I have a heavy post coming very soon, but it seems worthwhile first getting in this quick, light one.
Once upon a time, before going off the rails, I was a (semi)regular mathematician. I proved theorems and stuff like that. I was a committed lecturer and, with all due humility, a very good lecturer, but I had no specific interest in “mathematics education” and I knew nothing about school mathematics. That began to change around twenty years ago when, back in Melbourne, I somewhat randomly began talking to mathematics teachers. I soon realised that most Victorian mathematics teachers, even very dedicated ones, knew little mathematics and understood less. I began giving talks to teachers and then public talks, and I discovered the obvious about myself: I am significantly better at telling jokes than proving theorems. Burkard then appeared and it all took off, first with the popularisation, which Burkard has continued, and now with my gadflying. Some years earlier, however, before all this began, I bumped into my future occupation, and into a maths ed titan. This is the story of that bump.
In the mid 90s I attended a lecture at Melbourne University. I think it was part of a mathematics conference, but this particular lecture was somehow singled out as special and was on mathematics education. I cannot remember why I attended; I cannot remember the specific topic and I had never heard of the speaker.
I arrived late, well into the lecture. It was being held in the main, large theatre of the mathematics department (Theatre A), and the theatre was not packed but it was crowded. My assumption, perhaps due to the unfamiliarity of the faces, was that the audience consisted largely of teachers. Whoever they were, they did not appear to be pleased. There were mumbled frowns as the speaker spoke.
The speaker was calm but strong. He spoke clearly and measuredly, choosing his words with evident care. He seemed aware of the tension, of disagreement within the audience, but seemed not at all perturbed by it. He answered some rather direct, if not accusatory, questions from the audience in a polite but equally direct manner.
I remember nothing of the content of the lecture, except for a single line. At some point, possibly in response to a question/accusation, the speaker pronounced,
“Mathematics textbooks from fifty years ago were much better than they are now.”
Of course I don’t remember the precise wording, which was probably more careful and more elegant. Perhaps there was some specification of the textbooks being compared, or the manner of their comparison. Perhaps it was textbooks from a hundred years ago. Perhaps the “much” was not so strongly emphasised. But you get the gist, and so did the audience. There was outrage. The mumbled frowns turned to loud denials.
The speaker was not remotely perturbed by this. He seemed not at all surprised by the reaction, and he responded politely but firmly. I cannot remember his response in any detail, but I can remember the general message: I’m sorry, but I cannot change the facts for you.
I remember very clearly my reaction to all this: “Huh!”
I was struck by the speaker’s claim about old textbooks; I think that was the first time I had heard a clear claim that school education might be going backwards, and significantly so. I was astonished by the audience’s reaction, my first indication that mathematics education had “camps”, that there were areas of strong dispute. And I was impressed by the speaker, his clear and thoughtful manner of speaking, and his composure in the face of strong public disagreement.
The lecture stuck with me but not the name of the lecturer. I guess I knew his name at the time but definitely not as time passed. Until, a couple years ago, it occurred to me. In 2021, while fighting the guerrilla war over ACARA, I mentioned the lecture to Tony Guttmann and to another Tony. Nothing could be confirmed, but it became pretty clear in my mind: the speaker who had so impressed me and who introduced to me a new, fertile ground of dispute, was, very probably, Tony Gardiner.
One mystery solved.
The remaining mystery is whether your “assumption, perhaps due to the unfamiliarity of the faces, was that the audience consisted largely of teachers.” was correct.
“Whoever they were, they did not appear to be pleased.” Maybe they’re more pleased nowadays with the results of their indirect complicity.
It would not have been an MAV Conference because in those (good old) days the MAV conferences were held at Monash University.
Assuming it was Tony Gardiner, there is a (very) faint possibility that he remembers the lecture and will also accept blame for creating Marty the Monster.
I’m pretty sure the audience was predominantly teachers and/or maths ed academics, though I’m not sure why I’m sure. I have a memory of it being an event outside my normal world. And then the audience reaction meant it was clearly not a crowd of mathematicians. It was definitely not an MAV conference or any type of maths ed conference.
“Indirect complicity” is way too tough. Teachers are to some extent complicit, but much more than that they are ignorant, and they are victims.
I asked Tony, and he remembers giving such lectures in Australia, but couldn’t pinpoint this lecture. But, to either his credit or discredit, Tony didn’t create me. That lecture wasn’t a turning point. It’s only looking back that I see the lecture as significant.
Knowing of Tony Gardiner, I’m sure he had evidence to back up his contentions. I wonder what evidence the audience had for its “outrage. The mumbled frowns turn[ing] to loud denials.”
Again, I don’t know remember the specific topic of the lecture, and it’s possible the textbook discussion was a digression. I don’t remember Tony (or whoever it was) giving any evidence for older textbooks being better, but I remember there were some claims as to *how* they were better.
Hi Marty
It was Aust MS 1995 and I attended that talk. Lots of angry edubabblers that day. At that stage I actually had a lot of time for educational researchers and teachers. I was somewhat confused by Tony’s angle of attack. I naively thought that here were mathematicians and lovers of maths who focused on education as well as proving the odd theorem or two. But that talk motivated me to look much more closely.
Now I have an extensive library of texts from about 1890 through to about 1970. They are my treasures and for anybody who has doubts about the comparative quality of texts of the 1950’s to today’s Yrs 7-11 offerings, they need only search 3 words:
Barnard and Child
Thanks, Simon!
Sadly there are many maths teachers who don’t know maths. Just recently my son came from school and told that their teacher hasn’t got a clue what triangle inequality is. The teacher has asked them to build a triangle with side length 2,4,6 and when my son told him that such triangle doesn’t exist the teacher has got into stupor.
I’m not sure that’s an honest telling.
I basically had the same thing happen to me in school (a teacher thinking that a triangle violating the triangle inequality exists), so I’m inclined to believe Dr. Mike’s son.
Though admittedly this was in primary school.
Of course I believe that a primary teacher(s) incorrectly gave impossible lengths for a triangle. I am sceptical of everything else.
It’s very easy to tell specific stories of individual teachers screwing up, and I have about a thousand I could tell, including of my daughters’ teachers. And, including of myself. But I don’t like such stories, I don’t typically think such stories are appropriate and I don’t trust such stories. I don’t ever take such stories on face value.
Teachers are a very easy target, and a teacher’s job is *very tough*. They are on stage for N hours a day, for a large value of N, and it’s impossible to not continually make mistakes which, taken in isolation, and when reported by young reporters prone to embellishment, look very bad.
Of course some teachers are much weaker than others, will make more mistakes, and will be more clueless and/or defensive when the mistakes becomes apparent. There is obviously no shortage of weak teachers, and plain bad teachers. But teachers are too easy a target, and honing in on one mistake is too cheap a shot.
If teachers (and school leaders) focused less on bulltish PD on ‘better’ teaching pedagogy and more on PD that developed and consolidated mathematical knowledge and understanding (a tall order given that the latter PD barely exists) then teachers would be less of an easy target.
But they don’t. They (generally) take the easy bulltish PD every time. Many teachers are clueless by choice. In my view that makes them a fair target for criticism. Yes, a teachers job is very tough. But teachers can also make choices.
You only have to read the offerings at so-called Mathematics Conferences to see the sort of crap that teachers flock to. And Initial Teacher Training (ITE) fosters this bulltish. It’s crazy to assume students enter ITE with adequate mathematics skills. The bottom line is that you cannot teach something that you don’t understand yourself.
Teachers have been conned into thinking they have to learn how to teach things better. Teachers will never be able to teach things better unless they better understand what they are trying to teach.
“bulltish” isn’t clever.
Arguing generally on the deficiencies of teachers is way different from focussing upon a single episode of a specific teacher, based upon a single, unsubstantiated report.
Punch up.
Marty, it is an honest telling! I can video my kid telling this and privately send to you.
Sorry, Mike, the story doesn’t interest me. I’ve explained why.
Yes, and as Tony explained, the truth that I noted is not a license for beating up individual teachers.
Barnard and Child “Higher algebra” is still in print and not expensive, as is their”Elements of geometry”
What’s the easiest way to get your hands on excellent old textbooks? Are there any uploaded on the web?
Not easy, but archive.org may have some. If they’re old enough and classic enough then you can buy from places like abe.com, but they don’t tend to be cheap.
Used book fairs. A lot of people seem to keep there old books until they die. Then in the clean up they end up there. Probably mostly upper high school though.
I use eurobuch.com very often (down under you’re better off with abebooks.com). A really really great resource for German readers is https://mathematikalpha.de/mathematikbuecher by a now retired math teacher from the east. You can basically download almost all maths schoolbooks published in the GDR during the 60s and 70s (many translated from Russian), plus most problems from their excellent local math olympiads. A few German textbook authors who are pi**not amused by those offered nowadays have placed their out-of-print texts online.
JJ,
one worth reading by Mr Hardy first edition 1941 (who collaborated with Littlewood and Ramanujan) reprint 1967
Click to access 196174216674_10151379429531675.pdf
Steve R
Not a textbook.
Marty,
true … a good read nevertheless completed when Hardy was 61 years young
at the other end of the spectrum I also liked the Schaum Outline Series originally written on many mathematical topics in the sixties aimed at science undergraduates but with many examples some suitable for year 12s
eg https://doc.lagout.org/science/0_Computer%20Science/3_Theory/Mathematics/Theory%20and%20Problems%20of%20Differential%20and%20Integral%20Calculus.pdf
Steve R
I love the Schaum Outline Series!
Leonard Euler, “Elements of algebra”, Cambridge University Press, is still in print.
Feller, “An introduction to probability theory and its applications”, vol. 1. 3rd ed. (Wiley, 1968).
Not really a school book; but vol. 1 uses no calculus as far as I recall. In any case, it is an outstanding piece of work; still in print.
An amazing book, but off topic.
Targeting Poms (even by embarrassing them) is almost as much of an Aussie sport as Footy and sledging!
My thanks to Marty and to Simon T for dredging this up – for it raises a key issue.
Our attention is naturally drawn to the visible summit – of whatever (whether serious mathematics; student performance; or quality teaching).
But a mountain can have no summit without a base; and the base is mostly, well, er *base*.
Yet this base – despite its very variable quality – is what we depend upon to throw up and to support the summit.
So I suggest that Marty is right in his apparently contradictory stance:
(i) refusing to be interested in *stories* about individual teacher’s flaws (sometimes well-founded, but a distraction),
(ii) while also recalling his 1995(?) realisation that “most Victorian mathematics teachers, even very dedicated ones, knew little mathematics and understood less”.
It is not Dr. Mike’s son’s teacher who is at fault (and pupils need to learn to value their teachers for what they *can* contribute, rather than to correct them harshly when they err).
Why has the England curriculum *never* mentioned the “triangle inequality”? Because *those who lead the profession* are unaware that there are such key ideas! So how could the individual class teacher possibly know better?
And how come those who lead the profession in the UK are so ignorant? Because those who could enlighten them have retreated into their academic ivory towers. Every academic in the UK is now obliged to focus exclusively on being part of the “research summit” (with the result that our home-grown research mountain now has almost no base, so many/most of our academic mathematicians now come from other countries – countries who have not yet progressed to our enlightened neglect of the need for the mountain to be “joined up”).
Let us go back to Simon T’s “three words”: Barnard and Child.
Barnard and Child were not alone: there were loads(?) of others (Durell; Godfrey and Siddons; Hall and Knight; Hall and Stevens; EA Maxwell; Quadling and Ramsay; and later Snell and Morgan; Parsonson; Durran; Bostock and Chandler).
But who were these astonishing textbook authors? It is often surprisingly hard to discover!
Typically they straddled two worlds – those of academia and of school maths. Samuel Barnard is listed as having been both “Assistant Master at Rugby School” and a “Fellow of Emmanuel College, Cambridge”; John Mark Child is listed as having supervised Dame Kathleen Ollerenshaw’s studies in “algebra and geometry” at the University of Manchester. However, instead of living solely near the summit, they made the effort to be interested in the *lower slopes* – not for their own footling sake (exercising skills that go round in circles and lead nowhere), but in order to devise sequences and exercises that made it possible for students to gain access to those regions further up the mountain-side, making it possible for some to climb eventually to the summit. This can only be done by those who combine knowledge of the upper slopes with an interest in and sufficient imagination about the foothills. (This is quite different from being a good schoolteacher, which requires much more patience, enjoyment of repetition and endless correction, and an interest in children and adolescents.)
Well said.
And thanks for the pointer to the other authors.
For some odd reason, I find the 1st year university texts easier to locate… to the markets I must go apparently.
The uni texts are for a larger market and the subjects change less frequently and dramatically. So, the texts hold their market value better. Older school texts are more comprehensive, more like uni texts, and so similarly hold value.
They also cost a lot more… If anyone knows Springer publishing a high school textbook, I would love to know about it… Can be US, UK, anywhere.
Gelfand and Saul, “Trigonometry” (Springer)
Gelfand and Shen, “Algebra” (Springer)
Gelfand et al. “The method of coordinates” (Springer)
I use parts of these books in teaching Year 9 students. All are still in print.
Learning isn’t a one-way street. Open-minded teachers learn from students the most. “Much have I learned from my rabbis, even more have I learned from my colleagues, but from my students, I have learned more than from anyone else.” The success of learning is proportional to the degree of questions and discussions.
I never said that my son harshly corrected the teacher, and he didn’t. I merely provided an example to Marty’s statement in his post, and you, Tony, mentioned under point (ii), “Most Victorian mathematics teachers, even very dedicated ones, knew little mathematics and understood less”. It just coincided.
Thanks, Tony. It’s preferable to target you English with bouncers, or underarm throws at the stumps, but my cricket isn’t very good. I do what I can.
I’m not sure when I first started to realise that Victorian maths teachers didn’t know enough maths. It was 2001 when I decided to try to do something about it (ha ha), but the realisation must have developed over time. At some point Tony Guttmann decided that I was a literate loose cannon, and tried to point me towards maths ed; he was going nuts, I remember, with his daughter’s Year 9 textbook. That was probably around the same time as your unimelb lecture.
Your explanation for why UK academics have deserted the maths ed field is very interesting, although I wonder. The similar desertion by Australian mathematicians drives me spare, but I’m not convinced it can be blamed totally on the treadmill. It used to be that the big shot professors led Victorian school mathematics: Thomas Cherry and E. R. Love, guys of that stature. Of course the bureaucrats and politicians and maths ed crowd have worked hard to marginalise mathematicians, but I don’t see any mathematicians objecting. Big shot professors still have the time if they care. I don’t believe they do.
It really feels to me that in Australia a lot of it is about class. I’ll bet that the clear majority of Australian mathematicians went to good private schools, and that this is becoming truer each year. Then these mathematicians get their good students and future colleagues from the same good schools, and on it goes. Most Australian mathematicians simply don’t care about the plebs.
I was fascinated by your comments about who were the authors of these classic English texts. It would be great to learn more. I don’t think Australia ever had any such tradition of high school texts, until it was almost too late. My understanding is they simply imported English (and Irish-Catholic) texts, until at least the early 60s. I do have a (legal) PDF of a very interesting Australian text from the early 1900s: I plan to write about the book but simply haven’t found the time.
The 70s, give or take a few years, was the only time for decent Australian texts. Australia had grown enough in all ways to put proper thought into schools texts, and the curriculum had not yet declined into nonsense.
A few years ago I talked to Peter Galbraith for a long hour. Peter was the co-author of “Fitzpatrick and Galbraith”, the beautiful pure and applied school texts from the early 70s. (Peter once also played football with Bob Murray, which is even more interesting, but another story.) I asked Peter why their texts were so good. Peter made clear that he had no mathematics training beyond a (presumably strong) undergraduate degree, and he remembered Bernie Fitzpatrick having a Masters in fluid mechanics or something like that, but no more; neither was by any stretch a mathematician. So, then, how were the books so good? Peter, perhaps with false modesty, gave most of the credit to Bernie, and his simple explanation was memorable: “Bernie was a scholar”.
This seems to fit in very well with your comments about the English authors, concerning themselves with the foothills. Yes, the authors must be intelligent and sufficiently knowledgeable, but the main thing is to have genuine, proper concern for what they are doing and for whom it will affect. They must care enough to get it right.
Re: 70’s secondary school textbooks. We musn’t forget Lucas and James. “Fitzpatrick and Galbraith” and “Lucas and James” are the textbooks (Lucas and James also wrote a Yr 11 textbook) that will never be beaten in Victorian education. Cambridge textbooks are a very pale imitation of “Fitzpatrick and Galbraith” (third rate textbooks amongst fifth raters) – the influence is obvious when looking at the exercises.
Yes Lucas and James is another excellent text and ay one stage you could pick up a copy for $4 at the second hand book store.
Marty, the effect that these texts ( I got to thank Bernie Fitzpatrick for writing them) and the teachers who used them was enormous in retrospect. You have mentioned previously coming from Macleod High; not an altogether working class area, but not one of champagne and chandeliers either. But these resources and teachers at least gave you a chance.
I came up through Bell Park High in Geelong. In 1985 we had 23 doing Pure and Applied Maths. Geelong High had 27. North Geelong High had 17. Belmont High had 32. Throw in another 50+ across the other public schools in a working class town and it’s about 150 students at the top level. Just in public schools. Add in another 200 from private and Catholic schools and another 50 from The Gordon Institute of Technology. 400 hundred students doing Pure and Applied in a town of 112,000. Not too shabby for a working class town. But the system, the curriculum and resources we had then allowed for that to be possible… back then….
Today across the whole state there are 3858 students enrolled in Specialist Maths. So one town of 112,000 in 1985 had more than 10% of the current number of students doing Specialist across the state.
In the era of Specialist there are now have less than 180 across the whole of Geelong- including the private schools. It is near non-existent in the public schools.
Disgraceful
Thanks, Simon.
You make a really good point, that these 70s texts massively increased the number of students who could attempt Pure and Applied, and the number who might succeed. I imagine a not-strong teacher could get by with those texts and teach a pretty decent subject. That is impossible with the current MM and SM texts: if your teacher doesn’t know *really well* what is going on then you’re pretty screwed.
Of course it was also the case that in the 70s there were many more good maths teachers and, generally, public education was far superior. Macleod in the 70s, and definitely in the 60s, was pretty solidly working class. If there were white collar jobs they were bog standard public servant jobs and the like. I had no friends with doctors or lawyers or whatever for parents; the majority were tradesmen. The place wasn’t poor, except in the sense that pretty much all of Melbourne was poor in comparison to now, but there wasn’t much in the way of money, or leisure for parents. But good public education was a real thing, and mattered hugely. It’s too strong to say it gave everyone a chance: I don’t think kids in Preston had the same chance as I did. But undoubtedly it gave very many kids much more of a chance than public school kids have now.
Macleod High was mostly a standard public school, I think, but it was in ways a little different. It was a designated music school, which attracted some good students and also added some cultural aspects. It was great for me, the best aspect of the school: I knew nothing about music beforehand. But the main thing is simply that public education was different then. And textbooks were different.
The textbooks are bad, but I don’t think they are that bad. Outside of probability/statistics (and I’m guessing logic now), I think a teacher teaching verbatim from the textbooks could do an adequate job preparing a class for the VCE exams, especially combined with the near two decades of past exams available.
Nonsense. They are that bad.
My VCE math teachers taught largely verbatim from the (Cambridge) textbooks. From memory the only things they taught substantially differently were CAS tips and tricks, probability, Specialist 1&2 stuff, and we had more comprehensive exam preparation. My cohort did reasonably well, though anecdotally many if not most of the people in my classes had tutors.
Most had tutors. What does that tell you?
I can’t think of anyone who put in the work, did the exercises and past exams, and still didn’t manage to get into at least your stock-standard BSci or BA, irrespective of whether they had a tutor or not.
For most I think the purpose of a tutor was comfort, or preparation for entry into competitive degrees like medicine, law, or engineering. Most still didn’t get in, though undeniably tutors could increase the likelihood massively.
I don’t think even a hypothetical “perfect” textbook could replace this role, without substantial changes to the VCAA exams and other tests like the UCAT. Rote memorisation of a set of question archetypes is just too important for these exams.
The Cambridge textbook doesn’t do a good job of teaching the material, but I think it does a reasonable approximation of an adequate job.
Edit: Actually, now that I think about it, considering that the average VCE marks are around 55% or so, many of the people who got in the 25-35 range likely weren’t taught adequately . So I’m changing my mind, slightly. I still don’t think there is a huge difference though for the purposes of just meeting prerequisites.
Let them eat dreck.
Yes. I don’t think of L & J as being in the same class as F & G. They’re not nearly as elegant. But they’re of course very good texts, and orders of magnitude better than the current swill.
Hi Tony,
Thankyou for your clear exposition of the problem(s) and why the maths education issues of today are so pernicious and (unfortunately) ongoing.
I focused on Barnard and Child primarily as they were not only 2 of the finest authors of their kind but as their texts are still used as textbooks in India they are available in print.
But yes there are many, many others. A couple of others that people may like to look for are (Charles) Smith with his Treatise on Algebra (it can be found online, plus other titles he wrote) and Burnside and Panton. And yes that Burnside- he of Burnside’s Lemma- these people were often top notch mathematicians as well as educators
“And how come those who lead the profession in the UK are so ignorant? Because those who could enlighten them have retreated into their academic ivory towers. Every academic in the UK is now obliged to focus exclusively on being part of the “research summit” (with the result that our home-grown research mountain now has almost no base, so many/most of our academic mathematicians now come from other countries – countries who have not yet progressed to our enlightened neglect of the need for the mountain to be “joined up”). ”
I would have thought that a sufficient “base” would be taught during undergrad. I don’t know how it is in the UK but the Australian undergrad math subjects seem to be decent. Of course, I’m not a mathematician so I could be entirely wrong on that point.
My explanation for academic mathematicians coming from other countries is simply because there’s billions of people in less developed countries, and coming to Australia or the UK is very desirable for many.
Some of the upper level subjects at some Australian universities are “decent”, but the majority of standard subjects are cookbook, and to-be secondary teachers can get through with few such subjects and very little understanding. It’s very weak training to be a teacher. For the to-be primary teachers, it’s much worse: they get essentially nothing, from anyone.
Of course it’s not ideal that a large proportion of VCE mathematics teachers have never taken real analysis, or even worse in some cases. However, for the aspiring mathematician, the Australian undergrad math subjects should be good enough, right?
No.
Thanks all for your suggestions – will look them up over the holidays.
The other huge issue is just keeping students in any textbook. Not sure if I can specify paper textbooks only so I can minimise Alt-tabbing. How do others do this?
No-one has commented on the IB textbook factory in Adelaide (Haese, Haese, and Haes – who seem to have bought out the original co-author and cricketer Kim Harris).
Marty’s comments on “senior mathematicians who cared” (Cherry, Love, et al) struck a chord. Cherry died in 1966, but his portrait used to hang in the Melbourne Uni mathematics coffee room (maybe still does). EA Love was still around during my visits (1979ff). The change Marty comments on is real – and I put it down to “globalisation”. Time was when each university was like the local church or cathedral: built to serve both God and the local flock of parishioners. Its “bishops” were serious servants of mathematics, but recognised a calling to convert the local heathen – so were rooted in their surrounding community. Now a university is more like a hotel room: a temporary base from which one can liaise with one’s natural (global) research community. Students can come and learn how to be part of that global community if they choose, but there is relatively little urge to *go out into the surrounding highways and byways*, or to devote time to checking the papers set by VCAA et al.
In England we never had a national or even local curriculum until the late 1980s. And there was no central scrutiny of exams. The old (pre-1900) academic system (warts and all) was driven by Oxbridge entrance for the few: that is the rather narrow goal these excellent textbook authors were really aiming at – though they improved school mathematics for a wider group. These authors/teachers had gone through the system, and saw teaching in a public school as a (slightly lesser) extension of teaching as a fellow of an Oxbridge college (sometimes because college fellows could not get married!).
This approach was too elitist for the new provincial universities in the late 19th century, so they formed groups that managed slightly less demanding exams (School Certificate and Higher School Certificate, which became O levels and A levels in the early 1950s), aimed at preparing a slightly larger group for entry to these other institutions. But in 1961 there were still only 4% of 18 year olds going to university. For example, the Joint Matriculation Board was set up to run such exams in 1903 by five northern universities (Birmingham, Manchester, Liverpool, Leeds, Sheffield); by 1970-90 it was mainly guided by Manchester academics of the old school (with hangers-on like me, and an increasing number of schoolteachers).
I’m tempted to try to explore the origins the good textbook authors.
Thanks, Tony.
Yes, I forgot about the Haese IB books, which are very good. I think of that as being more a global than Australian thing, but that can’t be totally true: the Oxford IB books I’ve seen are appalling.
ER Love was still around in the early 90s, tutoring and I’m not sure what else. At Terry Mills’ suggestion, I invited Professor Love to LaTrobe Bendigo to give a talk. He gave a beautiful talk, by memory on Legendre functions.
I’m sure you’re right, that globalisation is part of the reason the bishops have disappeared. But I don’t think it’s the only reason. There are plenty of Melbourne mathematicians who were born and bred here, and many others who have been here for decades. But, the only big shot I know of who, at least since I’ve been active, has exhibited any serious concern for school mathematics education is Tony Guttmann. I’ve approached a number of other big shots over the years, and none of them gave a damn, or at least enough of a damn to actually do anything. I’ve given up on that approach.
There are some VERY good IB books I’ve found secondhand which are lovely for vectors, matrices, calculus, proof… pretty much all the nice bits of high school Mathematics.
The fact that they don’t cover the VCE is of little consequence.
Peter Smythe had one published in 2000 which was simply called Mathematics HL.
I’m a secondary teacher and I do love Haese and Harris (the IB verison, not so much the Australian Curriculum version, which falls into the typical Aussie trap of quantity over quality in the exercises). Thanks for the other suggestions – I’ll look into them!
I find I pretty much always have to supplement textbooks as they don’t tackle many common misconceptions and almost never mention boundary problems (where does the concept we’re looking at cease to apply). That’s easy enough for me at junior levels. But at VCE, particularly when they keep changing the curriculum and content, sometimes I’m struggling to keep up with the curriculum as set, and I just don’t have the knowledge (or time to invest to gain the knowledge) to know exactly how to supplement.
Thanks, Claire. Of course it is much easier to write a good text for a good curriculum. So, yes, IB will always be better than AC.
I think it’s natural to have to supplement texts, most obviously with a knowledgable and cluey teacher. Such a teacher, for example, will smell that a 7 in the polynomial, rather than a 6, means you’ll manipulate it differently. They’ll encourage students to also smell such nuance.
Texts can be better and worse at such variations, and at covering the edges. But I think a text that tries too hard to cover all such possibilities is trying too hard. It is trying too hard to be the teacher, and it makes the text less rather than more helpful.