the quantitative game: assuming that everything is reducible to useful numbers.
There are some things in this world that are simply not measurable in any meaningful way. Sometimes, those things are important, even critical. I would argue that the supposed lack of precision in the arts and humanities is not the weakness it is sometimes presented as, but a sophisticated acceptance of, and response to the un-measurability of much human experience, in a way that an objective approach sometimes fails to capture.
Then there are the matters of whether measuring something actually can actually help improve it – and whether we risk valuing what we measure rather than vice versa. I was reminded of the proverb “You don’t fatten a pig by weighing it more often”. And even if you do succeed in fattening the pig, there is no guarantee that the fattest pig will be the most flavoursome. Even though a recipe that involves pig products may begin with quantities of ingredients, there is no guarantee that the tastiest dish won’t have been improved by the intuitive adjustments made by an experienced chef.
I would not for one moment suggest that the relatively objective approach presented by subjects like Mathematics has no use – but I think we need to be wary of seeing it as a panacea. Those who approach life from a purely factual/logical approach may have an easily-made case – but it is not the only one with validity.
Quite often the things that really make a difference are purely qualitative, even indefinable. For example, can we really be so sure that the best teachers are simply those with the best statistics behind them? Adopting an excessively numerical approach, especially to matters as complex and culturally-laden as education, may result in our over-simplifying the nature of what we are really dealing with – and missing the very qualities that gives something its inherent worth.