Eugenia Cheng is one of the happy new faces of mathematics popularisation. She is adored by all. Well, almost all.
As a mathematical evangelist, Cheng wants everyone to join the Church, to fall in love with mathematics. To that end, Cheng has given a zillion talks, she writes a monthly column for the Wall Street Journal, and she has written a number of popular mathematics texts. Cheng has just released another book, Is Maths Real (reviewed here). Last week, to promote her book, Cheng had an article in The Guardian, What if nobody is bad at maths? It is not a good article.
Cheng begins in the familiar way, lamenting that people are so willing to say they are bad at maths, but that this attitude only develops later, after they are “scarred” from schooling:
But one thing I know is that when I help five- and six-year-olds with maths they typically scream with excitement, and only learn to fear it later.
Yeah, like when they have to learn to pay proper attention and do it.
The basic problem, in my view, is that in our haste to convey content – fractions, percentages, algorithms – we don’t pay enough attention to feelings.
Really? Maybe in England or America, but for primary kids in Australia the attention appears to be overwhelmingly on feelings, which is exactly the problem. Anyway, Cheng then tells us where it goes wrong:
I ask [her undergraduate art students] what they found so disagreeable, and there are clear recurring themes: memorisation, especially of times tables, timed tests, right-and-wrong answers, and being made to feel stupid for making mistakes.
Heaven forbid there be right-and-wrong answers. In maths. And again, always, with how cruel it is to make kids learn the multiplication tables. There is obviously a problem with unmotivated students, we may (and do) argue about and disagree on how to motivate them, but the suggestion that learning a few dozen patterned multiplications is arduous, or is optional, is plain nuts.
Often they felt alienated because they had searching questions – such as why does -(-1)=1; do numbers exist; is maths real – but they were told these were silly or irrelevant, and they should get back to their repetitive, algorithmic homework assignments.
We don’t believe it. We cannot remember ever meeting a maths teacher who would consider, let alone tell a student, that such questions are “silly” or “irrelevant”. A teacher may not offer much time to provide answers, and they may well suck at giving any decent answers, but for 99% of teachers that’s the worst it would get. Cheng is pretty much just making stuff up.
After, correctly, slamming Rishi Sunak for his idiotic plan to make maths compulsory to 18, Cheng goes back to fixing the problem. Which appears to be by treating kids forever as if they’re five years old:
When five-year-olds first encounter the subject, it’s as a creative, open-ended activity, involving play and exploration. They learn about numbers using colourful blocks that join up in different ways. They fit these shapes together and tell different stories with them. Just a year or two later, though, maths becomes a discipline with strict rules and a forbidding regime of right or wrong answers.
Yes, because that’s the way maths is. Eventually you have to get on with building the structure. Which comes with rules.
Instead we should try to maintain that sense of exploration and open-endedness, of trying out different approaches to a problem and seeing what works.
Really? Got an example?
What’s important about times tables, for example, is not the answers, but the different possible relationships between numbers.
Reverse mic drop.
Does one really have to point out how bad this is? Probably, not, but we’ll do it any.
First of all, of course the goddam answers are important. Secondly, yes, you want students to be familiar with, and always on the lookout for, relationships between numbers; that is, as it happens, one of the means by which the tables get solidified, and why it is simply not that arduous to learn the damn things. Thirdly, when you really get into the number relationships, you’ll do it with algebra, and there’s not a snowflake’s chance in hell of doing that with any success, or pleasure, if you don’t first know the damn tables by heart.
Cheng continues with the boringly familiar sales pitch, for the Real World and classroom gimmicks, “maintaining interest” in maths by making it less mathsy. She then takes a right-angle, and addresses the question posed by the title of her article:
The idea that anyone is naturally “bad” at maths is pernicious in several ways. It ignores the amount of work it takes to get good at it. And it does take work. But that work doesn’t need to be hard – it can be challenging, but with a sense of adventure and ultimately reward, rather than discouragement.
Well, no and yes. That work does kind of need to be hard. That’s the nature of work: it’s work. But, true, the work can be enjoyable and satisfying along the way. However, work aside, it doesn’t mean some people don’t just suck at maths. But apparently suggesting this as a possibility sends the wrong message:
The “bad” trope also provides people with an easy reason to give up, and the education system concurs by writing them off as fundamentally unsuited.
We’re anything but an apologist for “the education system” – ask ACARA – and we regard as unmitigated evil the premature writing off of kids who were never given a proper chance to enjoy and to excel at mathematics. But there is still reality to deal with.
As it happens, we don’t see that it matters to a teacher whether the student in front of them is “fundamentally unsuited” or not: the student is what they are, for whatever reason, and the teacher deals with what they’ve been given. But on the larger scale, truth matters.
Cheng closes with the obligatory “it’s not your fault” bit:
One thing is clear: if you think of yourself as belonging to the “bad at … ” camp, it’s not because you failed maths. It’s because maths failed you.
We really wish these popularising superstars would spend less time earning easy adoration and more time telling people the hard truth of what it takes to not fail at maths.