jsburbidge | Entries tagged with education

Paul Krugman, today on Substack, talking about voters blaming governments for conditions (specifically inflation) out of any individual country's control: "The race is not to the swift, nor the battle to the strong, neither yet electoral victory to parties with good policies; but time and chance happeneth to them all."

Koheleth is always apposite in some way, especially in the Authorized Version, or maybe the Vulgate. (Vanitas vanitatum et omnia vanitas.)

This touches on my reactions to posts elsewhere about people who have never heard of the Odyssey. Although there is actually no obvious reason, given today's education system, that one should have run across Homer at any time during elementary or high school, it enriches one's experience to have read the Nekuia, or the recognition of Odysseus by means of an old scar (a passage chosen for discussion in Auerbach's Mimesis), or the destruction of the suitors, or indeed almost any other passage. (Plus it's a foundation for reading other texts.)

(My daughter, who has three years of Latin and also has a Greek Myths component in her English curriculum but clearly only a glancing familiarity with Homer, called me up a few weeks ago asking about the Odyssey. I told her to read it in a decent prose translation. She asked if she could borrow my copy, and I told her that it wouldn't do her much good, as it starts with ἄνδρα μοι ἔννεπε μοῦσα...)

There is a post on Charlie Stross's blog regarding a pledge by Rishi Sunak to eliminate degrees which lead to less well-paying jobs. Aside from noting that such a programme would likely lead to the abolition of Greats, the degree held by the current PM - as a rule, degrees in classics are not roads to riches - this would seem to be irrelevant, as Tory party members seem to give Liz Truss a pronounced edge (not because she's any brighter, but because she is more in their image).

But what is the value of a university degree? In the STEM area, generally, the "useful" (engineering end of the scale) degrees apparently now have a genuinely useful life of about five years. If you have a degree in pure math, it doesn't age at all, but it is about as useful as a degree in philosophy (which also doesn't age at all, at least if it covered core subjects).

On the other hand, my current employer not only wanted proof of my degrees from the early 1980s in an unrelated field (well, two unrelated fields) but apparently had the same demand of a colleague whose degree is from the late 1970s. It didn't care what they were in - experience rendered that irrelevant - but they certainly wanted proof of graduation.

Whatever Sunak believes, most degrees which are not specialized professional degrees have about the same value: employers want "a degree" for a vast number of middle-class office jobs and don't particularly care what in. For all that university calendars pitch the practical application of the most abstract of disciplines to students, a course of studies spent studying Peter Abelard, Guido da Montefeltro, and Dante is generally just as useful as a credential as one spent studying the most "relevant" of subjects.

Not that the former is very likely, these days. Many if not most smaller universities have abandoned anything even loosely related to the kinds of education which would satisfy anyone with a real appetite for systematic or eccentric knowledge. (Larger universities retain them because they need to support schools of graduate studies across a full range of disciplines.)

I have three degrees, each with its own lesson in later years.

The first was a BA from Trent University. In those days - which are now, I gather, considered part of the "early days" despite my very clear sense that I was nearly a decade after the real early days - it was a reasonable place to go for a small-class humanities degree, even if its tutorial system did not approach real Oxbridge tutorials. I did a major in English Literature and minors in Mathematics and Classics. What I did would now be impossible; the calendar no longer supports the courses I took.

My second was an MA taken with the course work from a doctoral programme at The Johns Hopkins University. I got out because I disagreed with where the discipline (and the humanities in general) were going. I cannot say in retrospect that my assessment was mistaken.

I then proceeded to a law degree at the University of Toronto. I was really the only student in my year who approached it out of an interest in law as such, and got the greatest amount out of courses in jurisprudence and legal history, including a directed research course in legal history. I did not get an offer to article at any of the firms I interviewed at. However, the degree did give me the one actual "practical" use of any of my degrees: it gave me a foothold as a legal editor at a Toronto publishing firm.

While there, I eventually shifted function and became a software developer, which is a long and complex story in itself. By the end of the 1990s I was experienced enough to get a place at a dot com startup, and went from there into development in the financial sector. At no time from that time on did anyone ever show any interest whatsoever in what I had studied at university, or what my grades were.

In retrospect what I "should" have done from a professional point of view was taken the Descartes scholarship the University of Waterloo was happy to offer me and, instead of taking pure math (which was my then current interest) should have taken a course in math and computer science. I would have taken a short cut of nearly 15 years to the same career with better credentials and a better choice of employers. I'm not sure that would have been my best choice otherwise; my collections of classics and mediaevalia argue otherwise. (Though there's certainly an argument to be made that taking a second bachelor's degree in Computer Science rather than going to law school would have been a better idea.)

So what was the economic value of the degrees I have? Relatively limited; indeed, a single four-year degree that I did not take would have almost certainly had a bigger impact than the three degrees I did take. Their benefit was not at the vocational level but at a purely intellectual level. Most of the skills I have I had when I graduated from high school, although with less practice (with the exception of software development, which I did not take up until after I had finished university entirely).

There is a frequently made case for abstract knowledge that it eventually turns out to be more useful than practically-directed research (a classic example is the applicability of Lie algebras to particle physics; or, a level down, of understanding of particle physics and quantum mechanics to the use of semiconductors in computing). I am more inclined to make the argument that abstract knowledge is a value in itself, and that the willingness to support the extension of abstract knowledge is one of the things society is judged on.

"After all, damn it all, we can’t have the boys runnin' about all day like hooligans—after all, damn it all? Ought to be havin' a first-rate eddication, at their age. When I was their age I was doin' all this Latin and stuff at five o'clock every mornin'. Happiest time of me life. Pass the port." - T.H. White, The Sword in The Stone

Literature

The foundation of all education from the late ancient world on was dependent on literary studies.[1] "Grammar" meant not only learning the written language but learning its use in authors who were models to follow or at least quote (Virgil, pre-eminently, in the Latin West).

In the Nineteenth Century there was a transformation from classical to vernacular studies (though Classics is recently enough a core requirement that when I was born Latin was required for University entrance for non-science students in at least some universities).

There followed a gradual shift from the study of vernacular classics to such contemporary and local works as are assumed to be able to catch students' attention.

In my day, I got Shakespeare, Emily Bronte, Hardy, Dickens, Twain, Samuel Butler, Conrad, Tennyson, Eliot (T.S.), Browning and Pound in addition to Heinlein, Tolkien, Bradbury, Davies, Laurence, Atwood, Knowles, and Salinger. My daughter got Shakespeare; the government has now allowed Shakespeare to be dropped from the curriculum. The rest of her set texts were recent bestsellers. No challenging or classic poetry made up any part of her curriculum.

Of course, the way to take this turns on what the purpose of an education in letters is. Although one might think that the shift reflects an academic/critical turning away from the idea of a canon - and it's arguable that that is an influence on the curriculum - it's generally clear that whereas the older aim was to provide an elite with the tools of a shared culture in the service of rhetoric as a preparation for a public role, and the aim of, say, seventy years ago was to acculturate the populace with a common culture of high prestige, the aim of the present curriculum is to ensure that most people have a grasp of business English, and that the rest have the basic literacy needed to read signs and essential notices and to be able to do basic online navigation.

(The mediaevals classed all literature / poetry as "ethics", and an education in letters was a moral education. Some element of this view of the end of an education in literature survived into the Twentieth Century, but seems to have died under the twin attacks of teaching letters as a purely pragmatically useful discipline and the shock the mid-century had on the assumption that a good cultural education would bolster ethical behaviour (see Steiner in Language and Silence for his discussion of the impact of the Shoah on this assumption). The last trace is that we have a curriculum designed to inculcate "Canadian Culture", without further investigating what the end of a cultural education is generally.)

Ignoring the question of whether this change in aim is a good thing, does it work?

In Ontario, at least, the OSSLT gives a partial answer. The test assesses basic literacy: the base skills needed to function as a generic worker, or as an informed consumer, or as an engaged citizen. For anyone who regularly reads anything at all, passing it is trivial. Specific preparation is available, and, as schools are in part graded on their students' performance, there's incentive to provide that preparation as well as to teach to the test generally. I will note that the skills required to pass the OSSLT are not sufficient to write a competent university essay or compose a business report.

The government's data indicate that, consistently, over 90% of the "academic" stream English students pass the test on first try. About 40% of applied English students pass on first try (this has fallen over the years from 50%). (Special needs students are excluded from these figures.) It's reasonable to assume that some part of the numbers reflects ESL students, though the numbers of students who speak mainly another language at home sits at 7%; some ESL students also get special assistance.

A majority of students take the academic stream (this is in contrast to my day, when a majority of students took the 4-year courses and left the system at the end of grade 12; about 30% of my class went on to Grade 13).[2]

So a majority of students pass the OSSLT on the first try but a significant minority do not. As far as the success of the curriculum at encouraging reading goes, a questionnaire administered as part of the test indicates that about 30% of girls and 15% of boys read fiction at all regularly (the parallel numbers for reading websites (in any way) are 55 and 46%).

I am not sure this counts as a success. I am likewise not sure that taking that level as a baseline is useful, even pragmatically; one would ideally expect a somewhat higher level of ability after ten years of training. And I have a good deal of concern about the retreat from an aim to educate the whole person via letters to an aim to educate baseline competent work[place drones.

Mathematics and Natural Science

Although there is a long history of formal training in mathematics and some subjects we would now call "science" as part of the standard curriculum - arithmetic and geometry make up two of the four parts of the quadrivium, and astronomy is a third - the Anglosphere has generally been fairly poor at doing general mathematical training going beyond ciphering. At the very high end mathematics was considered acceptable - Cambridge had its Tripos as it's distinctive degree. Similarly the US produced a trickle of very highly skilled mathematicians, scientists, and engineers, but general mathematical literacy was not widespread. (One can look at C.P. Snow's The Two Cultures for a sense of what England was like.) One of my father's cousins, born in the 1920s on a farm, became a prominent physicist; the rest of his family, who were by no means stupid, remained farmers.

The shock of the Sputnik launch turned the low level of mathematical and scientific training into something About Which Something Must Be Done, at least in the US and Canada. Math and science curricula were beefed up - I was one of the early cohort taught with the "New Math" - and analysis was added as a high school topic. The aim was, if not to produce a mathematically and scientifically aware public, at least to feed more people into technical jobs and generally improve numeracy.

I am poorly situated for evaluating the mathematical education I received. I have a natural aptitude for math and would have absorbed my primary school curriculum regardless of the skill of my teachers, although I will note that it struck me as repetitious, slow, and unambitious and today seems to me all the more so. By high school I was one of a set who got to skip out of math classes in the middle of the year to prepare for math competitions. The senior math teachers were competent - one had an M.Sc. - and I know of three engineers and two software developers among the members of my 60-odd Grade 13 class, plus a couple of medical doctors.

I can, however, assess the curriculum, and the teaching skills, provided to my daughter, who is not good at math. In general, the curriculum was not well designed - it would have been well matched to neither the very good nor those struggling with math; the teaching quality, not only in elementary but in secondary school, was on the whole poor. (I recall one good chemistry teacher.)

The level of training for public school math and science teachers has declined; they now staff at least in part by shoving teachers with no strong math or science background through short qualifying courses and let them cope with curricula which they barely understand.

As far as results go - I work in a field which requires broadly mathematical skills, and certainly a high degree of abstraction, and the majority of my co-workers have been and continue to be those with English as a second language, i.e. immigrants. In the same organizations, as soon as one moves to other skill sets the proportion of native-born Canadians rises dramatically.

EQAO results show similar patterns to those in the OSSLT results for English - about 80% of Academic level students score at or above the provincial standard, and about 40% of Applied level students to the same. Of the Academic students, only about 35% indicate that they like mathematics.

Part of this problem boils down to money. The government is unwilling to provide the funds necessary to compete for competent math and science graduates in a workforce where those skills carry a premium.

Part is cultural; the cliché that the Chinese, even as expats, tend to do well in math and science classes has no grounding in genetics but it does reflect a culture which takes brute force studying seriously. The English, Americans and Canadians tend to be a little suspicious of the bright, and "intellectual" carries negative connotations which it lacks in France and Germany.

History and Civics

Compared to literature and mathematics, history is a latecomer to the elementary curriculum. Works of history, especially classical history, were sometimes covered as literature: Tacitus, Caesar, Plutarch, Thucydides, Herodotus. But modern histories were rarely of such a status (and Gibbon, who had the status, took a classical theme for his substance).

In the 18th and, more, the 19th Century, a standard narrative was imposed on recent history, with an agenda which made it an appealing subject for childhood formation: the Whig Interpretation of History, with (in England) industrialism, parliamentary democracy, and laissez-faire ideology as the pinnacle of a curve of progress beginning in the Renaissance. (In the US and France, substitute other forms of representative democracy and an emphasis on more sudden dislocations than in the long curve of British history). This cascaded to the imposition of teaching this history as a formative influence in the young.

Of course, school children were not given Macaulay to read, at least in general. (When they were, it was more likely to be the Lays of Ancient Rome than the History of England.) Schoolbooks had a schematized and simplified version of essentially the same story. That story served another more general purpose (aside from generally equating progress = good = liberal values): it provided a basic grounding in what otherwise might have been taught as straight civics.

With the extension of the franchise to larger and larger groups in the Nineteenth Century (beginning in the Eighteenth Century in the United States) it became a real concern to ensure that the population as a whole had the minimum understanding of civics and the public domain to participate well. This led to significant emphasis on civics classes in some jurisdictions and, everywhere, the provision of history / geography / "social studies" classes designed to support that function.

This pattern has continued, mutatis mutandis: Canadian children no longer learn about the Princes in the Tower, the Armada, the Commonwealth, and the repeal of the Corn Laws, but they get a narrative including Wolfe and Mackenzie and MacDonald / Laurier / King (to which some coverage of aboriginal peoples has now been added) which has the same general ends.

(Even high school history has almost nothing to do with learning how to do history (distinguishing between primary and secondary sources, assessing reliability, developing and supporting a thesis based on research): it's essentially narrative divorced from sources and with an utterly spurious impression of certainty attached to retailed events which are, at best, probable reconstructions.)

It has failed miserably. It never was much good at giving the population a good historical sense, but that might be an unfair criticism given that that wasn't really it's purpose. But the populism of the past decade in the Anglosphere reflects a population which hasn't even progressed as far as the Bourbons[3]: they have not even absorbed the past, let alone learned from it.

In Canada, this became blatantly obvious in the reactions to the Harper prorogation of Parliament, where the specious justification that people had "voted for the government" and having the Governor General potentially choose another PM would violate that: one of the first principles of Westminster-style representative democracy is that one votes for an MP, not a government, on the basis that the MP will use his or her judgement as seems fit to them over the term of the ensuing Parliament. (This includes crossing the floor, which is, properly understood, an assertion of democratic principles - it means that a leader can't just abandon the principles an MP ran on and count in their continuing support - rather than a denial of them.)

In the US and Britain the recent political circuses have displayed for all to see that whatever the population as a whole was doing in school, it was not getting an effective grounding in civics or history.

Future prospects

The common theme in all these areas is a twofold failure: first, the failure to provide genuine universal education at the level intended and, secondly, shortcomings in providing an education which will provide effective grounding for those going on to greater specialization.

One obvious cause is an unwillingness to spend money. Large class sizes, poor training, curricula which are shaped in part by what half-trained teachers can pass on (teaching serious literature, real math, and historical research techniques is probably beyond most school teachers; certainly capability in all three together is probably as rare as hens' teeth[4]), and one-size-fits-all curricula can all be remedied, over time, by enough money.

The second cause seems to me to be a third rail of politics: recognizing that there are gradations in inherent capacity which constrain effective education (at one end) and ideally call for an ambitious and challenging curriculum (at the other).

This is a no-go area because either of the possible causes for variations in capacity would require unpalatable solutions.

To the degree that it is caused by variations in home (or other early childhood) environments, any effective solutions would involve not only money but an aggressive intrusion inside family boundaries. (Consider the current CAS system and all its problems, but expand the category from "neglected children" to "environments physically or socially not conducive to or encouraging of learning", including nutrition, parental literacy, active intellectual stimulation, and anti-intellectual subcultures.)

To the degree to which it is caused by genetic variations in capacity - and note that we have no good way of identifying or analysing such variations, as all of our current data aside from identical twin studies and the like tangle up cultural and genetic transmission, and genetic causation of complex traits is not something of which we currently have any deep understanding - recognizing and responding to it would involve, essentially, streaming from early childhood based on heredity (or early testing standing in as a proxy for heredity), which is not a position likely to be politically palatable to any current political party. It might very well have been acceptable to the Tories of Meighan's day, or Wellington's, (and possibly to socialists of the Webbs' day, given their support for eugenic programmes).

In both cases, it is easy to imagine implementations where the cure is worse than the disease.

The current trend is away from streaming, not towards it. Both the politics of the left and the "right" (neoliberal/mammonite; the real right of George Grant style conservatism no longer has any space on the public political spectrum) for different reasons shy away from tailored programmes for more capable children (although the left does support programmes designed to make up for historic or systemic inequality).

And both approaches would be expensive.

It is not that we have an educational system which is falling apart; it is that we have one which is effectively committed to mediocrity, and in some areas mediocrity has an enhanced impact on society as a whole (civics, scientific literacy in addressing climate change or epidemiology) or on public culture.

Any real change has to begin not at the level of politics but at the level of cultural change. And the levers for that are in the hands, not of the politicians, but of the makaris: writers, artists, musicians, producers, to the degree that they are in anyone's hands.

[1] We can catch glimpses in the oldest Greek literature of a different educational model, in a culture not entirely focussed on literacy, which was based on memory and ad hoc oral composition, with reading a less emphasized skill, and writing probably left to specialists. It was still based on poetry, even if not on, in the precise sense, literature. Traces of this remain in the place of rhetoric in the trivium.

[2] The province has indicated that it aims at ending the streaming (beginning with Grade 9 math in the fall of this year); if it does so it will probably have the primary effect of extirpating any remaining useful training beyond basic business English skills.

[3] "Ils n'ont rien appris, ni rien oublié".

[4] I could teach all three, if I were also trained as a teacher. I am not representative.

The Atlantic had an article on whether college has become too easy ( https://www.theatlantic.com/education/archive/2019/07/has-college-gotten-easier/594550/).

It's a bit like asking how big a basket of fruit ought to be: the question "for what purpose?" naturally presents itself.

There's a general level: do we want universities to turn out the brightest possible graduates to foster innovation? To provide critical skills for some majority of the population? To ensure universal literacy and scientific literacy? To provide paper credentials allowing HR departments to do easy first cuts of job applicants? It makes a big difference to how easy you want courses to be.

There's also a specific level. Learning to be an engineer is generally all-or-nothing: you don't want a generally able but not reliable engineer, good at arches but poor at failure analysis. Pieces of an engineering degree, or a chemistry degree, are of little use (unless the aim is purely to match interest, in which case the criteria are unlikely to be hard / easy but interesting / dull). But retaining a reasonable chunk of an English or history course is a benefit to the student in terms of understanding and critical thought without needing a high level of expertise or complete mastery.

Also, there's a difference between "Can exceptional students find challenging courses?" and "Do you need to have a high level of competence to graduate?". This is not quite the same as "is your economic strategy one of innovation or high quality implementation?" but close to it. Not that these questions are well answered in an either/or mode; you probably want both if you want one, and exceptional students will benefit more from courses where they are surrounded by at least very good students. (There's also no evidence that either is really a major goal of society, given the resources allocated. Highly competent people of either sort are not numerous enough to make a significant voting bloc.)

In my personal experience, courses need to be challenging to achieve effective outcomes. I have seen a lot of people in my workplaces over the years who were officially qualified but only "officially" - technical people who couldn't communicate clearly or do effective design or analysis (and whose code left one wincing), history majors with no sense of history, English majors who never read Milton and in any case lacked the skills to do so.

That doesn't mean that courses in software engineering, or core history or English are necessarily "easier" than they used to be; it just means that the graduates are able to avoid the challenging courses. Anecdotal evidence suggests that a lot of students just want their piece of paper with a grade they like, and they'll avoid anything that complicates that.

As a society we could, of course, decide to require that such avoidance is made as difficult as possible, which would mean that a few of them would become accomplished, and the rest drop out. But many of the positions these people are filling are manageable by an intelligent person with no more than a good high school level of learning, so it's not clear what would be the point of doing so. It would also impoverish universities and slightly increase the ranks of the officially unemployed. (One of the aims of extending education to greater ages is to remove the students from bring active members of the workforce). For many purposes, grading at pass/fail is the most that's required to fulfil the later use made by the students of their degrees.

A few decades ago, Ontario tried to address one aspect of this by creating other, more "practical", forms of post-secondary education - multiple community colleges and one polytechnic institute. An interesting thing happened, though: various pressures - internal ones, from teachers; external ones, from competitive and prestige issues - have led to these institutions becoming "universities", if ones which tend to have a decidedly practical tone to them. At the same time, the old universities have started promoting their courses as gateways to employment, with the side effect of generally reducing the strictness of requirements for a major. If the purpose of a major in French is to give you a general mastery of French Language and Literature it's reasonable to require that graduates have had some exposure to Rabelais, Racine, Voltaire, Baudelaire, and Proust, much as French Lycées require. If it is to give you the capacity to function in the Federal Civil Service, deal with French-speaking clients, and generate memos in comprehensible but not artistic French, it matters less what you study as long as it exposes you to the language.

By one judgement, the latter set of standards is "too easy"; by another, it simply follows function.

As an aside, if the difference between "easy" and "hard" is between, for some sizable block of students, getting a 75% average - the lower border of an A when I was in high school - and 66% - the upper border of a C at the same time - the main difference it will make is to the students themselves: except in applying for higher degree programmes, I have always found that nobody is interested in my grades. Employers just want to verify that I have the degrees I claim to have (even when I'm applying over thirty years later and have decades of experience in my current field of work).

My gut reaction is that university has indeed become "too easy", but my considered opinion is that the system itself needs thorough reconsideration in terms of the functions we require. My suspicion is that we are losing a lot of potential talent by failing to challenge those students who are up to it, I equally suspect that there is no good reason to raise the bar for many students for whom the relation between what they study and what they will do for the rest of there lives is one of formal credentialism. There's a broader crisis in terms of the role and structure of post-secondary education playing out, and easy as opposed to hard is not the main question.

I see that Laurentian wants to be "the Oxford of the North" by teaching courses about the Inklings.

(https://www.cbc.ca/news/canada/sudbury/laurentian-university-tolkien-lewis-the-inklings-oxford-university-1.5396083 )

Let me only note, as somebody who absorbed a great deal about both Lewis and Tolkien over the years (the article doesn't mention Williams) that if you really want to be like the Oxford of the 1940s, and particularly want to emulate what the Inklings found important - not necessarily an unmixed blessing, and Tolkien in particular was known as a dull lecturer - you don't want to be teaching Twentieth-Century speculative fiction. You want to be teaching Anglo-Saxon and Old Norse, mediaeval romances (not in translation, and that includes Middle French), Renaissance literature, and Milton.

In the aftermath of last night's leaders' debate, Metro Morning had a discussion regarding the two elements of the elementary school curriculum which Doug Ford has announced an intention to change. Unfortunately, the discussion was shallow and unenlightening.

On the sex ed. front, the interviewee mainly kept repeating the (entirely true, but unhelpful) point that there had been many years of consultation on the curriculum (in fact, there were two phases: once when it was being developed and once when the government got cold feet about introducing it in the wake of pushback from (mainly religious) minorities). The problem is that, regardless of whether Ford uses it as an excuse or not, "consultation" is not the issue with the curriculum. The issue is that although the updated curriculum has moderate support from a majority of the population – and many people feel it does not really go far enough in responding to the context of the present day (Internet, changing mores, etc.) – there is a minority of people who will not accept it regardless of how much consultation is done.

These are small-c conservatives, almost entirely belonging to conservative religious groups (Roman Catholic, Eastern Orthodox, Evangelical Christian, Islamic, Orthodox Jewish, at a minimum). In general, Canadians tend to keep religion out of the public square, and in this case the compromise was to allow parents to withdraw their children from the relevant classes if they object to them. This, of course, begged the question of the public policy objectives in having such a curriculum (a matter which the radio show also did not address) and the question of whether those aims effectively demand that the education should be universal. (There is some evidence that, on average, parents are much worse at providing this sort of education to their children than third parties are; there is also the aim of ensuring that everyone has a basis of the same common knowledge on matters of general importance in daily life; finally, there is the relation between this sort of education and anti-discrimination goals with regard to GLBTQIA individuals.)

None of this level of substantive analysis was provided, or even gestured towards. Nor was there any discussion of the politics of the matter. (Patrick Brown had avoided taking this kind of position on the entirely rational basis that the people who are opposed to the curriculum changes are almost all committed Conservative Party supporters in any case. It won't gain votes, and it may scare some away.)

On the other side, the person addressing the math curriculum issues was, if anything, less helpful still. Again, they failed to address the (divergent) aims being served by the current math curriculum, and in particular why none of those aims matches, any longer, the drill to which Ford wishes to return. Or, indeed, why extensive drill has gone from being a desirable part of the math curriculum to a largely irrelevant one

In my day, almost all of grades four to eight was taken up in repeated drill with arithmetic and "word problems", frequently involving converting between Imperial measurements which we had never otherwise heard of. This was genuinely important because, at the time, it was (justifiably, based on knowledge then) assumed that any arithmetic anyone did for the rest of their lives would be done with pencil and paper (the fringe exceptions – slide rules and room-sized computers – were irrelevant, as they would be used only by math whizzes (engineers and scientists) in any case). Really solid drill was one of the core components in a curriculum aimed at providing basic literacy and numeracy in a world where these were literally life-critical skills.

Then calculators came along.

Then they became so cheap they were given away like cereal toys.

By the time I reached the end of high school, my chemistry teacher was telling us that we needed to make an order of magnitude approximation on the back of an envelope before using a calculator (or slide rule - some of us still had them) to ensure that we hadn't made any stupid mistakes and were in the right ballpark.

I'll grant that the primary school math curriculum is a mess. Having spent years assisting my daughter with her homework (which was not, pace the commenter on Metro Morning, at all difficult to do) I consider it to be very poorly structured. It flits from one topic to the next, never providing enough of a continued development of a topic to get interesting, or indeed to provide students having difficulty with an extended period of connected work. On the other hand, it isn't any better at giving an idea of what really doing math is like than the old curriculum. (A mathematician is not particularly concerned about whether 7x8=56. The concern is rather (1) with defining the operation of multiplication (2) showing it's commutative, associative, and distributive over addition, (3) showing that you can even get to a number like 56 generally on the number system using mathematical induction…)

From the point of view of learning real math it would be more sensible to give kids a term of working with quaternion or vector spaces rather than a term of drill in arithmetic. On the other hand, very few people become real mathematicians, and only a relatively few more become physicists or other scientists who have to have a clear sense of, say, sophisticated symmetry groups.

A few more percent of the population become engineers, accountants, and others who, frankly, apply recipes and can normally rely heavily on computers to do the grunt work for them. (The engineers still need to learn analysis and Fourier series and the like in order to know how to solve certain sorts of problems numerically. But they don't need to be able to multiply.) They're not interested in number theory, abstract algebra, or foundations, though, except maybe as hobbies.

Almost everybody needs good education in doing things like back-of-the-envelope risk assessment, because humans are really bad at it, and it's important in everyday life. They need to have a gut sense of what compound interest does in order to make their way through the commercial financing world. They need a basic ability to structure simple calculations to feed to a calculator to determine things like how much paint you need to paint a room. They need some basic geometry to do certain kinds of practical handiwork.

This suggests that there should be three different math curricula, with only one subset being universal. How you stream or switch between them is another problem. (It wouldn't matter very much if a significant chunk of the population weren't demonstrably poor at thinkingabstractly, which makes them far more likely to struggle at math.)

In none of these cases is a great deal more drill useful.

As an aside, and while on the topic of small-c conservatism and curricula, I'd think that the obvious place to focus is very different: it's the humane letters curriculum, that is, in school, mainly English and History. Not only is it a quintessentially conservative concern to have the school curriculum inculcate solid cultural values but it is also traditional to inculcate those values by means of attention to European and particularly English literature and history. The recent decision to drop mandatory Shakespeare studies as part of the high school curriculum would, I would think, be a scandal to a well grounded traditional conservative. In addition the focus of the current curriculum on exclusively Canadian history and principally Canadian authors departs in its aims from the Conservative pattern of going to the "classics" for education: if not Homer, Sophocles, Virgil, and Horace, than at least Shakespeare, Milton, Pope, and Wordsworth. And a solid argument can be made for expanding the scope of a student's view so that it takes in people who thought and acted very differently, as shown by either their writings or their deeds. I could get behind a pledge to bring back Classics, and give the curriculum a larger spine of world literature and history.

I visited Toronto's Mackenzie House on Saturday. It included a tour of the house, a demonstration in the print shop, and a potted history of Mackenzie from his arrival in Canada (1828) until his death.

I was reminded of one of the real failings of the Ontario history curriculum. The two rebellions (Papineau's and Mackenzie's)[1] are always taught only in their local context.

The Mackenzie Rebellion (at least) has a significant ideological overlap with the Chartist movement, which began in England in 1838. The following decade would see a series of revolutions and rebellions throughout western Europe: France's Second Republic, uprisings throughout the German states, Chartist rebellions in the U.K. (as memorialized for SFF readers by Brust's and Bull's Freedom and Necessity). We were taught nothing about this in school.

Mackenzie himself was a product of Scotland, not Canada, and his views reflect Dundee far more than they do any local sources.

Indeed, it looks very little like a true grassroots revolt. The bulk of the opposition to Mackenzie was low-level, not high-level (not that the ruling classes were precisely friendly). The population was dominated by Loyalists (well, their children and grandchildren) and by Orangemen, who rallied around the established order. (The rebellion in Toronto was defeated by militia with a very small sprinkling of professional troops.)

The natural soil of the protests of the 1830s and 1840s was the new industrial classes and the cities (with a side of agricultural workers who were threatened by mechanization, as with the Swing riots - which has obvious linkages with other forms of unrest driven by technological change, and with Luddism): the Upper Canadian rebellions were based on independent farmers and tradesmen.

There was a true local context - still not covered much in the curriculum - which was the proximity of the United States. Mackenzie, before, during, and after the rebellion, was in favour, not of moderate reform of the colonial government and finances, but of the establishment of a Republic embodying many of the traits of Jacksonian democracy (Jackson finished his second term in 1837). As a second alternative he was willing to accept an American takeover. This had the tacit backing of the US - this was only a few years after the proclamation of the Monroe Doctrine and only shortly before the US formulation of the doctrine of Manifest Destiny; there's a continuity between the networks fomenting rebellion and the Fenian raids of the 1860s.

In addition, the economic conditions for farmers were poor; the rebels who did come out were playing out the age-old script of trying to kill the King when the crops fail.

The response to the rebellions had a larger context as well: the Whigs took power under Lord Melbourne in the mid-1830s, and their response to the rebellion (aside from giving them an opportunity of shipping "Radical Jack" Lambton, Earl of Durham out to the colonies for a while to keep him out of their hair) reflects in part the fact that their views were more sympathetic with some of the issues raised than those of, say, Peel or Wellington would have been. (Even Bond Head's appointment, which had provided support for moderate reformers like Baldwin, was a result of the change in English government.) We weren't taught about that, either, despite the fact that Melbourne's background was far more interesting than anything in Canada (consider Lady Caroline Lamb, his (deceased) wife).

It does nobody any good to teach history in a deracinated, decontextualized manner. It renders it less interesting, less comprehensible, and more liable to gross oversimplification.

[1]Actually 3, given Duncombe's Rebellion, which I wouldn't even know about had my father not grown up in Scotland, Ontario.

There's an article in the Atlantic called "My Daughter's Homework is Killing Me", by a father who tries doing his daughter's homework (in parallel, not for her) for a week. And although I do have a good deal of sympathy with the view that (except in languages, where sheer duration of drill is important) homework can frequently be profitably reduced, I have to say that, whatever the burden on the daughter, the father comes across as a special snowflake.

I mean, 40 minutes to reduce 11 polynomials to their simplest form? That's maybe 15 minutes. 20, tops, and quite plausibly 10, given the examples he showed. And similarly with the other examples he talked about. I don't know Spanish, and I can roughly parse the examples he gives.

An adult is supposed to have mastered this stuff long ago. The difficulty in helping my daughter with her homework is not how much work it is but how much my extra generation's worth of experience lets me waltz through things like translations from Latin or chemical bonds or historical analysis, so that I have to slow down, massively, to be helpful.

I'm prepared to make the argument that, with some specific exceptions, homework should be minimal until well along in school. The exceptions are straightforward: drill for foreign and classical languages (almost everyone needs this to succeed - unless they're in an immersion environment or are a linguistic genius); and background reading. (Much drill for math is oversold. It was a critical part in learning to do arithmetic in pre-calculator days, but that's no longer the thrust of the curriculum. And math problems are less effective as drill than sheer brute force memorization when it comes to the times tables. It's also worth noting that if the good students can finish their homework in class, it's not a matter of excessive homework but of student capacity.)

There is an argument to be made that learning to write essays requires a fair chunk of homework time. However, even an essay every couple of weeks shouldn't require more than a couple of hours at the length restrictions imposed at that level. An hour a week is not excessive homework.

In university, an analogue to "homework" is essential, but (outside the sciences, with their lab work) the normal load is about 10-15 hours per week in class (2-3 hours per course, five courses a week). In high school the norm is 30 hours in class or so. (26 and 1/4 hours a week in my day) and the daily or near-daily classroom time provides much of the practice needed to keep on top of studies.

But it does no benefit to the argument for reducing homework to overstate the burden it provides, or even to treat it as an undifferentiated lump to be measured by time. By presenting things that should be straightforward as difficult the author's approach is not particularly helpful.

Its entirely possible, too, that his attention is misplaced: that what is needed in his particular context is curriculum reform for some subjects and, for others, the simple realisation that some subjects are intractable and will require work for those who don't possess the appropriate knack.

For about the 100th time I have been reading a book of science popularization when it stops dead to explain the imaginary and complex numbers from scratch.

It's been almost 250 years since Euler's Elements of Algebra. Maybe it's time to introduce C and a complete coverage of the number system as part of a basic mathematical education in elementary school?

I greatly enjoyed, and benefited from, the time I spent as an undergraduate. I went to a small university which was focussed on undergraduate (B.A., B.Sc.) studies in the humane letters and core sciences. Its main distinction was not its specific programmes (although it had a few interdisciplinary areas: Environmental Studies, Native Studies, Canadian Studies) but its overall undergraduate focus, with small tutorials, a liberal arts orientation, and faculty who (in the absence of graduate studies) could focus on the more junior students.

The disciplines I took - English, Classics (Greek), Mathematics, French - had decently structured curricula and requirements which not only ensured that one would, if a major, get an even grounding in the discipline, but would also he able to plan fairly clearly what one wanted to take (for example, second year Greek offered a prose course (Attic 5th century) and a poetry course on Epic and Tragedy (a book of the Odyssey, a book of the Iliad, a tragedy by Sophocles, a tragedy by Euripides); as a Minor student I took the latter). The English curriculum had a few holes in its requirements - if one wanted to, one could graduate with an honours major without ever taking one of Milton or Pope (but not both) - but otherwise provided the necessary courses for a solid grounding. The French department required all majors to take Corneille and Racine, which made sense, given their preeminence. (I dabbled, having a lycée background in French Literature, and studied French poetry instead: I had already has my exposure to Polyeucte and Phèdre and wanted to cover some topics I hadn't already been as thoroughly exposed to.)

I received (yet another) appeal via e-mail for donations as an alumnus. I had been hearing things about the current state of the place - my father is a Professor Emeritus - and noting that advertisements I saw on the subway were increasingly vocation-oriented; so I downloaded a copy of the current academic calendar.

They've trashed the place. Why I say that will take a bit of explaining.

Why do we consider humane letters - literature, classics, history - to be worth supporting with public money for study at a university level?

The strictly utilitarian answer, represented recently by the Federal CPC's higher education policy, is that the study improves critical thinking to prepare students for the business world. However, this is at best an argument for some form of post-secondary education, and not for specific forms which are, honestly, as far away from the requirements of business as you can reasonably get before crossing over into the fine arts. This is the basis of innumerable jokes regarding arts majors ("Do you want fries with that?").

In fact, the use of first degrees as credentialism is well-embedded in HR departments mainly as a shortcut, weeding out people whose capacity was insufficient to get through a degree rather than preferencing those whose skills were enhanced by four years of studying Aelfric, Baudelaire, Greek particles, or the Raj. (It also has a less upfront goal of weeding out working class or poor students whose access to the system was less easy, and whose ability to succeed in university was conditioned, even once they got access, to mimic their middle-class co-students.)

And it certainly does not answer the question of why public money supports research into, say, Alcuin's letters.

(At the other extreme, the idea of pure "ivory tower" research, if taken seriously, may be a justification for funding, but it doesn't provide a model for what to fund; nor does it provide a reason why students who are not focussed on being dedicated scholars should be pressed into such an environment for three or four years.)

Note that I'm using funding as a shorthand for "social support": in some systems there is no public funding as such - just about any system until the mid 19th Century, to begin with - but there's a social/philosophical reason why such institutions have a (usually high-status) place made for them.

It's a much rehashed area, beginning (arbitrarily) with Newman and proceeding forward through modern educational arguments, and with roots going hack through the Querelle des Anciens et Modernes to the curricula of the ancient and mediaeval worlds. Anything I have to say about it will be profoundly unoriginal.

Two lines of thought seem to me to be fruitful, though.

First, as a culture and a society, we define our commonalities and values by reference to a bundle of core givens including art, literature, certain historical narratives. For literature and the arts, these form canons.

We can't really get away from this. We can drop and add works to a canon, ignore or rediscover or add in historical sub-narratives, and even allow for simultaneous but differing sets to coexist together as long as they share some common values (see, for example, Wieselter's Kaddish for a sense of what western history looks like from inside a Jewish perspective). A curriculum which officially rejects "the Canon" in favour of including works from marginalized voices is not escaping from the canonical but merely expanding the Canon at the behest of certain fundamental values.

Much of the 19th Century enterprise in American literature was about trying to define a Canon for that part of the New World. Like all such efforts, it built on what had come before - Shakespeare was wildly popular, Longfellow translated Dante, Bunyan was important, Milton influential - but added in new themes and authors: Thoreau, Twain, Hawthorne, Melville. The American Revolution and Civil War provided historical narratives used to define USAn identity.

The same can be said of the mid 20th Century and Canada: Davies, Atwood, Laurence, Richler, Munro, and so on have become (partly for quality and partly for other reasons) a substantial part of a high school curriculum and Canadian Literature has a secure place in any Canadian English Department. (Note that it's open at a tertiary education level to ignore parts of a broad canon in favour of getting a groundwork in foundations: an argument can be made that the serious study of literature in English can be best grounded in a study of the generally best and most influential works, which would tend to emphasize more heavily older works and those with an international impact.)

For the past several centuries, a normative mix would have been (still is, in many ways): material from the classical world (my daughter's grade 9 English course has a Greek mythology component, and she is able to take Latin; at large, classical literary themes, philosophy, and history still play a significant role in public discourse and thought); from the English Renaissance (mainly Shakespeare in the schools, but the Tudors and Stuarts still occupy a niche in our collective memory palace); from the early 19th Century and the Napoleonic Wars, although the Romantics and Scott have faded out somewhat. The Victorians maintain a foothold in both popular and scholarly culture. World War II now occupies a large block of the collective history remembered generally (look at the history section in any bookstore), and more recent, local histories and narratives supplement the core, as do some reflecting minority viewpoints.

Secondly, although the old belief in the extensive benefits of an education in humane letters has been somewhat constrained by the experience of the 20th Century - see Steiner's Language and Silence - there is still an argument to be made that such an education produces benefits in the recipients which make them better and more informed citizens, possibly more discerning moral agents, and better equipped to improve their own quality of life.

This argument leans on both arms of the old defenses of literature as pleasant and utile, and on the perception that not learning history condemns one to repeat it. (Of course, one could repeat it in any case, like the Bourbons, forgetting nothing and learning nothing. You can lead a horse to water...) As such, it relies on the choice of topic, preferring the better over the worse as topics of study.

(As an aside, yes, there really are such absolute distinctions, unless one is genuinely ready to consider Milton the peer of Heavysedge).

The new curricula have thrown all that overboard. There are no longer, for example, any firm requirements regarding what one has to take to get a major in English. The department recommends some groupings, and a dedicated serious student could more or less approximate the courses I took, but the majority of courses are thematic in nature, some restricted to a given period, some diachronic. The better courses would in fact - at least as titles - make good graduate courses for students who already had a solid grounding; as undergraduate courses they amont to dabbling.

The modern language department website does not talk about literature at all; it's all about the uses of language in government or business. There are some courses in the standard canonical French texts in the syllabus, but none are required for a major in French (some small amount of study of Québécois literature is mandatory).

There is no set content for courses in Greek; they are of the form "Continuation of ancient Greek syntax and grammar, followed by readings from ancient authors". No specific texts are listed; conceivably the same course could be Homer in one year (it's at the level I took Homer at), Xenophon in another, and Procopius in a third, based on the inclinations of the teacher.

Cross-disciplinary programmes abound. I love good cross-disciplinary work, but the good work I see is produced by authors who have spent their years in the trenches of slog.

There's a frequent vocational tone to the material addressed to students: "Students of philosophy develop advanced skills in critical thinking, problem-solving, and communication – valuable foundations in any number of career choices"; "You will develop exceptional research and communication skills [in History] that can be applied across many career options". We have let our community colleges become universities, but we our universities, at the undergraduate level, are promoting themselves as glorified community colleges.

(As far as skills in the workplace go, I'm not sure I use any skills which I did not develop in high school or, alternatively, on my own and not in my university years (like computer programming). I did start out for about six or seven years using knowledge I acquired in Law School, which is a very different kettle of fish from an undergraduate programme.)

Put bluntly, the appeal is a combination of the superficially glitzy and the unabashedly mercantile.

This "small university" is now four times the size it was in my day; they have sold their birthright for growth (and considerably upped the size of the graduate programme as well: the government funds graduate students much better than undergraduates.

The characteristics which I consider the important ones from my day are gone. I can no longer in good faith recommend it to someone looking for advice on university choice.

The Ontario Government is getting into a frazzle about the failure rate of public school students in mathematics, offering bonuses for teachers doing skills upgrading. Fingers have been pointed at the teachers' math skills, their math teaching skills, the curriculum, and other possible culprits.

There is, of course, a long-term issue with teachers and math skills, in that someone with good math skills coming out of university can find more attractive areas to specialize in than teaching.

However, I have spent the past several years watching my daughter deal with the curriculum, and I do think that there is a problem with it: it fits the needs of almost no children. It flits from topic to topic in such a way that students who have difficulty do not get enough drill to master the issues; but it also allows for no real exploration of the issues by students who are good at math, for the same reason.

They will have a two or three week unit on series, for example, which could be extended to any number of interesting things to explore; but then there will be a sharp break and they'll move on to an equally short unit on, say, geometry.

And while we're on the topic of math skills in the general population, maybe we should ask: what skills?

A few weeks ago I was on public transit and saw an ad designed to popularize the idea of a need for math skills. The example problem it gave was a simple word problem of the sort which requires conversion from words to a simple polynomial and then solving for x. It was soluble by someone with high-school math trivially. But I thought: for someone who does not work in the sciences or engineering, where is that type of skill necessary? Certainly not in everyday life; nor, I think, in accountancy or other similar fields, where numbers tend to be delivered and manipulated in quite a different way. So for a student with an interest in (say) history and languages, there's no obvious reason for this sort of skill to be considered a critical one: yet the provincial curriculum makes it important. In contrast, estimating probabilities and risk in a back-of-the-envelope manner is probably more important in day-to-day life; humans are notoriously bad at it. Understanding some of the underlying issues around encryption (such as the difficulty of factoring large primes, or the ease of doing frequency analysis) is becoming a generally useful skill set (not the ability to do it, but the understanding of what is hard and what is easy).

Students who have the potential to be good scientists, mathematicians, engineers, and the like need a far more challenging, ambitious, and interesting curriculum than we are giving them. (A genuinely competent 17-year-old should be able to handle Hardy's Course of Pure Mathematics if properly prepared.) Students who are not going there need only a fraction of what we are shoving down their throats. (When was the last time I really needed, say, trigonometry at the high-school level? I don't have to measure very many things by angle-and-one-side mechanisms; either I need more -- Fourier analysis, full-blown trigonometric functions, etc., or I need none.) And the relatively rare students who have the ability but are interested in everything -- literature, history, philosophy, and languages as well as maths and sciences -- can handle the more difficult stream and benefit from it.

This story in the Globe and Mail about social promotion reminds me of one side of this issue that's rarely canvassed.

Stories like this -- about the various reasons for the disappearance of "failing a grade" in the public schools -- tend to have a great big unstated assumption: that the North American model of teaching -- one curriculum per grade, centrally set and common (at least) to all the children in a given class -- is an unchangeable norm. (I suppose I could just as easily call this the French model, since it also applies to the Lycée system -- which, however, incorporates far more streaming of individuals early on.) However, this model is not, and historically was not, the only system, although there was significant political bias in favour of it when it became the dominant/exclusive model in North America in the first half of the twentieth century.

Other models (which have, for example, been tried in the Netherlands) where each student effectively works to an individual contract worked out with the teacher at the beginning of the year within very broad constraints decouple the social and academic aspects of progression through the school system so that the conflict between the two is much reduced for students who depart markedly from the average.

(The other side is the issue which isn't addressed in the article -- the fact that if students with greater needs for "catch-up" are promoted in a cadre system, they may be better served, but it drains away resources required for other students, and tends in the long run to drag down the level of the curriculum. But that's another issue.)

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The Advantages of a Decent Education
University Degrees with "Earning Potential"
Eddication
Too Easy?
An Observation
Curricula
The Farmers' Revolt
Homework
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Math curricula
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Entries tagged with education

The Advantages of a Decent Education

University Degrees with "Earning Potential"

Eddication

Too Easy?

An Observation

Curricula

The Farmers' Revolt

Homework

i

Why I am disowning my undergraduate university

Math curricula

Social Promotion