Some wykehamist has argued that all young people should be forced to study Mathematics until they are 18 years old.
What nonsense.
I've nothing against Mathematics or mathematicians. On the contrary: the subject seemed to attract the same analytical minds as Latin and Greek. So very often, sensible young people chose Greek-and-Latin-and-Maths for their troika of subjects. They revisited the College years later, their faces distended by the exertions of London's clubs, with their tales of dangerous life in the distant and arid wastelands of the Treasury or the Foreign Office.
But if 'too few' of the young opt for Mathematics, the guilty women and men are ... not the poor young people themselves, but teachers who fail to make their subjects compelling or even tolerable.
In our current debate, bouncy people keep getting interviewed on TV (for a fee?) and rabbit on about how totally fascinating Mathematics is. Perhaps it is is for them; but why, then, are their former students queuing up in such vast droves to opt out of the subject?
Last time we had this same national discussion, we were told that those prepared to teach Mathematics should be paid more. (Why, if it's such fun?)
I can think of nothing more subversive of good Common Room relationships (both personal and professional) than this. How are the rest of us expected to feel, seeing crass and ineffective fools whose students attain lamentable grades in public examinations, being paid more than us just for "being Mathematicians"?
In principle, teachers who consistently show poorly in the public examinations of their students should be invited to move on and to take the fascinations of their subject elsewhere.
Tough but fair words. There is this statististic notion that the god of economic growth will be unhappy, very unhappy without the offering of a big portion of our youth. I recall from secondary school that while some maths teachers were excellent, most were terrible as teachers. They might've been good at this great language of mathematics, but teachers have to have a pedagogic ability to communicate this love and skill to the young folk.
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ReplyDeleteI fail to see how young people can possibly not be forced to study mathematics until they are eighteen. But then, the idea of studying three chosen subjects and nothing more at that age is foreign to me.
We had four subjects to choose to write the final exam and have them counted more. Mathematics did not need to be one of them (which they've changed for younger people, a move I do love maths too much to agree with), but if not maths then some natural science had to. But these were only those we took the exam in. We had to study the rest of the important subjects as well, and that included maths, and it did make some countribution to the final grade. Among these important subjects, of course there's one's own language (that is to say, literature); history; religion; physical education (with the specialty that among all compulsory subjects, that its marks could be replaced by other ones for the final grade); and except for the very last year either art or music. It doesn't, sorry for that, feel natural to me to expect from the young that are about to enter universities any less than a solid general education in all of that; and not the only, but certainly one of these things sure is mathematics.
Well, why? Only concurrently because you need to calculate much in professional life or because physics happens to be formulated mathematically or because you can make a good fortune working for insurance agencies when you have a fine university degree in mathematics (though school-mathematics won't suffice there) or because you quite likely have something of an instinct for programming when you are trained in mathematics. No; these are all secondary. University-level mathematics does, and school-level mathematics should, teach students firstly and foremostly that truth is a thing that has its justification of existence within itself, and searching for truth is a worthwhile pastime even if nothing comes of it.
At least a great part of the reason for the mystery that so many people hate mathematics is, probably, the failure to take that step. "I do not understand", they say. Then you go and explain it meticulously. More often than not, then they can understand, and their next step will be "oh yes, that much is clear, but what does it mean?" Well, its meaning is the proof that you yourself just grasped and called "clear". The proof of the pudding is in the eating, and the proof of the theorem is, well, its proof.
I think a great part of the "disappeal" of mathematics is simply the students' failure to make that mental step. Or more precisely, they would make it - all students are particularly awake when the teacher says "this will not be in the exam, just for those interested", and despite all their "but what do we need that for", even fourteen-year-olds may give that retort when the teacher presents group theory, but will be much less interested in adding and multiplying fractions, a thing you obviously do need -; but somehow feel they morally ought not to do it.
ReplyDeleteOther contributing factors are obviously the societal atmosphere that allows disliking maths; the personal failures many associate with it (but hey, sorry for bragging, but I did manage to love phyiscal education despite being better in all but one subject); and maybe even the idea even some mathematicians seem to share that it is the lesser mathematicians go to schools (which might be behind the, granted problematic, "let's pay them more" idea).
To be able to enjoy truth for its own sake and to get that you are allowed to enjoy the beauty of mathematical theory is a thing that I do consider important (like I said: as other things are important) for a future unversity student, or even religiously for a Christian, at least an educated one. (The Lord did not restrict himself to say: "I saved you by My death; go and sin no more, and receive the Sacraments, and hope for Heaven". He did say that; but he also said: "Oh, and by the way, the Father and I and the Holy Spirit are One.")
- And yes, this is rather obviously a mathematician, at least b.sc.-level mathematician, speaking.
Dear Father. I read this probably forty or more years years ago but it has stuck with me:
ReplyDeleteHe is a man well-skilled to deal with indices and surds,
X2 + 27X = 11/3rds.
And of course, one of the points of schools is to learn subjects you, on your own, would hate. Except with a great measure of self-discipline, you need to become at least comparatively good at a subject in order to be able to love it. (To balance what I wrote above: I was, especially when taught competently, not quite the failure at physical education, either.)
ReplyDeleteMany, I guess, don't acquire that in a lifetime. Those that do mostly don't have it already developed in their teen age. And even those that have it need it to be triggered by an answer to the question "why should I be interested in that?", which may be not obvious for a subject to those that do not already know it.
Hence the point of school is at least among other things to force people to learn what on their own they would not learn. It is fun to read Tacitus, or at least Cicero, or at least the Archipoeta's "A vagant's Confession"; but you have to be punched through vocabulary and grammar first. When some say "the appetite comes with the eating", it is fun - I do not mean snobbery, I do mean fun - to prefer to say "l'appétit vient en mangeant", but you have to be punched through at least a bit of introductory French to grasp that. And at least part of the school's job is to punch people through subjects far enough that they might like them. That includes bad marks, detentions and the rest of it.
One of the problems of maths is the question whether school comes far enough, of course. Which is why in my view elementary geometry is so important a branch of school mathematics. Not many university students have lectures in that (though the aspiring teachers do), but it really is mathematical, and it really is an area where students can be brought far enough to experience some "non-preparational thing" even in school. Coincidentally, even students that hate maths tend to hate it less than the other branches.
A few years ago I saw a notice advertising maths classes on a board at Reading University. No, this was not at an institution for the mentally challenged. It offered classes in arithmetic, percentages, basic statistics and a few other arcane topics. It was plainly a judgement on British secondary education. I suspect it was aimed at psychology students who thought they had signed up for a soft option and discovered that arithmetical competence and statistics were needed.
DeleteI was atrocious at mathematics when at school.
ReplyDeleteThis was good preparation for Catholic clerical life, where 2+2 may sometimes = 5.
I'm sure that I'll go far!
3 Types of Mathematical Thought
ReplyDeleteSpatial/Geometric Reasoning. Spatial visualization involves the ability to image objects and pictures in the mind's eye and to be able to mentally transform the positions and examine the properties of these objects/pictures. ...
Computational Reasoning. ...
Logical/Scientific Reasoning.
For me I think mainly in the Spatial/Geometric way, and was top in the Maths Set and bottom in the Greek Set. I also have a strong appreciation of the sound of a language, and was completely screwed when after one year of Oxford pronunciation of Greek as it was in 1949, we switched to Cambridge pronunciation.
I congratulate you, Father Hunwicke, on having summed up the ethos of this blog in just three sentences in recent posts:
ReplyDeleteSentence 1 (27 January): “The 1940s were a better decade than the 1960s.”
Sentence 2 (29 January): “I dislike People.”
Sentence 3 (also 29 January): “I can't stand Good.”
It seems to me that notwithstanding the apparent erudition of the content, much of what is written in the blog derives from two psychological traits:
1. A sort of “zeitgeist-phobia” summed up in the song title “Things ain’t what they used to be”;
2. A form of implicit misanthropy that I personally find hard to reconcile with Mark 12:31.
Nevertheless I find myself in agreement with your suggestion today that it would be unacceptable to force all young people to study mathematics until the age of 18. I have written about this here:
https://tinyurl.com/5apww8hk
Terry Loane
Indeed, Father. A mathematics teacher (and a very good one) told his colleagues at a conference a few years ago that they needed to face the fact that their greatest achievement had been to teach 85 per cent of their pupils to hate maths.
ReplyDeleteI did not complete my mathematical studies at the university forty years ago. I can however offer four pedagogical remarks:
ReplyDeleteWhen taught rigorously, mathematics is cumulative -- you cannot skip a year, or easily recover from a year in which you lost the thread of what is being taught.
People learn at different speeds.
There is a limit to one's ability, which good teaching and diligence may help one to attain.
Entering into the mind of a learner who is struggling with mathematics is a skill in its own right. As a teacher one must trace the confusion back to its source, before it can be dispelled. If not dispelled, the course of instruction may as well end right there -- because the subject is cumulative.
Any state-imposed pedagogical system which fails to take account of all of the above is nothing more than a silly gesture.
In my interactions with people in daily life I would be glad to settle for a general competence in mental arithmetic and some awareness that a billion is larger than a million -- and maybe very simple geometry. As far as practical motivation (since it's now generally assumed that innocent curiosity won't get anyone very far): the number of students who will specialise with a Master of Science degree in "Financial Mathematics", and then proceed to a lucrative career as a derivatives trader in one of the world's leading investment banks, will always be fairly small.
I taught what was fairly elementary maths in programmes up to master’s level. Juggling the figures and geometry was entertaining at least for me. However the more mathematically advanced ideas always led to the worst of all questions “ will this be in the exam?” Eventually it exhausted my limited patience and I gave up teaching.
ReplyDeleteA story is told about an old Irish Monsignor (I can’t remember his name) who was a famous mathematician and chaired the Mathematics department at one of the universities. At a reception one night he was approached by a matronly woman of the ‘hoity-toity’ persuasion who enquired: ”And what do you do, Monsignor?”
ReplyDeleteWithout missing a beat and smiling benevolently, the Monsignor replied: “Madam, I teach sums.”
Good to know from esapelion that I am not the only one whose Greek was totally scuppered by the switch to the "new" pronunciation. After five years of HO HEE TOE, TON TEEN TOE, TOW TEES TOW (as in ouch), TOE TEE TOE a new broom arrived and confused the Blazes out of us. And then I met Modern Greek. Result: Stick to Latin...
ReplyDeleteDear Terry
ReplyDeleteAre you American, by any chance?
Some things just don’t work when crossing the pond.
Father, I suspect that having grown up with no calculators and using pounds, shillings and pence your arithmetic skills are much better than young people today.
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