I recently had the misfortune to revisit some episodes of the “math wars” — the ongoing struggle over mathematics education and curriculum, mostly at the school level. It’s an important struggle, with great ramifications for our education system, not to mention one in which I have a personal stake, being a mathematician and all. But very few professional mathematicians have been involved in them, and when they have, they have not always inspired confidence. The very worst behaviour in these “wars” has come from professional mathematicians.
Putting aside the worst behaviour (but only temporarily), I wondered why. Indeed, I’ve never gotten myself involved in it. I think the reasons are worth examining.
Immediate disclaimers are necessary regarding (1) “math” and (2) “wars”.
I say “math” rather than “maths”, because, as with many of struggles over human culture in the West, the focal point of the struggles have been in the US. Of course, those struggles have their resonances and reverberations in Australia — the turbulence splitting off an Oceanic vortex across the Pacific.
And I detest the “war” analogy. It’s not a war in any meaningful sense. It’s a policy debate with some important political-economic and ideological undercurrents. And war analogies are overused and our society is over-militarised.
So, this is a bad usage, but it’s a standard usage. Hence the scare quotes. It’s “math wars” all the way through.
So why would mathematicians sit out the “math wars”?
For myself, the “math wars” are not a debate in which I’ve often felt I have much to contribute — despite having been involved in mathematics teaching, in one way or another, for over two decades. There are several reasons.
Firstly, my experience of learning mathematics is far from average, in any sense, and so I am naturally skeptical of any attempt to generalise to others those learning or teaching techniques that have worked for me. Arguably, I look like the best but am in fact the worst qualified person to opine on the topic.
Secondly, at the school level, my teaching experience is almost entirely limited to the teaching talented or advanced students. This type of teaching presents its own challenges, but it does not reflect the average teacher’s experience in the slightest. The challenges of extending precocious geniuses are essentially completely irrelevant to the challenges of getting the average class interested in and proficient at mathematics.
Thirdly — of which I am reminded every time I actually teach — I’ve never felt like a natural teacher: a natural explainer, perhaps, but teaching is much more than that. At most, I’ve become an experienced lecturer, I know what works for me and think I do a good job of it, but I recoil from the idea that this gives me any authority to speak on what others should do.
Because, finally, all my scientific and political commitments militate against pronouncements on the topic. The mathematician’s allergy to over-generalisation, the scientist’s skepticism to the applicability of findings beyond their domain, the anarchist’s aversion to telling others what to do, the socialist’s solidarity with a class of underpaid and underappreciated workers, and the general democratic injunction against thinking you know what is best for others in their own profession — all these, when I have some idea about classroom teaching, scream in unison that in fact I don’t know the first thing about teaching the average maths class in Australian schools today, and that greatly limits what I could say about the curriculum that should be taught.
Essentially, I have enormous respect for primary and secondary teachers — they do a thankless but crucially important job, are underpaid and overworked — and for all that, suffer the disrespect of parents and students every day. Telling them what to do, what curriculum is best for their class seems not only distasteful and uninformed, but also, in a certain sense, wrong.
On a deeper level, I’ve always felt that battles over curriculum and teaching are not the real issue, and that it is really simply the policy end of a much deeper cultural problem.
Australian culture, in general, despises mathematics. It is the only essential school subject where an Australian can declare its uselessness, and generally be assured sympathy. It is the only school subject on which, generally speaking, one can confess their ignorance or incompetence and be assured of understanding rather than embarrassment, without a hint of guilt. One can confess to not being much good at geography, or history, or other sciences — and even if it is more a celebration of ignorance than charming self-deprecation, it is still a confession, with a hint of remorse. Not so with simultaneous equations and the like, upon which opinion may vary from collective recollection of terrible classroom experiences, through to vengeful abuse of the educational system.
Given that cultural status, is it any surprise that students might be uninterested in mathematics? That there might not be many students studying mathematics to a high or advanced level? That there might not be many people studying to be mathematics teachers — and hence, a shortage of qualified mathematics teachers? And hence, the reproduction of a populace which despises mathematics?
On cultural matters I tend to throw up my hands, if not in despair, then because of my inability to do anything to change it. I can explain mathematics to people, why it is interesting and fascinating and beautiful and so on. But, in news which will come as a surprise to no one, I don’t really like my chances of making it cool.
Of course, all these difficulties — general derision for the subject, declining enrolments, teacher shortages — run together. An improvement in one can lift all the rest, and a failure in one can lower all the others. But being so total makes the problem a formidable one.
And that leads to a great sense of disconnection. I feel an enormous chasm between my experience and interests, and those of the general population. Why wouldn’t everyone want to try to figure out what on earth (on earth!) this universe is, and what it is, and the mechanisms that underlie it? How can it be that not everyone is captivated by mathematical truth? Antipathy, or even indifference, to mathematics is to me an alien concept.
Of course I understand that people have different interests, and diversity of human interests is a good thing. And this chasm does not of course prevent me from trying to convince others that these topics are fascinating, nor from trying to promote understanding of these topics. And of course I’m aware that the secondary mathematics curriculum can be boring and lifeless. (At school I much preferred history classes to my official school maths classes.)
But all this does give me pause as to how to address such a radically different audience. The reality is that I am the radically different one, not everyone else.
So that is my navel-gazing examination of my reticence on the subject. And much of it will clearly generalise to the mathematical community, though much will not. Not every mathematician shares my politics or my cultural background, but I think many would feel a long way removed from classroom teaching of their subject, a sense of being cultural outsiders in their embrace of mathematics, and despite their expertise in the subject, a general lack of knowledge about what would actually work in classrooms.
But this reticence, though perhaps justified in each individual case, may collectively be counterproductive. Arguably mathematics curriculum and assessment have descended into various domains of stupidity. Arguably the whole debate would benefit from more involvement by knowledgeable mathematicians.
And as per Bertrand Russell, “The trouble with the world is that the stupid are cocksure and the intelligent are full of doubt.” Not to suggest I am at all intelligent on this matter, or that anyone else involved is not — but I am certainly full of doubt. (It’s about the only thing about which I have no doubt!) Perhaps Russell’s observation is a reason for some of us who are knowledgeable on the subject matter, at least, to put aside some doubts occasionally, as to what we can and should say.
And even though mathematicians may not know the answer to every question, one does not need to know the answer to every question. It is sufficient to be able to say something. Or even, simply to say something is bad.
This is nothing new. I grew up learning mathematics in a curriculum that was essentially universally understood by all those who taught me, and all those who I respect, to be heading in a ridiculous direction. Everyone decried the increasing reliance on calculators as a substitute for mathematical understanding. That has continued, with whole exams now written as a test of calculator usage. (Who even uses calculators any more? Phones are more powerful devices.)
Trends continue. My recent years of teaching first year university students have been marked by the steadily decreasing knowledge of incoming students. There is always some need to remove topics from the secondary curriculum, and never any room to strengthen it or include anything new. It can always be hollowed out and weakened, but never filled out or strengthened. I then have the task, in teaching university classes, of filling in the gaps and bringing students up o speed.
But these are not the main reasons I think mathematicians should say more about mathematics curriculum and teaching. Rather astonishingly though it sounds to say it, I think the most important reason why more mathematicians should say something on these matters is to make for greater civility.
Now, civility is one of the worst topics in political discourse.
One terribly overused, and bad, contemporary political argument is that extreme voices dominate political debate, and we need more civility. In one sense this is true: more and more right wing and even fascist voices have become prominent and even dominant in politics across the world in recent years. And debate increasingly happens on social media platforms which algorithmically promote extreme content because it generates “engagement”. But more usually the argument is made by centrists who decry this alongisde some supposed left-wing equivalent, such as the political movements behind Jeremy Corbyn or Bernie Sanders. There is just no comparison between their mild social democratic politics, and the resurgent reactionaries on the right. To the extent politeness or civility towards such reactionary forces normalises or strengthens them, we need less politeness or civility. Civility is not the problem here.
Even worse, the charge of incivility is often brought up against those who are genuinely and justifiably angry at the system. It can combine with racist and sexist attitudes to depict people of colour as irrationally angry, women as shrill, and so on. This sort of incivility, an expression of justifiable rage, is necessary for social change, and criticising it for its incivility is beside the point.
But the “math wars” are another matter. They arouse great passion and controversy in some mathematicians, educators and teachers. And this is a legitimate controversy, with deep political and ideological divides. But there is nothing to justify incivility, in the way that there is to justify rage against police brutality, misogyny, or fascism.
In my experience, the incivility is largely between mathematicians and mathematics educators. And the incivility is completely in one direction: by the mathematicians, towards the maths educators.
It’s not uncommon for mathematicians to express contempt for mathematics educators. It is not the only attitude, and in my experience in recent times not the most common one, but in my experience it is a standard attitude.
It’s disturbing how this contempt fits gender stereotypes. Professional mathematicians are overwhelmingly male, and mathematics education researchers are overwhelmingly female — and even if the contempt of the former for the latter is purely based on intellectual or political differences, it can easily look like misogyny.
Incredibly, the “math wars” have their own “cancel culture”. In the worst incident, though now over a decade ago, a group of prominent mathematicians tried to discredit a leading maths education researcher, and get her fired. Their accusations of misconduct which were found to be baseless, but not before succeeding in driving her out of a university position.
Legitimate criticism of the views or research of others is one thing. This was another.
This sort of incivility has to stop. If mathematicians on one side of the debate feel that they have been “losing” the “math wars”, this kind of incivility is part of the reason for it. More civil voices need to be heard. Mathematicians need to reject such incivility, and contribute in a democratic spirit.