The Quality Assurance Agency for Higher Education is a UK body, “an independent charity working to benefit students and higher education”. QAA proposes and checks upon standards for higher education, with some degree of authority. In September, QAA released for public consultation its revised Subject Benchmark Statement on Mathematics, Statistics and Operational Research (MSOR). Compared to the 2019 Statement, the 2022 draft Statement has been most noted for the introduction of a “cross-cutting theme” of “equality, diversity, accessibility and inclusion”, as well as themes of “sustainable development” and “employability, entrepreneurship and enterprise education”. The draft is bad.
The mathematician John Armstrong wrote and publicised an open letter, subsequently signed by other mathematicians, strongly objecting to these and other aspects of QAA’s draft Statement. Armstrong’s letter is well-written and covers the ground well. The draft’s headline absurdity is a call for “decolonising the curriculum”, which Armstrong tears to bits. This headline absurdity, however, has distracted people from other problems with the draft, and more generally from considering the intrinsic dangers of such quasi-authoritative statements.
First, to semi-clarify the regulatory status of QAA’s benchmarks, the draft Statement notes that QAA Statements “are not sector-recognised standards” under England’s regulatory framework. Elsewhere in the UK, however, QAA’s Statements have a more official status. In Scotland, which ironically might be feeling a bit like a colony right now, QAA’s Statements are “a key reference point … for academic standards”. Whatever its official status, the draft reads as if it were official. The language is unceasingly of certainty and necessity and urgency, of an unquestionable authority.
I will quote and slap specific aspects of the draft Statement, but I first want to raise a general objection, which Armstrong also touches upon: ignoring the obvious absurdities of the draft, what is the supposed good purpose of such a benchmark statement? How are from-on-high “benchmarks” for all tertiary courses on mathematics and/or statistics and/or operations research in the entire UK going to benefit anyone? If the benchmarks are too specific then they will not fit many institutions, if any; they will encourage or demand a boring uniformity, and probably a dumbing down. If, on the other hand, the benchmarks are couched in general terms then they are effectively just motherhood statements. Except, these motherhood statements, always framed in terms of students’ needs and students’ rights, and never in terms of students’ responsibility for themselves, become a weapon, which is then happily wielded by every lazy malcontent who expects an A for doing bugger all work. Unless one is Mother Theresa, honest attempts at motherhood don’t cut it anymore. Academics have already been beaten into submission by university administrations’ feeding, and feeding upon, the ever-strengthening culture of narcissism. Statements from organisations such as QAA inevitably make it worse.
For specifics, QAA’s draft Statement makes for easy pickings. The easiest such pickings are, of course, in the section on equality, diversity and inclusion, beginning with the very first line (1.21):
Equality, diversity and inclusion (EDI) is essential for the health of MSOR …
Yeah, we’re all for peace, love and understanding, but what does the statement mean? What, exactly, is essential, and why? If the subsequent paragraphs are intended to clarify, they are not reassuring (1.23):
Values of EDI should permeate the curriculum and every aspect of the learning experience to ensure the diverse nature of society in all its forms is evident.
Yes, “permeate” and “every aspect”. They are not thinking small. Or thinking. Let’s continue (1.23):
MSOR providers should reflect on their curricula and processes to ensure that no group is disadvantaged or othered;
There’s a group right now that I’d really like to be othering, but let’s get to the headline absurdity (1.23):
for example, decolonising the curriculum can involve explicit reflection on the history of MSOR knowledge generation, as well as reflecting on how delivery or admission practices might adversely impact on certain subgroups within the student cohort.
Remember all that eurocentric history you got in your linear algebra class? Well, no more. The era of white male scalars is over.
The obvious point, which Armstrong hammers, is that there is essentially no history in standard mathematics classes. This may be considered regrettable, and it is reasonable and good if a lecturer wishes to include some history in their already crowded subject, either as a little catch-your-breath colour or more intrinsically. If so, it may be natural to mention critical contributions of non-European individuals and cultures. Which pretty much any lecturer would already do, without the hectoring to do so. But for QAA to be pushing the incorporation of a specific view of specific history to serve a specific political agenda is obscene.
To continue (1.25):
It is imperative that students encounter a wide range of role models within higher education. This is particularly important given the well-known gender imbalance in the subject …, retention and attainment gaps, …
Maybe. I’m yet to be convinced that the role model thing is all that relevant, and there is a troubling resonance. Calls for role models can lead to dark waters. But continuing (1.25),
… and the strong focus of curricula on the historical work of white Western males.
The white Western males who are rarely if ever mentioned, and even more rarely discussed or pictured. And if so, then so what? What do you want us to do? Change history? Wear a hair shirt for some ills of the past?
To continue (1.25):
There is a need for inclusive language and scenarios in all publicity and teaching material, and for courses to be informed by the student voice …
Always with the “student voice”, as if no one is now hearing it loud and clear, or that anyone has any choice in the matter. Let’s go on (1.25):
… and taught in a way which makes the resources meaningful to all students and with topics and examples which have relevance to a wide range of people.
Because if it is not demonstrably relevant to the student, it’s not worth learning.
This interminable section on EDI then continues with a list of “implications for all aspects of provision”. It includes a second call for “visible diverse role models, … diverse staff in all roles”, and then it’s back to micromanaging the curriculum and more decolonising (1.26):
the curriculum should present a multicultural and decolonised view of MSOR, informed by the student voice. Where possible, it should present the work of a diverse group of MSOR practitioners. Students should be made aware of problematic issues in the development of the MSOR content they are being taught, for example some pioneers of statistics supported eugenics, or some mathematicians had connections to the slave trade, racism or Nazism.
Yes and, mostly, no.
There is plenty more to criticise in QAA’s draft Statement. In particular, I wanted to attack the snake oily section on “enterprise and entrepreneurship education” (1.49-1.60), and the pushy section on “sustainability” (1.44-1.48). But it’s probably more important to stick to QAA’s nazis.
There is something dangerously obtuse about QAA’s campaigning for students’ awareness of “problematic issues”. It may well be natural to mention that some important mathematicians were less than exemplary human beings in their research. If one is teaching game theory then noting that Von Neumann was almost literally Dr. Strangelove seems well worth the digression. It shouldn’t be mandatory, but it’s not stretching to suggest that such connections be made. But then QAA pushes too far. Why “should” students be made aware of “connections to the slave trade, racism or Nazism”? What purpose is there to this other than to play yet another round of Good Guys And Bad Guys, a game with nothing intrinsically to do with mathematics?
The important mathematicians Oswald Teichmüller and Ludwig Bieberbach were full-blown nazis. Felix Hausdorff, pictured above, was a German Jewish mathematician, who committed suicide rather than be sent to an internment camp. I only read about Hausdorff’s tragic end a few years ago, and I was struck and saddened by the discovery. If I had known when teaching my course on measure theory, I definitely would have talked to the class at least some about Hausdorff’s life; I then may well have brought up nazi mathematicians. I don’t think I “should” have, but I probably would have. If someone had more or less ordered me to do it, however, I would have told them to bugger off.
There is more that could be said. There’s a double-edge to much of what QAA is attempting to mandate. But that’ll do. QAA should simply be told to bugger off.
Decolonising mathematics is big in the UK. Maybe Australia is next.
It’s already underway.
And the ACARA curriculum is leading the way.
Not to mention many universities now requiring their students to complete various cultural awareness modules (in order to be eligible to attend exams, access results, graduate etc) and requiring cultural awareness statements to be included on submitted assessments (under sufferance of losing marks otherwise).
It’s only a matter of time before mathematics identified and labelled as ‘European’ (by some gormless administrator trying to earn woke brownie points) is banned from the classroom because it’s deemed non-inclusive and insensitive.
Thanks, John. I’m willing to consider ACARA being guilty of everything up to and including the Kennedy assassination. But what is your evidence that ACARA has embarked upon this particular crime?
To be (un)clear, terms such as “decolonisation” can be less or a-little-more precise. QAS never define what they mean by the term, which is ridiculous. But the general “cultural awareness” thing, whatever its merits or otherwise, and whatever the merits or otherwise of its means of enforcement, is not in the same category as altering subject content.
Plenty of pushy material, such as QAS’s is vague to the point of meaninglessness, and slides dangerously from one concern to another. Attacks on such material should avoid the same errors.
Re: “But what is your evidence that ACARA has embarked upon this particular crime?”
The amount of gratuitous links to Aboriginal and Torres Strait Islander mathematics. For example:
“within the probability and statistics strands, stochastic reasoning is developed through Aboriginal and Torres Strait Islander instructive games and toys.”
Cultural links to mathematics (and a general appreciation of the history and philosophy of mathematics) is a very good thing. But not when so many of the links are so strained, embarrassing and plain silly. The agenda motivating the curriculum and its links is here:
https://www.australiancurriculum.edu.au/f-10-curriculum/cross-curriculum-priorities/aboriginal-and-torres-strait-islander-histories-and-cultures/
When I learn and mathematics, I don’t deliberately look to see myself, my identity and my culture reflected in the mathematics (*). I just look at the mathematics. The purpose of making cultural links is noble and good, but the execution is becoming more and more political and sinister.
* Must we see this before we can appreciate the beauty of what we’re learning? Can we not learn something purely on its own merit?
No. This is exactly the kind inaccuracy I’m asking you to take care to avoid. To my knowledge, ACARA never refers to anything like “Aboriginal and Torres Strait Islander mathematics”.
There is a massive difference between using aspects of indigenous culture to illustrate mathematical ideas, and claims of indigenous mathematics. The former may be natural or contrived, but don’t overstate what ACARA is doing. Or at least provide clear evidence.
You may well be able to make your case with ACARA’s science curriculum: I haven’t looked carefully, but it seems likely. I don ‘t think you can make the case, or at least not as easily, with the mathematics curriculum.
I don’t want this blog to become an idiotic episode of Sky News, where people feel free to fire a shotgun at an over-general target, without care for exactly what the target might be, or what might be hit.
OK, I see what you mean. I might look at the science curriculum later (unless I’m beaten to it).
Hmmm. There was a mathematician who collaborated with ACARA, Matthews somebody? Did he give some talks? I feel like I saw a talk by him where he mentioned decolonising math explicitly.
Perhaps ACARA were a bit careful on this point.
Yes, Chris Matthews, although the nature and extent of his role is unclear.
Yes, on the face of it, it seems ACARA was careful on this point, but it is weird. They were certainly more than happy to pile on the ATSI elaborations, many of which show no care whatsoever. And, as I suggested in reply to JF, I don’t know that the Science curriculum is so reticent to make pretty profound claims.
For what it’s worth, here is a link to the ACARA Science Curriculum:
Click to access science_all_elements_f-10.pdf
Certain patterns become evident as you scroll through it.
Glen, Chris Matthews is the name you’re looking for.
He “was a senior curriculum advisor for the Australian Curriculum, Assessment and Reporting Authority (ACARA) for the National Mathematics Curriculum where he worked to include Aboriginal and Torres Strait Islander perspectives in the curriculum.”
I would still not jump to (and will delete) conclusions assigning too much credit/responsibility/blame to any one individual.
Bravo! This WOKE approach to history is now contaminating mathematics. Last week my attention was drawn to a NOVA presentation titled “From Zero to Infinity,” on the history of mathematics. It gave disproportionate credit to the Muslims and the Hindus and downplayed the European contribution. In its treatment of calculus, it talked about the computation of the area of a circle by slicing up a pizza, while avoiding any reference to Archimedes or Newton. Anyone who didn’t know the history of mathematics would have thought that mathematics developed mainly from outside Europe. There was an obvious attempt to change the relative contributions of the different ethnic groups to the development of mathematics. Those who promote the WOKE agenda justify the distortion of history with the assertion that we must encourage non-whites and females to study mathematics by giving them role models of their own ethnicity or gender.
My concern is that, in recent decades, we have been attempting to atone for the previous discriminatory abuses, by establishing a policy of reverse discrimination. The egalitarian agenda was behind the recent denial of giftedness by the California Department of Education. An ongoing witch hunt in the egalitarian movement seeks to purge history of any references, however accurate, that might show unequal contributions by ethnicity or gender. This so-called quest for equity continues to pervade all academic study, including mathematics which has been called, “racist.” I have great sympathy for anyone who wants to write a history of classical music if the world demands a balance by race and gender.
Of course, my opinions could be dismissed as reactionary and defensive. However, it seems axiomatic to me that any writing of history should be objective, with facts presented as accurately as possible, providing all the events, including the good, the bad, and the ugly. Refusing to teach the history of the development of an academic discipline would be tantamount to the Soviet Union prohibition of the study of genetics.
Thanks, Brendan. You have a lot there, but some brief thoughts in reply.
1) I avoid using, or responding to, the term “woke”. Perhaps there is no better term, but for me it is too vague a term to be of use, and ends up simply being an insult. (Not that I’m intrinsically against insults …)
2) I guess I’ll look at the NOVA documentary although I’m not looking forward to it, for reasons I go into here. However, without having (yet) watched the documentary:
(a) I would have thought naturally to refer to “Indian” and “Middle Eastern” contributions, rather than “Muslim” and “Hindu”, particularly if you want to pick fights about contributions relative to “Europeans”.
(b) Such civilisations, however they are termed, deserve plenty of credit. It would surprise me if the NOVA documentary gave them undue credit, but I’ll watch.
(c) If, as you suggest, the human aspect of European contributions is relatively downplayed, that would be odd. Again, I’ll look.
(d) I tend to agree on the role model thing, but I’ll have to watch.
3) I don’t know anything about the Californian “giftedness” issue to which you refer. If you suggest what to read, I’ll try to look. There is no doubt, however, that there is a general push towards mediocrity, and a disdain, if not contempt, for excellence. It’s why I posted this and this, and pretty much why this blog exists at all.
4) I don’t think history is so easily characterised as objective or otherwise but, yes, that doesn’t mean we cannot call out blatant lying when we see it.
5) Indeed, the Soviet genetics example is depressingly pertinent. John Armstrong points to a couple pretty appalling examples, similar in nature.
6) Clearly your views *are* reactionary. So are mine. I don’t regard the label as derogatory.
I’ve now watched the NOVA documentary. The main thing is that it is bad, to the point of being painful to watch.
I thought the parts on the Indian and Middle Eastern contributions were mathematically fine. I didn’t like them, for the same reasons I didn’t like any of the documentary, but I had no particular objection. I agree, however, that having come to the topic of infinity, and having previously emphasised so much the human element, the lack of reference to greats such as Archimedes and Newton was notable, and unbalancing, if just artistically.
Was this omission of European Big Guys a conscious tipping of the scales? I’m not so sure. There was consideration, for example, of Hilbert and Cantor and Zeno. Moreover, there were plenty of places where the documentary jumped awkwardly or had strange weighting; this felt to me like the consequences of an amateurish script and poor editing, rather than of planned manipulation. Still, it seems clear that documentary has a “give the other guys a go” agenda, so who knows?
When I have taught students about the history of mathematics, we concentrated on mathematics. We read three original works in translation during the semester: the Rhind Mathematical Papyrus (Egypt), Euclid’s Elements, and Fibonacci “Liber abaci”.
Attached is a picture of my class on Euclid in Papua New Guinea in 2014.
Lovely photograph.
Your first sentence is SPOT ON! Hear hear.
CRAZY IDEA:
If we take the QAA’s premise of the mathematics community needing to reform as a given (which is contentious) would the following be sufficient- the declaration of a mathematical “year 0”
This would involve the renaming and rebadging of mathematical concepts/theorems to remove all indicators of sex, gender and race and to have the previously named mathematical concepts given more utilitarian names e.g. The Cauchy-Schwarz Inequality be renamed as the Inner Product Inequality. If a respected professional organisation such as the MAA did this rebadging and it was accepted (by other mathematicians) then it would take about a decade before this new terminology would become the standard. And the maths would stand alone as gender neutral, asexual and non-racial.
The question needs to be asked. If the mathematics community made this huge concession and put its house in order under its own volition would the QAA consider mathematics as a whole to now be more inclusive and equity focused?
If the QAA would be unsatisfied with this then I think that it’s position would be unjustifiable and rightly rejected.
I doubt they really know what they want, except for history to be different.