Belabouring the Real World

Bridget Phillipson is UK Labour’s shadow minister for education. She is proposing a new program, “phonics for maths”, which sounds like a good thing. Countering Rishi Rich’s idiotic demand that everyone study mathematics until they’re 50, Phillipson gave a speech a few days ago, with a decent chunk on primary school mathematics:

“Maths is the language of the universe, the underpinning of our collective understanding. It cannot be left till the last years of school.”

“… it’s why I’m proud to tell you today, that we’ll tackle our chronic cultural problem with maths, by making sure it’s better taught at six, never mind 16.”

Great. And how is Labour to do this? Well,

Labour says it will replace Rishi Sunak’s demand for compulsory maths classes until 18 with improved maths teaching for younger children and “real world” numeracy lessons for pupils in England.

Bridget Phillipson, the shadow education secretary, will tell Labour’s conference in Liverpool that its curriculum review would “bring maths to life for the next generation”, using practical examples drawn from household budgeting, currency exchange rates for tourists, sports league tables and cookery recipes.

Not quite. Phillipson tinkered with her speech after feeding it in advance to the media. So, “real world” is no longer there. But, the real world message is:

“Because be it budgeting or cooking, exchange rates or payslips, maths matters for success.

And I want the numeracy all our young people need – for life and for work, to earn and to spend, to understand and to challenge, I want that to be part of their learning right from the start.”

Yep just like phonics, which is, of course, all about the real world.

These people are always the same, the emphasis on “the real world” demonstrating only that they understand nothing of mathematics education. Greg Ashman responded perfectly to a tweet making this point: “It’s a ‘tell’ as the poker players would say”.

Phillipson may have deleted “real world” from her speech but there are still plenty of tells.

19 Replies to “Belabouring the Real World”

  1. Maybe Marty had a rough week!

    1. Sunak’s “maths to 18” is not entirely idiotic. After all, rather a lot of countries seem to do something similar.
    The idiotic thing is to use school maths to make political headlines, without first addressing the underlying issues (well-documented weakness of lower secondary maths teaching in England; lack of maths teachers; etc.). Failure to address these first means that those continuing maths to 18 are unlikely to benefit (repeating previous failure, building on sand, without any professional craftsmen, etc.).

    2. You say (perhaps flippantly) that Phillipson’s “phonics for maths”, “sounds like a good thing”.
    Does it really?
    Phonics became compulsory here in 2014.
    The school maths equivalent sounds to me like “arithmetic” (working fluently with numbers in terms of how they are made up from components, via addition and multiplication) – which has been with us somewhat longer.
    So it is a headline slogan with no obvious content.
    Again we see the same crass error: using maths to make political headlines, without thinking things through.
    This was pure playing to the gallery. I cannot trace anyone competent who may be serving as her adviser on such matters (but I am well out of the loop). It seems to stem from .
    The report is worth reading; but it is commissioned by two unions, and produced by a lobby group that was Conservative – until it saw the writing on the (red?) wall.

    1. Thanks, Tony. As it happens, I have indeed had a rough week: idiots to the left of me, idiots to the right of me. But, I still regard Sunak’s maths-to-18 thing to be idiotic. At least the version of such things in Australia seems to me to be idiotic. The later year “maths” for the weaker kids seems little more than watered down versions of the maths the kids didn’t get in the previous twenty-five years.

      As for “phonics for maths”, yes it does sound good to me. Of course it’s not everything, but God I wish the Australian curriculum had something phonicsy for early maths, rather than learning addition with Aboriginal dancing.

  2. Not quite as bad as the odious Michael Gove, former education secretary for England, demanding that all children achieve above-average test scores (2016).

    1. BiB: I hesitate to “defend” Michael Gove. But here goes.

      Teachers are often “political” underneath – without being active, experienced politicians. So it is tempting for them to trivialise matters by picking bogeymen. Michael Gove is a natural candidate.

      I’m not sure whether they register in Australia, but two other such popular ‘bogeymen’ among teachers here are Nick Gibb [who has been the ‘number two’ Minister for Schools more-or-less since 2010], and Dominic Cummings [who was Gove’s “special adviser” 2007-2014 in Education, and subsequently ran the Brexit campaign before becoming Boris Johnson’s “adviser”].

      Everyone in politics has their flaws – and none of these three are exceptions. (I remain in contact with two of them; and the other I met several times and partly knew.) They are not specialists. So they need advice/support. And they get this from all directions – so your, or my, advice is most unlikely to be blindly followed: it has to compete with all sorts of other inputs.
      Hence, the distinction one should make is between those politicians and officials who want to improve the lives of ordinary voters, and those who are merely driven by personal ambition, by factional interests, or who bend with the wind.

      I prefer to focus on their strengths as well as their limitations, and to consider what they actually achieve.

      All three (of Gove, Gibb, and Cummings) have made remarkable contributions (not all positive!) to education policy in the UK in the last 15 years.

      After 2007, we had been left (partly thanks to an appalling Australian – KGB) with a curriculum probably far worse than ACARA’s current version. Neither teachers nor educators had lifted a finger against it. So we owe a lot to Gove and Co for having had the courage to reverse this, to introduce phonics, and to press for and to try to consolidate more coherent maths teaching in primary schools. Mathematics educators responded by resisting these (basically sensible) changes, and by using bogey-words like “odious” (which may be partly true of Gove, but which is unanswerable, irrelevant, and scarcely a serious argument).

      Gove is not an attractive character (just as Albanese is not as photogenic as Gough Whitlam); but it is not easy to climb the political greasy pole in a class-ridden country like the UK, having been initially “in care”, and then adopted – as Gove was.
      When a politician wishes to point out (as Gove did) that “educators are colluding in keeping achievement low”, and that, given the chance, almost everyone could do an awful lot better, it can easily be misconstrued in the media as suggesting “everyone can do better than average”. What was clear (and I plead guilty for repeatedly saying as much in print) in the UK in the late 1980s and 1990s was that, if we improved certain things, then, *by the end* of 10-20 years, almost everyone could be achieving better than the average *at the beginning* of that period.

      The actual out-turn was not quite as good as this bold prediction. This was only partly due to Covid. The main drag has always been the conflicting “noise” from different factions, and the difficulty of getting a complex system to deliver. However, it is hard to dispute that the international evidence indicates some kind of progress along the predicted lines:

      (a) For international assessment of reading we have PIRLS 2021:
      “After a decline in performance between 2001 and 2006, average achievement increased steadily [in 2011 and in] 2016. Between 2016 and 2021, the average reading achievement of year 5 pupils in England has remained stable. The stability of the trend in England between 2016 and 2021 [contrasts with] the overall trend internationally over this period. The International Median dropped 19 points between 2016 and 2021, and [unlike England] most education systems scored significantly lower in PIRLS 2021 than they did in PIRLS 2016.”

      (b) In England, for international comparison of Year 5 pupils in mathematics, we have TIMSS, where the average scores for England were: 1995: 484; 2003: 531; 2007: 541; 2011: 542; 2015: 546; 2019: 556.
      And on page 41 of the 2019 TIMSS International Report we see that:
      In 1995, 54% of Year 5 pupils scored at or above the “Intermediate Benchmark” of 475 (which may serve here as a first approximation to “the top half”, or “above average” at that time). In contrast, in 2019, 84% of Year 5 pupils scored at this level (which may serve here as a first approximation to “almost all”). [The Australian figures are 1995: 61% (i.e. better than England), and 2019: 70% (i.e. worse than England).]

      The point that Gove and Co were making is that we were selling our children short and could do much better. [Notice two things: First that the reported “improvements” are in fact of limited value, because they did not lead to the subsequent improvements at secondary level that should be the goal. Second, the measured “improvement” in primary school maths started after 2000, when the previous administration made the same “odious” observation.]

      Gibb is widely vilified by teachers. Again, he is an easy target. His instincts are very “conservative”. But even before he came into Parliament, he could see that the progressive, post-modern initiatives constituted child-abuse and a waste of state funds (in the 1980s his mother had to close her primary classroom door to conceal the fact that she insisted her pupils should still learn their tables). So, when he became Shadow Minister for Schools in 2005, he went and looked for evidence (as much as any politician ever does). Later he stuck it out in the same job, beavering away, despite the antagonism of the profession and despite never being promoted, for longer than any politician in living memory. (I recommend an extended interview he gave to one of our best political observers and analysts which was broadcast last week if it is accessible: .)

      Cummings is even more of a public bogeyman – largely unfairly. Underneath he is a very gentle (but very intense) character, who happens to be very thoughtful, very bright, and who is mathematically literate in a way politicians almost never are: Whereas most of us operate on a very small canvas (and so fail to see how our own little world fits into the bigger picture), he is a “strategist” (and so can misjudge how a sensible-looking major change might affect, or be undermined by, less obvious features of the larger canvas).

      1. Thanks very much, Tony. You’ve mentioned “KGB” before, but I don’t know who that is.

        You wrote,

        “Hence, the distinction one should make is between those politicians and officials who want to improve the lives of ordinary voters, and those who are merely driven by personal ambition, by factional interests, or who bend with the wind.”

        One should also sub-distinguish the politicians who want to improve the lives of ordinary voters: between those who have the intelligence and humility to succeed, and those who are too blinkered in their ideology, too arrogant, or just too plain stupid to do so.

        I have no opinion on Gove or Gibbs. But Cummings? If you really want to defend him, feel free to give it a go.

        1. I’m not here to defend anyone (even myself) – especially in maths education (which is tough territory). I simply observe that knee-jerk pigeon-holing of hate figures does not help – and is often way wide of the mark. It is also potentially futile to try to defend someone when everyone present already seems to have swallowed the Big Lie.

          Most of us live out our lives as “Little Guys” – away from the spotlight. But we depend on that small number of souls who are prepared to risk the larger stage. Increasingly, that stage is restricted to celebs and chancers – from Katie Price, to Donald Trump, to Russell Brand. And many of those who start out as idealists, thinkers, and analysts get sucked in to this superficial culture, and cease to be of any serious interest. So I value those who refuse to play safe, and who try to focus on the issues – even where the issues are difficult for one person to grasp, so that mistakes are inevitable.
          Rather than read my words here, I encourage us all to struggle with .

          Cummings’ difficulty is that he is both a thinker and a doer. Very few serious thinkers/analysts ever get the chance to be serious doers; and if they get the chance, it is rarely on the same scale. So what should one do if one gets the chance, and discovers the extent to which “the system” is not fit for purpose? Should one try to change it (and risk resistance and failure)? Or should one accept that the risk is too great, and leave things roughly as they are?

          Almost everyone on this list will sympathise with a thinker/analyst who concludes that the school system in country X is not quite as God intended it to be. Having reached such a conclusion, we each try to respond every day. But we are small-scale practitioners, and hands-on builders; so our response is on a corresponding small scale, and designed to address/fix specific flaws or opportunities. (Whatever Marty’s adolescent self might claim, when this site criticises ACARA, or VCAA, or particular items in particular textbooks, or whatever, these are “local” comments, consistently aimed at enlightenment and improvement; they are only indirectly the seeds of potential revolution.)

          But politics is different.

          Politicians (and political analysts) are *not* practitioners. The best *ordinary* politicians probably restrain themselves by listening, trying to understand, and identifying small tweaks that might cumulatively lead to some kind of steady improvement, or improved awareness. But what if you aspire to being an *extraordinary* political analyst?

          If one is young, and deeply convinced that the system needs more than “tweaking”, the sensible (conservative) approach may not appeal. Yet, even if one’s analysis is more-or-less correct, and one’s vision/proposals is/are 90% sensible, their implementation still depends on *others*. Lots of others. And these others are children and beneficiaries of the system one is trying to change; so they may not see its flaws in quite the same way, and may value things which are threatened by one’s grand proposals.

          There are areas of policy where a serious change of paradigm, or approach, can lead to significant improvement. But education (and especially maths education) is not really like this. I don’t know exactly how Cummings landed as Gove’s adviser (he was Director of Strategy for the Conservative leader Ian Duncan-Smith 2002, aged 30, and became Gove’s adviser 2007-2014); but I suspect education may simply have been where his first *specialist* policy opportunity arose.

          Young guns can often see the weaknesses in a system, but may be less inclined to treasure its stabilising features. In 2010, impatience was entirely appropriate. In 2007, KGB (Ken Boston – plucked from NSW*) had delivered a curriculum turkey, which invited a serious “conservative” response. And when Gove and Co landed in power in 2010, one could sympathise with the observation that Department for Education officials and structures were part of the problem. Gove, Gibb, Truss (yes she!), and their main advisers had little experience of the wider system (e.g. state schools!). They worked hard to understand details (e.g. of school maths), but politics sometimes got in the way of insight. They got some things right; and some things wrong.

          When things are a mess, and one comes into power, one has to decide the best way to achieve positive change. Upheaval may be intended to have a certain beneficial effect; yet it may fail, because it overlooks a number of key features. But I am reluctant to simply condemn – unless there was then failure that was eminently predictable.

          It is hard to assess Cummings’ influence on *education* policy 2010-14. On Brexit (2015-16), Boris and Co did not expect (or wish) to win the referendum, but Cummings and Co delivered. 2016-19 witnessed a kind of gentlemen’s civil war, which can have done nothing to moderate his assessment of the problems.
          When Boris became PM, Cummings knew that he would be a national liability, but decided to risk serving as his adviser on three conditions (which he viewed as potentially sufficiently beneficial to the country to justify the risk). He then decided (probably long before most others) that Boris was much more of a disaster than he had thought, but soldiered on (to no obvious personal benefit).

          And as a person? Such things are private. But we should all know to mistrust conventional wisdom (which has become far more untrustworthy of late).

          * KGB: “His previous positions had included director-general of education in South Australia, and general manager of educational planning and policy in Victoria.
          In 2001 Dr Boston – his PhD is from Melbourne University – was made an Officer in the Order of Australia for services to education and training.
          He is a fellow and former president of the Australian College of Education, a fellow of the Royal Geographical Society, and a fellow of the Australian Institute of Management.”

          1. Thanks again, Tony. I’ll read carefully what you’ve written, in both your comments, and I’ll read the Cummings post to which you linked. (Other Cummings posts appear to be paywalled, but presumably they are of less relevance?) It’ll take a few days for me to get to it, and to reply.

            For now, I’ll make a few more general comments, which don’t address the substance.

            (1) There has always been a football team aspect to political and social debates: you barrack for your team, the ref is biased against you, and so on. This seems to be getting way worse and is often absurd. The retractions from the Harper’s letter come to mind.

            (2) I try pretty hard to avoid such knee-jerk barracking on this blog, to concentrate upon the substance of issues. That has included, in particular, defending/applauding people that most readers of this blog would loathe. Most notably, I (mostly) applauded Alan Tudge for his opposition to ACARA and for his attempt to have the new Australian Curriculum be halfway decent.

            (3) Still, a person may have done something notable and valuable while accumulating a history of awfulness. Alan Tudge is such a person. He is an asshole. This does not negate that Tudge was right and strong on the Curriculum, but his correctness on the curriculum only marginally mitigates his general assholeness.

            (4) Similarly, it is quite possible that Cummings, for instance, was good, or great, on education, but with plenty otherwise to trigger contempt or disgust. I won’t argue that here (at least not yet), except to pick up on one point you made. If Cummings didn’t realise, years before becoming his advisor, that Boris was an unprincipled and dangerous Born to Rule grifter, then Cummings was working *very* hard to not realise it.

            1. Marty and this blog are unusual in being willing to take to task those who set themselves up as public figures, and to challenge their views and their actions. That is much needed.

              But while we should assess (and if necessary, criticise) the actions and views expressed by such players as part of open debate, I suggest we should be more understanding of (a) those who do *more* than think pure thoughts in the pub; and of (b) those who *go further* than putting sensible-sounding ideas in writing.

              It is already a struggle to sort out how to teach subject X (subtraction? fractions? …) to group Y (choose your target group).
              To assess broader policy (as a head of department, or as a guru for other teachers, or as an adviser to ACARA) is a tougher challenge.
              To master the political and bureaucratic processes to the point of being able to implement anything at all on the wider stage is a completely different, and much rarer, skill; and we need to value those among this group who remain basically honest, and not be too judgmental about the compromises they have to make.

              If I am a 30 something adviser, my role is to tag along with someone who seems tolerably sane and to help them do slightly better than they otherwise would. I should perhaps hesitate to serve Ivan-the-Terrible. But, if there is some prospect of advising Boris-the-not-so-Terrible in a way that delivers something valuable, then I help no-one by walking away to protect my own “purity”.

              1. Thanks, Tony.

                I’ll confess, I find it astonishing that I have wound up so tough on Australia’s educational authorities and experts, and their Glorious Leaders. It didn’t start that way, not even close. But, God, they deserve it.

                As for Boris, I’m not gonna say he’s Ivan the Terrible. But I don’t think Dominic can be too surprised or consider it too unfair if he wound up with a lot of fleas.

      2. Tony, many thanks for your detailed, thoughtful and insightful reply (and apologies for not thanking you earlier).

  3. The most important Gove-Cumming innovation by far (so much more significant than tinkering with curricula exams etc) was the quasi-privatisation of the school system.

    Local education departments were largely broken up, and schools turned into independent ‘academies’. These academies were then allowed to group into a multi-academy trusts, each containing a number of schools – possibly spread out across the country. Rather like the Victorian charity schools with which mass education began in England, they attract the earnest ‘philanthropy’ of finance executives and Conservative peers and, naturally, are managed by their own new very highly paid executive class:

    And there is a new ballooning industry of ‘education law’ – with thousands of solicitors now managing all the contracts entered into by these pseudo companies (a friend of mine is an expert in this, and freely admits to me that his job – and hundreds like it – was simply unnecessary in the old, public service days)

    In fact, England and Wales are now close to the point where it is no longer possible to even talk of a ‘state education system’. The academies aren’t even obliged to follow the national curriculum that Gove was heroic enough to reform –

    Maybe the education system in England has improved as a result of all this, but the PIRLS statistics quoted above by Dr Gardiner do not strike me as triumphant – they certainly don’t come close to what was promised. And there is no clear evidence that the new, semi-privatised ‘academies’ are any better than those schools left in the old system –

    The Blair Labour government renamed the education department to be the ‘Department for Children, Schools and Families’. I can imagine that this would be the sort of change that would get many regulars on this blog into full-on sneer mode, but it reflected the social reality – ‘educating’ children is a complex, social business, from which housing, poverty and working conditions cannot be bracketed off. Gove and Cummings, of course, had no time for this kind of sociological waffle, and changed the name back again: schools for them were about learning – oh and utopian thatcherite experimentation.

    I can accept ‘industrious’ and probably even ‘clever’, but the suggestion that Dominic Cummings might be a ‘thoughtful’ man is baffling.

    1. Joe Pugh is quite correct in indicating that *systemic* changes have a major impact. The problem is that we find it hard to address the impact of such systemic changes without our own politics, or social philosophy, getting in the way. The great strength of Marty’s blog is its determination to be guided (as far as possible) by the interests of mathematics for human beings, and to focus on *mathematicalcrap* rather than political crap: if something is called out here, it tends to be because it gets in the way of kids learning (and teachers teaching) of *mathematics*.

      So while I share JP’s general concerns, and while I suspect we could agree on many things, his unstated (but nonetheless fairly visible) convictions may be a distraction. All I was trying to suggest was that name-calling and over-simplification are best avoided. The TIMSS and PIRLS scores suggest one should not simply rubbish recent changes: they show that significant change is possible (though in TIMSS I stated that what had improved was not what is needed at secondary level – as indicated by the Year 9 scores). The “academisation” programme was a wrong solution to a real problem, which – like the Emperor’s New Clothes – noone had the balls to challenge. JP’s version is much touted in The Guardian (Fiona Miller et al): for me it is wide of the mark – but my view is irrelevant! Every teacher operates in a system with serious flaws. We may disagree about the exact nature of those flaws, yet we can set this aside and focus (just for now) on how to teach mathematics better within our given context.

      (I agree that one can call the English academisation programme “quasi-privatisation”. I agree that it is truly ghastly. But it was an attempt to respond to the fact that local accountability via school boards, or local authorities, consistently failed to tackle poor provision. The approach was well in train long before 2010. If I were to blame any “adviser” or junior Minister, then I would go for Michael Barber and Andrew Adonis from the Labour government around 2000. Subsequent administrations – 2010, 2015, and the next Labour one in 2024 – all lacked the vision to go into reverse gear. I have absolutely no reason to associate it in any way with Dominic Cummings, but I am happy to be put right off-air: .)

      Maths teachers cannot change the context within which they operate. There is nevertheless much they can learn from maths teaching in flawed systems (including their own): old communist Poland and Hungary, or in the Soviet Union*, or in modern Shanghai, or in Singapore.

      * BTW: old Soviet maths texts and problem collections (maybe in German translations as Franz L indicated) are also worth looking out for – though they can be hard to use directly because they assume a very different background culture.

  4. Much appreciate your comments prof gardiner.

    I do disagree though, with your claim that social philosophy and political outlook ‘get in the way’ when discussing public policy. I think they are essential to such discussion, and inevitable.

    I have read passages of your work in which you persuasively lament the culture of short term, superficial progress and test attainment and its effect on maths ed in england. I’m an English teacher, and I suspect this problem is even worse for us. But i also think it’s important to ask how this culture has developed.

    The answer to that for me, admittedly applying my ‘social philosophy’, is the quasi marketisation of the system (which you’re quite right to state goes back further than Gove – the real start point was the 88 education act, which laid the ground work for the parent-as-consumer model). With parents expected to enforce market discipline, they needed to be provided with ‘information’ to make their ‘choice’ appear economically respectable. Hence the cult of measurable progress, data, testamania, league tables and all the rest of it.

    Anyway, much as I feel privileged to discuss this with someone of your achievements and wisdom, I feel that I may be abusing Marty’s hospitality to go on any further. I’d be happy for him to pass my email to you if you have any further thoughts.


    1. Happy for you both to continue, or to go offline if you prefer. I’m very interested to read what you are both writing, and I imagine many other readers are as well.

      1. 1. “I … disagree … with your claim that social philosophy and political outlook ‘get in the way’ when
        discussing public policy. I think they are essential to such discussion, and inevitable.”

        Perhaps I was not sufficiently clear. I half agree.

        If I try to make sense of Jane Austen, or Shakespeare, or how young children master arithmetic, my social philosophy and political outlook provide the backdrop to how I see things, and how I act day-to-day.

        But at the level of trying to understand *what is going on in a particular scene in a particular play or novel*, or *whether kids need to learn tables, and why*, or *how homework supports learning*, it may be best to avoid such background generalities and to focus mainly on the nitty-gritty (analyse the text itself – setting my philosophy aside; look at the evidence for and against, and the medium-term impact of kids either (really) learning or not learning their tables; compare schools in similar contexts where homework is used systematically, occasionally, or not at all; etc.).
        This is the lesson of “science”: “the art of (cumulative!) *objective* knowing”.

        Social philosophy and political outlook are important, but are much more subjective, and inevitably influence how each of us chooses to *apply* this objective knowing.

        I interpret the formal aspect of this site as encouraging us to focus on the more “objective” bits, which all reasonable maths teachers have a chance of agreeing on. Of course, the site’s unique character stems from Marty’s teaching insight and forthrightness – together with his personal digressions, where he reveals his social and political philosophy (but in a very controlled way).

        2. There is much to learn from what has been written in the past, and how maths is taught in other systems. Oldies (even dead oldies, like the textbook authors recently referred to), and those who teach in other systems, have valuable experience. But it is experience of a “former age” – so some of it becomes less relevant with time. Those still in the trenches, in a particular system, have to decide what still has value and relevance. (Fortunately, human beings change rather slowly, so many things hold their value across time and space, but may need to be translated.)

  5. As Marty has invited me to, I shall comment here – many thanks for the offer of the e-mail though.

    I am sceptical about the clear opposition you seem to draw between the ‘objective science’ of ‘what to do in the classroom to teach X’ and the ‘subjective’ business of politics/social theory. I am wary of many of the claims of ‘progressive’ educationalists, but I do think they have a point when warning us that what goes on in school cannot be reduced to a simple engineering problem of instruction-as-input and assessment-as-output.

    I didn’t used to think that – I used to think that education today is a bit like medicine was in the late nineteenth century – making huge mistakes all the time, but on balance better than nothing, and on the verge of incredible and rapid progress. I used to think that if we just could keep the politics out of it, science will do the rest, as it did in medicine (I guess this is not a wholly fair summary of what you seem to think, which is that in education things have actually gone backwards!)

    After teaching for a few more years, and in a range of settings, I now think that there is far too much politics, ethics and aesthetics in education for this ever to be the case – there will always be disagreement about what teachers are actually for, so how could we ever arrive at a consensus about how they should do it? Historical development in pedagogy would thus be analogous to development in architecture. A good architect ought to know about the latest developments in civil engineering, but this is only a part of what makes them a good architect.

    This might be an especially painful thought for those passionate about maths, since part of the attraction of the subject for many is its unworldly reliability. I do accept that there may be a special case to be made about how the language of maths – peculiarly precise and vacant as it is – best be conveyed (that is, there might be a final ‘right’ scientific answer about it how it is done).

    But maths – whether at primary or secondary level – still pretty quickly enters into the ‘subjective’ territory. Let’s say that we all agree that if there’s a reasonable chance of you completing a maths PhD, you need to have been introduced to trig before you’re 14. But what about if you want to be a hairdresser? Or fashion designer? How much of the maths curriculum should be oriented towards each of these groups/expectations/purposes? I don’t think could ever be an objective, ‘scientific’ answer to that rather cliched question, and yet it’s the sort of thing that is core to a lot of the controversy in maths ed.

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