Why do schools still get kids to do so much arithmetic?

As lockdown III rolls on, parents are once again getting a glimmer into their children's education. One thing I've seen some parents asking is why, in an age of computers, children (particularly primary school children) are still asked to do so much non calculator work. While I don't want to claim the balance is perfect or that there are no problems with the primary school syllabus (does it really make sense to try and get children to learn to identify subordinate clauses? What's the deal with all this formal linguistics they seem to be drilling into 9 year olds?) I do think that there is real value to having a really good command of arithmetic, even if calculators can do it for you. Befitting to the topic, here are some reasons in numerated list form:

1. It allows you to do quick mental approximation

Being able to do approximate calculations mentally is a useful exercise. It allows you to spot if statistics used in politics or advertising smell fishy. It tells you if a calculation in every day life (e.g at a till) is obviously wrong. You might well do the actual calculation to double check with a calculator, but knowing whether to bother or not depends on whether something sounds about right or sounds implausible. Even if you are using a calculator, it's worth knowing if the answer seems obviously wrong, as you might have pushed the wrong button, as often happens with longer calculations.  You can't do this without being reasonably comfortable with approximated mental calculations. 

2. It helps with algebra

There is a whole lot of algebraic manipulation which is fairly easy and intuitive if you understand it by analogy to relations learned in arithmetic (algebra in the school sense is after all a generalisation of arithmetic relations in symbolic form). Knowing that fractions can be simplified when a common factor can be taken out of the numerator and denominator helps you understand why you can simplify an expressions like the one below on the left but not on the right:

Maybe this can be learned without ever learning how to manipulate fractions, but I think it would be a lot more difficult to do so (some things are easier to learn by doing, starting with numerical expressions allows the 'doing' to start earlier; it also means you can see intuitively why certain relations are true: 2/4 = 1/2 can be shown by sharing up pizzas, x+1/2x+2 = 1/2 less easily). Mistaking changing the form in which a fractional expression is written and actually multiplying that fraction by something is pretty much the bane of my teaching existence teaching algebra, and the difference is most obvious to children who have a good command of fractions. Of course, there could be a correlation vs causation thing going on here, but in my experience otherwise high ability students can struggle with certain aspects of algebra if they weren't taught arithmetic properly in primary school. 

3. It can be fun

Some arithmetic is unfortunately extremely dull. I still have bad memories of learning times tables. But some numerical problems can be fun and challenging, and would be utterly trivial and dull with a calculator. Consider the problem below, which is no fun if you use a calculator: 

4. It helps you actually use calculators well. I can't tell you how much time I spend helping children identify order of operations problems they're having typing stuff into a calculator. This stuff is a lot easier to spot if you know how bits of the calculations work without putting them into a calculator. Children who don't really get that  -5² isn't the same as (-5)² almost always make mistakes using the quadratic formula, and the explanation as to why these aren't the same don't hit home unless you are really really happy with the fact that -5 × - 5 = 25. 

5. There are plenty of numerical relations that calculators aren't good at working out. Sometimes, being able to work with exact values is really helpful. In the example on the bewl, the shaded area is exactly half of the total. Children who can only approach this problem with calculators will almost always miss this, because they will round their answers as they go along. This is even more true once you get on to calculus. Calculators can even be remarkably bad at certain kinds of problems.
Try getting your phone calculator to work out the value of
ln(e^9999). It can't do it, because it tries to evaluate the inside of the brackets first, which is beyond its computational power. A human can tell you the answer is 9999 straight off.

None of which is to say that arithmetic isn't overdone, or that there isn't enough focus on learning how to use new (frankly, not that new) technology well. But the purpose of some of the old fashioned stuff might be a little less obvious than it seems at first sight. 



Why is the government always late to act on covid?

As I write this, the government is probably a few days, if not hours, away from announcing another national lockdown. What's puzzling is why this wasn't done weeks ago. This is nothing new: at every stage, from the initial lockdown of 23rd March, to the November lockdown, to the cancelling of Christmas relaxations, the government has delayed measures by weeks for no obvious gain and at catastrophic costs, which I'm sure readers don't need further regurgitation. 

This phenomenon is the subject of well deserved exasperation, but it is also just a bit of a riddle. It's well known and understood why delaying restrictions is harmful on a policy level (more people get sick, measures are in place for longer etc etc). What's less clear is why the government doesn't seem to understand this. What's driving these mistakes? Is it just stupidity, or is there some tangible gain, political or otherwise, which is accrued from these delays? I'm not sure I have the answer, but here are some possibilities I think are worth considering, some mutually supportive and some mutually exclusive. 

1. Stupidity. I've always assumed that even ministers of this government by in large understand the nature and dynamics of this crisis (the basic ideas aren't particularly complicated!), and I'm pretty sure Matt Hancock does, but you never know.  They are certainly under a lot of pressure from backbenchers and activists who really are stupid enough to not understand what is going on.

2. Blind optimism/motivated reasoning. This may be what drove reluctance to push for more control measures in the Autumn, when it is rumoured that Sunak and Johnson fell for some wilder ideas pushed by Gopta and Heneghan that the herd immunity threshold was already fairly close, perhaps due to cross immunity from other coronaviruses. This appears to have been largely an exercise in wishful thinking, as does the strong assumption that transmission from schools is negligible (there is good reason to think it may be lower in children than adults, but the belief that it was near non existent was probably largely just what people wanted to be true). Perhaps there is a similar kind of blind optimism that delays introducing lockdowns.

3. Blind pessimism. I think this is less important now, but in the early days of 2020, this was probably the crucial thing that prevented European countries from mimicking the success stories of East Asia, Australia and New Zealand. Quite simply, there was a widespread belief that it was naive and unscientific to think that the spread of the disease could be controlled to any meaningful extent (remember people arguing that the Italian government was being a bunch of crass populists by introducing a lockdown?). This kind of pessimism seems deeply inappropriate now (controlling covid in the short term is clearly possible, and vaccines are here, now!) but bad ideas have long shelf lives. Measures that are continuously too late can feed into this pessimism; we act to late, we do far too little to isolate cases when they are low, and people start to tire of measures that don't seem to work well enough. Moreover, the new strain certainly does raise questions about whether the measures the British government thus far been willing to contemplate will suffice (at no point have we closed non essential workplaces to the same extent Italy, Spain or France has). 

4. Public opinion. I don't think this is a real constraint on the government, but it is worth mentioning if nothing else in its negative form as this is frequently cited as a possible motivation for delays. Polling has consistently shown substantial majorities in favour of tougher restrictions sooner than they were announced, across the political divide (see here on school closures, for instance). I suppose you could still have a noisy group that opposes restrictions, and perhaps the government finds it convenient to be forced to act (probably why they tend to leak measures to select journalists hours before they are announced, so people are not hearing the measures from them the first time). There could be a bit of a bet that compliance to measures will be higher once people are afraid (i.e once the situation is obviously bad). But I don't buy that this can be a significant factor. It would make far more sense politically to bet that an already broadly supportive public would reward successful policy making.  

5. Poor management style in government. This for me is probably the most convincing part of the explanation. This government seems to favour a management system whereby individual ministers understand their brief to be about representing specific interests which they lobby for. The Prime Minister understands his job as an arbiter between these competing interests. Sunak lobbies for the Treasury, Hancock for the Department of Health, Williamson for his education priorities as they understand these. This is a uniquely bad way of running things in a situation where there are significant feedback loops and effective policy making relies on understanding the dynamics of a system of moving parts. The Treasury has come to understand (or feels it has to understand) its position as in conflict with covid restrictions, even though they are not. Williamson feels he has to lobby for schools to stay open, come what may, even though nowhere in the job brief for the Minister of Education did it say that better educational outcomes should come at the expense of large amounts of death. Still, this explanation does require a little bit of explanation 1. or perhaps something similar, as you'd expect that intelligent ministers would realise the interdependence of their departments and the mutual benefit of just going for maximum viral suppression. At the very least, competent leadership from the Prime Minister would enforce this view. Which brings us on to point 6.

6. Incompetent and weak leadership. Lockdowns may be necessary, but in the short term, they do have significant costs associated with them. These are hard decisions to make, particularly if you aren't that comfortable with thinking about mathematical and scientific models. Even if there is no gain from delay, incompetent and weak governments may simply put off decisions until they are out of options, as they are so put off by the short term costs that they end up just paying much higher costs when they are forced to. 

On Aristocratic Populism

One of the great questions about Boris Johnson has always been his apparent shifts in attitude. From a Telegraph bore/eurosceptic of the '90s, to the liberal (ish) London mayor of the 2000s, to the face of right wing populism and Brexit we know today, Johnson's persona appears to have seen, as Jonathan Lis put it, a number of mutations. The most common explanation for this is self interest: here we have an individual who will say and do anything for power. But I'm less sure. I think there is a kind of consistency to Johnson's attitudes, and it's one that is rather familiar. It's one of the aristocratic populist. 

Aristocratic populism is not opposed to privilege. But it is not averse to the idea of service, either. It entails the belief in some form or other of noblesse oblige- the idea that privilege entails obligations. For the aristocratic populist, this obligation chiefly entails the idea of being in touch with 'your people'; their ideas, traditions, practices etc as you see them (this may have large fictional elements). Crucially, this means not dismissing commonplace ideas as backwards, incorrect, or bigoted. As Roger Scruton, one of the most influential thinkers on the modern British right put it, it means that politics must "reassure people that their prejudices are true". 

This ideology is, on one level, inherently anti-intellectual, or at least opposed to certain types of expertise. It rests on the dichotomy of common wisdom, found in life experience and practical interactions on the one hand,  and theoretical, intellectualised understanding on the other. It is the idea that the prejudices of the common man are, for all their flaws, ultimately more sensible than the fashionable theories of intellectuals. It is, in many ways, a deeply patronising belief, as it assumes that 'ordinary' people are disinterested in and incapable of thinking beyond gut reactions, prejudice and acquired practical experience.

It is this kind of thinking that allows people like Johnson to have their reactionary cake and eat it. He does not have to actually belief, for example, in anti immigrant rhetoric himself. He can be perfectly familiar with the fact that economists tend to believe that the case against immigration has broadly been debunked. But he can believe that he is doing a kind of service, and following this sense of noblesse oblige  by not disavowing it either. Indulging common prejudices is a way of showing in-touchness with the people you govern, and a kind of act of solidarity. It is not about what you believe privately, or whether you, personally, have a problem with other ideas. But it is about whether in your mind you side with the fashionable theorists or the ordinary people, believing that the latter hold some kind of  greater legitimacy and deeper, if ineffable wisdom. 

Contact budgets, work from home and "letting the team down"

I don't want to trivialise the potential harms of work from home. Clearly, there are at the very least some quite steep short term costs to services geared towards inner city office workers. True, there are presumably knock on benefits too, in the form of extra demand for cafes and businesses nearer to where people live, and presumably over the longer term you'd expect some businesses to be able to relocate. But even such changes have a cost associated with them, and whatever longer term shifts to patterns of work, you'd expect that if and when the covid threat does recede (through a vaccine or otherwise) there will be at least some degree of a return to the status quo ante. In purely economic terms, pushing against work from home does have some plausible rationale to it, even if this rationale is not particularly ideologically consistent with the mantra of the party in government. 

What is harder to understand is how this push against work from home is remotely consistent with the government's covid strategy. The government's stated ambition is still to suppress viral transmission to the extent that a second wave of exponential growth is avoided. Covid cases already appear to be rising, and this is before we have seen the effect of school and university openings. There does not appear to be much room for increasing inter household close contact whilst maintaining the suppression strategy, if any at all. Encouraging people back into communal office space, (presumably) via public transport, in order to get more people into shops, cafes and pubs in city centres at lunch and after work is more or less definitionally going to push up viral transmission, presumably very substantially. And the government has offered absolutely no indication as to how this can be offset elsewhere or what the costs of doing so would be. 

What would offsetting the shift back to the office mean? One way would involve massively increasing testing capacity and attempting to isolate larger proportions of infections, but the government has given no indication that this is indeed its intention, or how this would be logistically feasible in the necessary timescale. The alternative would be simply to reduce interactions between households elsewhere. This would presumably mean shutting other things down, though it is unclear what these things would be, or what the associated costs of doing so would be either. 

Put simply, if we want to keep suppressing covid, there is, assuming limited efficacy of test and trace systems, only a certain amount of inter household contact that can be sustained. As Tony Yates puts it, we have a kind of 'contact budget' that we have to decide how to allocate (what, exactly, this is, may be difficult to determine and fluctuate according to levels of immunity in the population, seasonality, etc).  So long as the government wants to maintain a suppression strategy, it isn't good enough to point to the harms of work from home on parts of the retail sector, however real they may be, as sufficient grounds to end it. It has to demonstrate that hauling people back to the office is a good thing to shell out what is almost certainly a gigantic portion of its covid contact budget, if such a budget even allows a proper return to the office at all. This seems, to say the least, a rather dubious proposition.

In this light, it is particularly galling to see government cheerleaders trying to guilt people back into the office, claiming, as Sun editor Harry Cole does, that they are "letting the side down" by staying at home.Yes, some other areas of life have returned to normal. But this does not imply office work should do so too.  Because of its effects on covid transmission, an end to work from home would make it harder to keep schools open, not easier, would make it more of a problem that people are going to pubs, not less, and would make life for those who cannot work from home riskier, not safer. If the conclusion is that covid suppression simply is not worth it, so be it. But until and unless this is concluded, the government's messaging makes no sense.

Work from home: some thoughts on the tradeoffs

Thinking about the economic trade-offs in the pandemic, I'm reminded of a line from Marx's Theses on Feuerbach: "All social life is essentially practical". While I'm sure this isn't strictly true, it gets at an important relationship between economic and social life. Most economic activity is social. This is true both on the supply and the demand side: most work is does with other people, and an awful lot of consumption is social consumption. The problem is, social activity is also precisely what leads to viral transmission. This, in short, is the square policy makers are trying to circle. How do you reduce viral transmission in a way that is least economically harmful, when one side of the equation seems to demand less socialising and the other more?

Note that this is distinct from the question as to whether we should accept short term economic costs in order to suppress the virus, or whether the in the long term suppression is in fact economically beneficial. Viral suppression is the stated objective of the UK government, and almost all governments in rich countries. So we can take it as a given that at least in the short term, some (but presumably not any) costs are worth it for viral suppression. The question is, then, how do we minimise these costs, for any given level of suppression we wish to achieve? Which activities can we reduce most whilst having least economic impact?*

On one level, therefore, the government's eagerness to end work from home seems bizarre. We are essentially talking about a shift the way in which an economic activity is done which allows you to minimise viral transmission without restricting that activity. It seems to square the impossible circle of reducing social interactions without a direct economic cost. Of all the measures that can be taken, this is surely the easiest, at least in terms of the stated tradeoff. All other things being equal, if the choice is between shutting one thing down or shifting another to a different work setting, it's surely easier to do the latter than the former. 

Now, there are admittedly knock on effects to work at home that are quite significant. No doubt work from home has been devastating for those businesses which cater to office workers in cities. But there are knock on benefits too, in the form of increased demand for businesses located closer to where people live. Now the former may well be outweigh the latter, and outweigh it quite significantly. But that in and of itself does not tell us work from home is not worth it. Rather, we have to ask, do the knock on harms so greatly outweigh the knock on benefits that we should minimise work from home given that the alternative is minimising social interactions in some other way, presumably with more direct economic impacts (i.e shutting down pubs, closing workplaces where there are cases discovered). And the knock on effects of office work aren't just economic: people have to commute to offices in cities, and public transport is a major viral vector. 

Put concretely, as case numbers in the UK trend upwards, we are, as Chris Whitty says, quite likely at or above the limit of the level of social interactions which allow viral suppression. We are also about to open schools and universities. Assuming that we want to continue to suppress viral transmission, we will have to do less socialising, not more. Yes, work from home has some unpleasant knock on effects. But are these worse than the impact of shutting other things down? Given the enormous impact office work, commuting. indeed more eating out in cafes near workplaces is likely to have on virus transmission, one will presumably necessitate the other. I haven't seen the government modelling, but I would be surprised if the one big response available that does not involve directly stopping people from doing work is amongst the most harmful. 


* This is, admittedly, quite a miserable calculation, as it seems to suggest that social activities with no economic element are superfluous. It does seem to miss the best bits of life. 


The pandemic and the public sphere

One thing that's often missed when discussing why Sweden hasn't followed suit with the rest of Europe on lockdown is the legal dimension. The Swedish constitution does not allow for a state of emergency to be declared in peacetime, and it is unclear therefore whether general restrictions of movement could be done legally. Leaving aside the question of what effect this has had on the progression of the epidemic, it is illustrative of the enormity of the restrictions which other countries have put in place in an attempt to contain the spread of coronavirus. Perhaps even more significantly, the pandemic has led to quite fundamental shifts in what is considered the private and what is considered considered the public sphere, in what aspects of life are considered to belong purely to the domain of individual choice and which of common good.

The chief reason for this is simple. Disease control measures are not primarily about levels of exposure and the risk posed to the individual, they are about preventing viral transmission. Face masks are the most obvious example of this: they are supposed to prevent the wearer transmitting the virus, not protect the wearer themselves. The point here is that it if this is the justification, it is no good to talk about individuals being willing or unwilling to take certain risks: the costs of those risks aren't born by the person taking them.

Almost all disease control measures have at least part of this rationale built in to them: whether you are allowed to go to a large gathering isn't just about preventing you from getting infected, it's about the impact that would have on viral circulation in the general population.

This is exacerbated by the stress the pandemic puts on health care systems. The fear of hospital wards being overrun or other treatments being put on hold (as happened in the UK, most notably with cancer treatments) provides further impetus for 'risky' behaviour to be regarded as a public question, not a personal one. Think, for example, about the fact that the slogan "protect the NHS" was a core component of the mantra used to justify lockdown in the UK.

This all may well be a perfectly necessary and rational response to the situation, and will hopefully by a temporary one. But it does represent a gigantic shift in what counts as the domain of the individual and what counts as the business of wider society, in a way that under other circumstances would be quite unnerving. What you wear, where you go, who you meet up with etc etc are now all viewed as legitimate questions of public discussion, not individual choice. Indeed, even the government's new drive to promote healthy eating is framed partly in terms of personal obligation: the healthier we are, the less likely we are to overrun the healthcare system.

Such changes in the relationship of the individual to the state and wider society could surely have profound spill over effects on politics and ideology more generally. This change has gone surprisingly under the radar thus far. Many people are perhaps rightly worried about undermining what are seen as essential measures for controlling the spread of covid. Moreover, those who do talk about these changes tend to be either cranks who peddle conspiracy theories or people who make a virtue of refusing to take responsibility for others. And I don't want to claim that this necessarily represents a kind of creeping authoritarianism: perhaps these shifts in attitudes will be temporary. But the impacts could be substantial, and they are probably worth keeping an eye on.

Why do some Conservatives think they are marginalised, despite being in power?

Chris Grey notes a trope amongst right wing pundits that has been bothering me for a while. "What is fascinating is this persistent sense of victimhood. Conservatives have been in power in the UK for 10 years, have achieved Brexit, have the support of much of the media, and... [y]et, still, they claim to be marginalised." I'm sure nobody needs me to hash out yet another attempt to knock this idea down: others have already done so. What I don't think has been asked enough is why this idea is sustainable. How do some Conservatives think themselves to be marginalised when they have all this power?

One answer is simply that they are being disingenuous. No doubt some pundits are: it's pretty hard to think, as Darren Grimes claims he does, that you are being 'sidelined by [the] mainstream media' when you keep appearing on TV. Another answer is that this is ideological: that the modern right thrives on conspiratorial thinking. There is probably some truth to both of these ideas. But I don't think this is all that is going on. Even if we allowed for the existence of some straight forward charlatans, their ideas wouldn't have much mass appeal if they didn't speak to some aspect of lived experience. This is where effective propaganda tends to start.

Part of what is going on, I'd suggest, is the prevalence of progressive attitudes in certain parts of mass culture, specifically advertising and entertainment. This is firstly about economics. Brands tend to focus a disproportionate amount of their advertising effort on younger people. There are a number of reasons for this. Firstly, this is because they are newer consumers with less existing brand loyalty, so there is more of a prize for capturing them as loyal customers. Secondly, they play a larger role in influencing the behaviour of consumers more generally: young adults tend to set trends, and tend to influence the consumption patterns of their parents more than the other way round. Associating your brand with youthfulness is pretty much universally appealing; middle age and elderliness less so.

This means large brands will tend to focus a disproportionate amount of effort marketing themselves to younger consumers, who tend to hold more progressive attitudes. In the last general election, for example, Burger King ran adverts parodying Vote Leave (a picture of a burger on buses with the caption 'Another Whopper on a the side of a bus!') and KFC also used anti-Tory sentiment as a brand boosting exercise. More recently, a number of brands have expressed solidarity with the BLM protests, including, notably, Yorkshire Tea and PG Tips, brands hardly known for their young consumer demographic. This is no new thing: this echoes how many brands responded to the youth movements of the late '60s, as shown in this famous Coca Cola ad from 1971 (right).

It's also the case that leading figures in pop culture, like actors, comedians, musicians, tend to be more progressive. I don't claim any great insight into why this is the case, but the trend does seem undeniable. This too, is no new thing: think how many American musicians were associated, loosely or more closely, with the civil rights movement and opposition to the Vietnam war. Academia does also skew somewhat leftwards, but this is a much less constant phenomenon, and probably has a lot to do with the right's mobilisation of anti-intellectual sentiment and the gradual increased prominence of US GOP-style anti-scientific thinking in the conservative mainstream (a number of leading figures in Vote Leave have dabbled in climate change skepticism, e.g Daniel Hannan, Douglas Carswell).

Finally, social media usage tends to skew towards younger (and generally more progressive) users. While this is most true of Snapchat and Instagram, crucially, it is true too of Twitter, which is the social media site most closely associated with political expression (figures shown below for 2019). 

This skew within particular areas of popular culture might go some way to explaining why Conservatives claim to be marginalised. This is not to say they are correct in doing so: associations of brands and pop icons don't translate into power in the way that dominance of the tabloid press or holding parliamentary majorities and controlling the executive do. But it can root an angst, however irrational, in a major part of lived experience.