Music and Poetry in English

If I ever get around to teaching English at secondary level, I will make sure that I exploit the analogies between music and literature. I think the analogy is quite illuminating, with regards to the distinction between “form” and “content” and the relationship between them. More importantly, it is likely to interest students more than a lesson that stuck solely to poetry or prose. Most school students have musical interests of some kind, and with a bit of prodding most should recognise that the appeal of a piece of music is bound up closely with the relationship between its form and its content.

In a song, of course, the relationship holds between the lyrical part of the work and the instrumental part. The distinction between form and content, when made out in this way, is easier to grasp than the same distinction as it is manifested in poetry. It is easy and natural to make a separation, even a physical separation, between the words and the music in a song; whereas it is not so easy to make the separation between the “message” of a poem and its “delivery” (Partly because a student needs to know about things like rhythm, rhyme, alliteration, assonance, metaphor etc., before they can give a full account of the distinction; and partly because the distinction is problematic in poetry anyway).

As well as this pedagogically convenient difference between music and poetry, there are pedagogically convenient similarities. Much of the “form” of a poem comes from its sonic effects. Also, at least one thinker (Walter Pater) has held that it is the mark of a good poem that it gets close to the condition of music; and some interesting poetry has been written on the basis of this idea (eg. Gertrude Stein).

Many of the ideas about the form-content distinction that one needs to learn in the poetry case, can be straightforwardly carried over to the music case. Here are some examples:

That a good piece of art should achieve a match between form and content; and also that there may be some exceptions to this rule.

That the same content, given a different form, can be given quite a different meaning.

That form and content can match up in different respects: they might match in their mood, their tone, their pace, their degree of order and regularity.
That the work can vary in these respects, and the artist take steps to ensure that form and content vary concurrently.

That some elements of form are (for various reasons) quite rigid and non-negotiable, while others are easier to manipulate.

That it is tempting to relax the more rigid elements to give the artist more “freedom of expression” (Radiohead, Walt Whitman); but that this relaxation can have its downfalls as well as its advantages.

One of the dangers of doing this sort of thing, apart from annoying the class next door, is that students might resent this intrusion of school life upon their music life. Putting Nirvana in a classroom might “take all the fun out of it.” But I should think it more likely that a student would welcome the opportunity to discuss and explore their out-of-school interests during class time. And the idea that excessive analysis can destroy an artwork, or at least fail to illuminate its appeal, is an idea worthy exploring; and another of the useful analogies between music and literature.

System, O My Darling

Following on from this little thing about method and matter, here is a little thing about system. A fine thing, system, and worth talking about. From one direction, it looks like the value of system is unique to matter: system is all about taking objects and arranging them neatly. But it is important to method as well. Methods are not just processes, but systematic processes. And the best part about teaching matter is ontology, the part where students learn how a subject is made up of a system of parts. System is not a bangle on the wrist of learning, but the fibre in her cloth, the leather in her shoes. Praise her!

Anyway, system makes things easier to remember, for the same reason that it is easier to remember Pascal’s triangle than phone numbers. But it also confers understanding. Indeed, arguably the pursuit of understanding just is the attempt to bring more system to our awareness of the world.

I guess some disciplines are more amenable than others to a systematic approach to teaching. Mathematics, that powerhouse of systematicity, should surely be taught so as to bring its neatness to the fore. Currently students are taught two different ways of solving simultaneous equations (substitution and elimination) when really they are the same thing. Subtraction is analogous to division, but you would not know it from text books. A lot school-level of algebra is based on a handful of basic rules (associative, distributive, commutative etc.), but this tends to get lost. Rediscover this, and school maths would look more like University maths. And maths in general would at once become easier and more interesting.

One senses that English might not work so well under a systematic tutor. Is there really a method for writing a poem? And would we want one? But still there are parts of that subject that make more sense when put in an ordered way. Like any other subject, it contains concepts and statements that can be illuminated by their interrelations. A simile is not something completely different from a metaphor, and pedagogy usually reflects this. A symbol is not completely different from a metaphor either, nor from an epitome or an image. And the following words all mean much the same thing: trait, characteristic, feature, quality, attribute. Pedagogy should reflect these things too.

A plausible objection to all this system is that it makes everything too rigid. It would be to deny the variety of mathematics, the way in which there are often many different paths to the right answer. And it would suck all the creativity out of the study of literature.

But there is no need for system to suppress the profuseness of mathematics. For most students the choice is usually between using a consistent and transparent method, and using either the wrong method or no method at all. And for those students who can see a variety of right methods, there is value in showing them how these are connected (eg. how geometric and algebraic methods are analogous to one-another). There is value, too, in showing them how some methods are better than others, in the sense of being more elegant or simple, or using less extraneous information (as in the case of simultaneous equations, mentioned above).

It is also wrong to conflate system with over-authoritative teaching, at least in mathematics. The fact that different aspects of any subject are richly interlinked would surely make it easier for the teacher to take a passive, guiding role in the learning process. They can point out connections and leave the student to follow them up, extrapolating from prior knowledge. How might you extend this formula to the 3D case? How might you solve a system of three equations rather than 2? Look for other ways in which negation is analogous to division. All of these are good exercises, and they rely for their success on the system that is just sitting there in all mathematics, waiting for teachers to grab it.

Almost certainly, an over-emphasis on system would indeed suck the creativity of literature. I expect it is easy to do it badly. But this is no reason not to use the system in the parts of the subject where it does exist. And it is still worth pursuing a kind of systematicity in more unruly parts of the subject. We want students to draw comparisons between different texts, to set characters alongside one another and see what we find, to look for repeated images. All of this is a move towards a more organised view of a novel or poem or whatever. (It’s just that we look along different lines in the English case: we look for similarities in respect of personality, manner, mood, instead of shape or angle).

It’s all very well going on about how system is the greatest thing since Dewey. It’s another thing to give some examples of how it could be achieved in practice. Given the right proportions of time, energy and brown bread, I will try to do this in some later posts.

Method and Matter

One complaint about current education is that it puts skills before facts. The nub of this distinction, as I see it, is the distinction between processes and results. Another way to express the complaint is to distinguish between method and matter. Here the underlying distinction is broader, since it is between processes and objects, where the latter includes results but other things as well.

Both distinctions make good sense. But the first one can be misleading because it is narrow. Clearly there is a virtue in teaching students to master a systematic processes for reaching conclusions, rather than teaching them to memorise conclusions that others have reached. But there are things that are not skills or facts, and which are also valuable.

I trust that the term “matter” has quite a lot of intuitive content. Think “subject-matter” and you are close enough. Roughly, it is the stuff that students apply their methods to. Only once the method has been fully applied will results appear – call this resulting stuff the end matter.

Here are some reasons why students should be taught matter, so defined, as well as method.

Methods are usually only applicable to certain classes of matter. Knowing these classes, and knowing how to match them up with the right methods, is an important part of the learning process. The methods of solving simultaneous equations are not much use for solving differential equations.

Is this a trivial thing, this process of using knowledge of matter to make methods work? Once we have learnt the methods for solving simultaneous and differential equations, do we really need an extra lesson to tell us how to apply them to the right sort of matter? Sort of. I guess knowledge of matter tends to be smuggled in with knowledge of method. Because of this, it would be hard to neglect matter even if we never thought about teaching it. But it is worth making the point, in case of situations (which I can’t think of right now) where the marriage between the two kinds of learning is not so tight.

End matter can also be useful as an examplar. One way to learn how to do something is to look at the end result and work backwards. This works partly because it is not always clear at the start what one wants to achieve (what does it mean to “solve this equation for x”? Showing a solution is a good way to answer this question). It works also because the end result usually contains information about its genesis (look closely at a finished building and you can get some idea of how they built).

I don’t recommend that students check the answers to every maths question before solving them. As a general method, this is close to useless. But as a method for learning how and why the right method works, it is quite useful.

Learning matter includes learning about the basic constituents of a subject, and how they differ from the basic constituents of another subject. In philosophy, questions about what is are at least as important as questions about how we know. Why not think the same of education?

One reason why not is that ontology is not very useful. If we know how to get the right results, and we know why our method works, what’s the use in learning more about the things we applied our method to? Well, perhaps there is not much use, in an instrumental sense. But if this kind of usefulness is our aim, why not forget about justification as well? The reason one would teach students why a method works (and not just how to apply it) is to enrich their understanding. This seems like a good reason to teach ontology as well.

Lastly, methods would not act at all if there were nothing to act upon. Sure, it is important for a History student to learn the general skill of writing essays. But they can’t write an essays at all without first learning something about History. Methods cannot be applied in every direction all at once from the beginning (one can’t expect a fourteen-year old to learn everything about an historical period from primary sources; some facts need to be taken on trust).

Of course, often it will be appropriate to teach matter in a methodical way. We don’t want just to tell students that maths is made up of such-and-such a collection of basic parts. We want to illuminate the process by which we came to possess this information, as for any other bit of information. But recognising that matter is worth knowing about is also an important step.

Boys Debating Nicely

Note: This post originally appeared as a guest post over on Philosophy Etcetera.

I note that there has been an upsurge of interest in all-male schools in New Zealand, and that part of the reason for this is, reportedly, the "feminising" of coededucational schools (no references, sorry: it was some time ago). According to one principal, coed schools are becoming increasingly unsuitable for boys because they do not cater for the "masculine" needs of boys; in particular, coed schools tend to emphasise "group discussion and deliberation," rather than more combative, aggressive activities of the kind that are attractive to young males.

Reports like this bring out a problem in school education thathas been suggested to me by a small amount of anecdotal evidence and a slightly larger (but still fairly small) amount of personal experience: namely, that the tendency among school-age males towards combative activities, and away from cooperative activities, looks to be at odds with some of the intellectual values that school is supposed to inculcate in students. Let us suppose for a moment that school-age males do favour combative over cooperative pursuits, including those in the domain of critical thinking. What kind of problem does this present, and how can it be mitigated or overcome? Is the problem exaggerated?

This question is interesting to me partly because intellectual values in question here are of a kind that is especially pertinent to Philosophy. One of the skills that study in Philosophy is meant to develop is the ability to argue nicely: to take other people’s views seriously, and to respond to them with charity and sensitivity; to be open to the possibility that one might be wrong, and to revise one’s beliefs when one discovers that one is wrong; to avoid simplistic dichotomies between right and wrong*; to regard the pursuit of truth as an inherently valuable activity, and not to sacrifice this end for the sake of other ends, such as that of beating a long-time rival, winning personal glory, or avoiding the embarrassment of public error. This may not be a comprehensive list, or an entirely accurate one, but you get the idea. And it is natural to think that the intellectual and social qualities in this list cannot be introduced unless the combative spirit of young lads is somehow softened or removed. What I want to argue here is that that the situation is quite so bad as one might think, given this brief analysis of the problem. Male combativeness is a real problem here, but it might also be part of the solution; and insofar as it is a problem, it is only partially a problem.

*I do not mean to say anything daringly post-modern here. I mean to say that many claims are too vague or complex to be straightforwardly true or false; and that the best way to arrive at a truth about such statements is to replace it with a set of more precise claims, whose truth-values may differ from eachother.

The first point to note is that arguing nicely is not the only end of communal discussion. We also want students to argue rigorously, and one way to promote this value is to encourage students to subject any beliefs or arguments to severe scrutiny. To be sure, an overly combative person is likely to bestow such scrutiny primarily upon the ideas of his opponent; and to ignore or obfuscate the errors in his own thinking. But at least this is a start. One might also object that a combative person is more likely than a cooperative one to be dishonest in his scrutiny: to exaggerate the flaws of their opponents' thinking by the use of deviant dialectical tactics, of rhetorical rather than philosophical forms of persuasion. But it looks to me as if that sort of dishonesty is more a function of the intellectual powers of the disputant, rather than their attitude to the debate. If all members of a dispute are good at distinguishing rhetorical tactics from philosophical ones, then it looks as if this problem would at least partly disappear. For, if one is really intent upon proving one’s opponent wrong, and everyone involved is aware of what constitutes a genuine proof; then any deviant tactics are likely to be counter-productive to one’s competitive aims. So one way to cope with a combative spirit, and to turn it towards worthwhile intellectual ends, is to improve the rational powers of students.

Of course, such rational improvement is not sufficient to guarantee a good discussion. Social and other intellectual skills are also important. But again, it is a good start.

Another point is that arguing nicely is something that one can be combative about. There is no difficulty, at least in principle, of getting a few groups of people together to compete against eachother with regard to their facility for dignified, honest, cooperative deliberation. Of course, there is some difficulty, in principle, in having groups compete against eachother with regards to the sincerity of their commitment to arguing nicely. If a student sees the worth of arguing nicely only when such a practice allows him to compete viciously with rival groups, then clearly that student is missing something important. But a facility for arguing nicely is, I think, at least as valuable as a desire to argue nicely for its own sake; it is certainly a good start.

Perhaps it is a little unrealistic, though, to think that combatively-minded young lads will be as enthusiastic about competing over something like communal inquiry, as over things like romance or wrestling. But if this is the case, then the problem may lie not with the combative nature of young lads but with their disinterest in formal learning: they turn away from communal inquiry not because it does not allow them to indulge their combative instincts, but because it is an intellectual rather than a sporting activity. This is still a problem, of course, but it is a problem for another day.

And, insofar as communal inquiry does fail to satisfy the combative instincts of energetic young lads, something can still be salvaged (conceptually at least) by clarifying the notion of "combativeness." So far I have used the notion of "combative" in a fairly loose sense. Now I want to distinguish a few senses of the word, because I think there are some kinds of combativeness that are more compatible with cooperative debate than others. It is possible to distinguish conceptually between these senses of the word; distinguishing between them in practice (ie. by separating out one sort of combative behaviour from other sorts) is probably a lot more difficult, and eliminating the undesirable forms of combativeness is probably more difficult again. But the conceptual distinction is a good place to begin. So here are three kinds of combativeness:

Antagonism. To say that males are antagonistic is to say that they enjoy situations where two or more people are not only fiercely engaged in some competition or another, but that they compete spitefully or maliciously. They genuinely wish to cause eachother personal harm, either physically or emotionally or socially; and if they cannot do it themselves they like to watch it happen.

Competitiveness. The trait of relishing any chance to set one's own abilities against those of another. Fierce competition need not mean antagonistic competition: one can "play hard but play fair."

Ambition. I use "ambition" to refer to a desire to excel, though not necessarily at the expense of others. A merely ambitious person will wish only to perform as well as they possibly can, enjoying the strain and excitement of a difficult challenge. The challenge need not be posed by another person, and the strain need not be against another person.

Now, clearly antagonistic people are going to be ill-suited to good communal discussion. Not only are they likely to see the activity as an effort of self-aggrandisement, but that self-aggrandisement will take the form of petty personal abuse. They are unlikely even to engage their opponent in genuine debate, except about his height or facial features or the habits of his mother. Competitive people will be more successful, since they will compete over the matter under debate (ethics, politics, religion, the quality of some work of art, etc.) rather than irrelevant personal details. And people who are merely ambitious, without being competitive (in the sense just defined), will be even more successful in arguing nicely: they will not only seek truth themselves, but also encourage the efforts of others to seek the truth, since by doing the latter they enhance their own chances of achieving that end. So ambition is not only compatible with arguing nicely, but also conducive to it: far from being removed or softened, it should be encouraged.

Just how these three different traits are manifested in the average male school student (ie. in what kind of interrelation and in what proportion), is something for phsycologists and sociologists and teachers to work out, I think. It is empirical question (though of course not a merely empirical question). But it would be hard to answer the empirical question without having the conceptual distinction already in place.

I have written all of this without ever having tried to engage young males in good communal discussion, and I would be interested to hear from anyone who has had practical experience in this matter. Is it as difficult a task as it is sometimes made out to be? And are there any other traits within the broad notion of "combativeness" that I have missed out, or that are especially prevalent in school-age males? Comments appreciated, as usual.

Education as an Ideal

Over here is a part one of my introduction to my interest in Education. The other two parts were posted over on Philosophy Etcetera, which kindly let me post as a "guest blogger" for a few days. So here are Education as an Ideal Part 2 and Education as an Ideal Part 3.

Class Misrules

I wonder if it would be wise for a school teacher to hand out “class rules” of the following kind ie. with plausible-seeming objections attached. The idea is that they are highly likely to provoke students into thought, because they hold out the possibility of real gains (ie. a change to the rules) for anyone who thinks carefully about them.

Perhaps a student would not really consider this possibility as genuine, since a teacher who gives out rules like this (the student might reason) must be pretty confident that the counter-arguments are flawed. But even in that case it is surely healthy for a teacher to show that he or she is willing to at least consider the counter-arguments, rather than just presenting students with the sheet of unjustified rules that they have seen hundreds of times before. And the student’s suspicions about the teacher might be outweighed by the apparent force of those counter-arguments, causing the student to genuinely believe that there is something to gain by taking them up with the teacher. Or perhaps they might have no doubt that the teacher considers the arguments to be flawed; but still take them up with the teacher, or think about them themselves, to find out just how they are flawed.

I think the rules and the counter-arguments should be such that some of the former do require modification in light of the latter. It would lessen the value of the exercise if students went out of it with no sense that they could actually change things by producing good arguments in favour of their own view.

What would other teachers think? Would they be enraged to find that some idiot of a teacher had handed out a bunch of excuses and smart-alec replies to students, which those students will use against their long-suffering teachers at every opportunity? Hopefully they would not be enraged. But even if they were, one could hand out a sheet of counter-counter-arguments, to rip out at its roots the anarchic impulse to think



“The class rules are in bold. If noone comes up with good reasons to change those rules, then they stand. Otherwise, they won’t.

Arrive in class on time (this rule seems a bit fishy. Why should students come to class on time? If they can do this without disrupting anyone else, are they doing anyone any harm? You might say that they are doing a harm to themselves. But surely the best judge of that is the student, not the teacher. What does the teacher know about the many trials and temptations that draw a student away from class, and thwart their earnest attempts at punctuality? But this may not be a good reason after all, so the rule stands).

Wear a tidy uniform (but this seems a bit fishy as well. What does a person’s dress sense have to do with their school work? A school is a place for education, not for cosmetics. And students can become educated, and very well educated at that, without having the least regard for their clothing. Socrates was notorious for his bad dress sense. Perhaps this rule has something to do with giving off a good “public image,” at cafes and bus stops and places like that; the school wants to be judged well by the public. But why should we submit to being judged on our clothing? We keep hearing that it is shallow and materialistic to judge a person by what they wear: why shouldn’t this apply to schools as well as to individuals?)

Avoid profanities (But suppose that everyone used profanities all the time. Wouldn’t the profanities then lose all of their meaning, like any words that are used all the time, so that they would no longer really be swear words any more? So if everyone were allowed to swear, there would be no more swear words. So why should we ban them? If we ban them, we’re loosing a good chance to perform a public service.)

Do what the teacher says (But is it not true that people learn best when they do so on their own initiative? And teachers are always saying things like “use your initiative” and “take control of your own learning.” So wouldn’t it be best if students were left to learn independently of the teacher’s commands?)

Don’t be a smart alec (But isn’t it one of the aims of education to produce people who are witty and intelligent, who can think on their feet and are able to defend themselves? If that is the case, then wouldn’t it be better if students were allowed to practice these skills on the teacher?)

Always do the best that you can do (Well, that sounds like a nice little saying, but it is obviously wrong. Clearly it is not right for a person to “do the best they can” to become a thief or a liar. So this little saying gives people no good reason to do their best at school: perhaps school is a bad thing, like lying or burglary. One reason you might think school is a good thing is that if the student does well they will have a better chance of getting a good job. But that reason doesn’t work, because a person who does an average amount of work can get the same mark as a person who does a lot of work, even if they have the same natural capabilities. The marking scheme is so crude that often it can’t distinguish between those two people. So why not just do an average amount of work and leave yourself more free time to do other worthwhile things? You might say that is “shirking” or something, but isn’t it just good time management?)

Never talk while the teacher is talking (But the teacher talks while the students are talking. So why the double standard? You might say “because the teacher is giving out important information that everyone needs to hear.” But….but…well, see the next one)

Don’t disrupt other people’s learning with violence, excessive talking, etc. (But when the teacher says “you ought not to disrupt other people’s learning,” isn’t that a moral claim? And hasn’t the twentieth century taught us that moral claims are always relative, so that what is morally wrong for one person may be morally right for another person? Some African tribes think that it is morally right for young children to be forced into marriage at the age of fifteen. In New Zealand we think this practice wrong, but we tolerate it because we know that the African people have a different moral scheme to our own. Why don’t teachers take such an enlightened attitude towards their more talkative students?)

Students will be treated as adults unless they act like children. If they act like children, they will be treated like children (But if a person gets sick and goes to hospital, everyone says “just treat them normally, as if they are quite well; that way they will get better more quickly.” And if a person starts acting like a dog, it would be foolish to start treating him like a dog: if you do that, he’ll just become more and more convinced that he is a dog, so he’ll keep acting like it. If you treat him like a dog, you have made things worse, not better. And if you agree to that, you would be inconsistent if you treated people like children as soon as they started acting like children.)

Make sure you can back up your actions with good reasons (That’s a bit fishy as well. Suppose Jack thought that your idea of what counts as a “reason” is wrong. Then you would have to back up your idea of what a “reason” is. But what kind of things would you use to back it up? You would have to use “reasons,” of course; but what sort of things will count as “reasons”? You would have to use your own idea of what a “reason” is. But of course Jack will not be convinced, because you have assumed as true the very thing that you were trying to convince him about. It’s as if you were to say to Jack “The moon is made of cheese,” and then try to convince him by saying: “the moon is made of cheese; therefore the moon is yellow and has holes in it and is made from cows milk; therefore it must be made of cheese.” Which is clearly a bad argument. So noone can give any good reasons to believe that their idea of “reasons” is the right one. So every reason is as good as any other reason. So as far as reasons are concerned, any action is just as good as any other action. Isn’t it?)”

Education as an Ideal (Part I)

Note: Links to part 2 and 3 of this series can be found over here

INTERVIEWER: Would you advise your students to become schoolteachers?
ANTHONY BURGESS: Only the ones that I dislike.

Let us suppose for a moment that Burgess was telling the truth on this one. If so, he shares a distaste for the art of schoolteaching that seems to me to have fairly wide currency among the general population. I do not mean a distaste for schoolteachers, but for what they do: the general population is on the whole quite pleased to have schoolteachers round to dinner, and if asked the general population would probably say that schoolteachers “do a fine job,” or something like that; but a lot of them privately consider that job to be one of the least appealing around. Since I have not yet had the general population around to dinner, I do not yet have a really accurate idea of its opinion on this matter; but everything I have heard so far seems to confirm what I have just said. If my impression here is correct, this is a bad situation, a really bad situation, and one that should change. If school education is really to perform its functions properly, and if schools are to be not just a kind of early zoo, or a sop to the prevailing ideology, it is not enough for the general population to have a vague idea that it is a healthy-minded occupation; there must be, among at least some people, and ideally among as many people as possible, a sharp sense of both the need for good schoolteaching, and the appeal of the job. We tend to think of teaching as a job, possibly as a profession, maybe as a career, but usually as the enactment of a set of ideas and capacities that are developed through formal training: what we need is for a large group of people to think of it as a vocation, the enactment of an ideal. The following is my first attempt to show why reasonable people can think of schoolteaching in this way. If my impression about the general population is incorrect, then the following thoughts can do no harm.

The following is also, of course, an introduction to a broader subject, namely Education. My interest here is not just in the vocation of schoolteacher; but also in the institutions of school and University; in other, less formal forms of learning; and in the academic study of the nature and purpose of Education, which I will call the Philosophy of Education. The latter is important because some of the repellent features of schoolteaching are, I think, contingent features that are peculiar to our time and our school system; and one cannot erase these features without making some changes to that school system. And Philosophy of Education seems to me the best place to go to get a better idea of just which features of modern schoolteaching are contingent, and what alterations to the system are the best ones to make.

With this in mind, I will start this, the first part of my little polemic, by expanding on my suggestion that the current jobs of schoolteaching really does have some repellent features. Low pay and ill-discipline are two obvious features of this kind. These features are easy to regard as peculiar to our current system, and for this reason I will disregard them for now. Here I will deal with one other feature of current schoolteaching that is less obviously contingent, and which probably puts a lot of people off. It is natural to think that schoolteaching is a regression, a regression partly of a social kind but primarily of an intellectual kind. A schoolteacher is asked to abandon all of the sophistication of adult life, including the sophistication of their own discipline, and work in a place where there is not only a lack of such sophistication but also (in many cases) an unwillingness to embrace it. A maths teacher is asked to stop studying Riemannian geometry, and start teaching adolescents how to find the equation of a straight line; an English teacher abandons the subtleties of James Joyce or Milton for the sake of marking bad essays about Flowers for Algernon. There is something very depressing about this sort of backwardness, is as if all of the work in between was a waste of time: it seems like a collapse into the past, the opposite of human flourishing.

It may be that current schoolteaching encourages this kind of regression, but it does not do so necessarily. In saying this I do not deny that maths teachers are, in some sense, asked to downgrade their mathematics in order to become school teachers: what I deny is that this is a full view of the matter. First I want to make the obvious distinction between the matter that is taught and the matter of teaching. It may be (I will raise some doubts about this in a moment) that the matter which schoolteachers teach is primitive compared to what they have learned. But the matter of teaching, the skills and ideas that are involved in the work of passing on that subject to the student, are not primitive at all. If one concentrates on the taught matter, one sees the teacher as similar to a highly trained surgeon who is asked to hand out plasters at a playground. If one concentrates on the matter of teaching, one sees the teacher (rightly, I think) as similar to the same surgeon who happens to have been asked to operate on children. The teacher’s key function is as an expert in teaching their subject, not in the subject itself, and the former requires just as much sophistication (though often of quite a different sort) than the latter.

Of course, I do not mean that the matter of teaching requires no knowledge of the taught matter. I do not think I would insult too many teachers (and I hope I do not) by saying that their knowledge of a subject is less refined than that of an expert in the subject. On the other hand, I want to stress that the subject-knowledge necessary to teach a subject is greater than one might imagine. To illuminate this point, it is worth making the distinction between the student’s knowledge of a discipline and the teacher’s knowledge of a discipline. By the first I mean the knowledge about a discipline that the student is meant to acquire as a result of teaching; by the second I mean the knowledge that the teacher must have of the discipline before she can teach it effectively. Even if the former were primitive, the latter need not be. Anyone who has tried to teach a subject will know that it is often demanding, and that the demands are placed not only one one’s patience, social skills and other general teaching skills, but also one one’s grasp of the subject at hand. It is one thing to be competent at drawing equations for straight lines; it is quite another thing to be competent enough at this task, and related tasks in mathematics, to convey the basic idea with clarity, brevity, with one eye to relating this problem to others and with another eye to making it all seem very novel and exciting. It is also worth remembering that the teacher is usually hopelessly outnumbered by students, because this allows one to recognise the breadth of subject knowledge that is required of a teacher if she is to satisfy the curiosity of all of the students in a class. As far as I know, a trained expert in Science (for example) is usually only expected to possess highly refined knowledge in, at the most, one of the three main branches of science (Chemistry, Physics, or Biology). A Science teacher, on the other hand, cannot call himself competent unless she has a sound knowledge of all of these branches, plus some knowledge of the History and Philosophy of the subject: a less refined knowledge of each of these than is possessed by an expert, perhaps, but knowledge nevertheless.

Another way in which the teacher’s subject knowledge, and also the student’s subject knowlegd, is less primitive than one might think, is by differentiating between two kinds of primitivity. Teachers are asked to return to the basics of their discipline, and this could mean two things: it could mean a return to trivialities, or it could mean a return to foundations. Knowing how to count is a triviality: but the idea of a number, which is most clearly expressed in the practice of counting, is foundational to mathematics. Likewise, the act of identifying some expression as a literal or metaphorical expression is (at least in most high-school versions of that act) a trivial exercise, something that an English student learns to do right at the start of their education, and which they do very easily after that; but the distinction between the literal and the metaphorical is, I would say, foundational to literature. And a similar point could probably be made about History, Art and Science: the first step towards learning these subjects usually brings a student into contact with concepts or skills that are, in one manifestation, the easiest to grasp; and, in another manifestations, the most essential to the subject, and because of this the most important to grasp. Now, it may be that current practices encourage the teaching of the “basics” as trivialities, not as foundations. But this need not be the case. To be sure, there a limits to how far one can go towards teaching the foundations of number to high-school maths students (and there are probably few professional mathematicians, let alone high-school students, who have trudged through Russell’s Principia, or have read Quine on the subject of the foundations of mathematics), and I suspect that the point generalises: it usually turns out that the foundations of a subject are the most difficult to grasp as well as the most important. But I also suspect that there is enough that is both foundational and accessible about the basic notions of any subject, to make the teaching of those basics less like a return to infancy and more like a return to home, a return to the core of a discipline.

I hope that the above points give some genuine support to my claim that schoolteaching is not a regressive activity; the kind of support, that is, which not only gives the claim rational warrant, but also gives it emotional pull. One further point, and one which I would be especially negligent to ignore, is that schoolteaching is in fact one of the most progressive and forward-looking activities one could possibly achieve, as long as one considers its full consequences for society as well as its consequences for the teacher. As Richard points out over at Philosophy Etc., to equip young people with the general capacity to deal with future problems is to give society a benefit of a second order kind. By becoming a doctor or a politician, a person enables themselves to contribute to the current health of people or of a state; by becoming a teacher, a person enables young people to contribute to the health of the people and the states that they will encounter in their own lifetimes. The difference, as I see it, is not only that the teacher contributes to future gains rather than present gains. It is also that (if her teaching is of the right sort) she contributes to a general ability to solve problems, rather than to this or that particular problem. It is also that she contributes to gains that are currently unimaginable, perhaps because we have not yet discovered the means to make those gains (though future humans will do so, if properly educated), or because we have not yet discovered the need to make those gains (though future humans will do so, if they are properly equipped to identify new problems). School teachers, far from regressing into infancy, are responsible for causing young people to progress into adulthood, and if they make good of this responsibility then they draw the future world into a better state.

So far in this post I have set out to beautify one feature of schoolteaching that is frequently regarded as ugly, or at least that is very easy to see as ugly. What I want to do in the next post is to continue on the same theme, discussing some other features of schoolteaching that should give it a genuine appeal to right-thinking people. These fall into two kinds, namely those features that obtain in schoolteaching at any time, and those that arise out of the peculiar difficulties that current schools find themselves in. Both kinds, I hope, would (if they were widely appreciated) be helpful towards moving the art of schoolteaching, and moving Education in general, from the dull suburbs of the public mind into the central city.