Monday’s post, on Greg Ashman’s column and Clarendon College’s teaching method, appears to have struck a bit of a chord. At least it did with me. Which is of course what matters most.
I’ve been pondering the comments, pondering my own ponderings, and I had a chat with a great mathematics teacher, let’s call him Andrew, who had emailed me. Andrew was surprised that I was largely supportive of Clarendon’s march step teaching, and I am also surprised, even subject to the reservations I’ve expressed. I am still trying to sort out my thoughts on this and I have a few posts planned for the next week or so. I’m not sure these will indicate what I’m thinking about all this, but they may indicate how I’m thinking about all this.
This post is about two plus one great teachers: an English teacher from the 1970s and a mathematics professor from Stanford University (and with a cameo appearance by Burkard the Mathologer). I’ll then chat about these two teachers in light of Monday’s post and the conversation with Andrew.
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I’ve already written about the English teacher. Jamie Bradbeer was my teacher at Macleod High in the mid 1970s, and he was wildly unorthodox, even for the times. I won’t reproduce it all, but here are the key parts:
The loosening of the rules at the top undoubtedly permitted more humanness within the classroom, and more individuality. Jamie Bradbeer, my crazy and wonderful English teacher in part of Forms 4 and 5, seemed unconcerned for even the vague and loose boundaries of the 70s. Mr. Bradbeer loved Bod Dylan and Gerard Manly Hopkins and he wanted us to love them, too. He played us Masters of War and read us God’s Grandeur, and he desperately tried to have us appreciate them as great works. He failed on me, and I think on the entire class, but his passion was a great lesson in itself. …
Mr. Bradbeer was sufficiently unorthodox that a few of the bluenose students, concerned for next year’s looming HSC, complained to the Principal about Mr. Bradbeer not teaching us the proper stuff. I don’t remember that the complaint had much effect, except that Mr. Bradbeer was deeply hurt and he told us so. As I remember, the clear majority of students were strongly on Mr. Bradbeer’s side. …
Mr. Bradbeer, of course, wouldn’t last a day in today’s schools. He also wouldn’t want to last a day. Few of the great teachers I had in the 70s would, or would.
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The Stanford professor, pictured above, was Bob Osserman. Bob was an amazing guy, as kind and as wise and as good humoured as his photograph promises. At one point in the mid 1980s, Bob co-introduced a year-long undergraduate subject, The Nature of Mathematics, Science and Technology. The subject was co-taught by Bob, Sandy Fetter, who is a physics professor, and Jim Adams, who was some kind of engineering-sociology professor. NMST was designed to be a more meaningful option for non-science undergrads satisfying a “distribution requirement”; a gentle introduction to mathematics, its role in the development of science (physics and astronomy), and then science’s role in technological innovation. A PhD student at the time, I was lucky enough to be asked to tutor for the subject. I jumped at the chance.
NMST was very popular, and deservedly so. The three strands were interwoven very naturally and all three lecturers were entertaining and accomplished. Sandy was more straight-laced than the other two, but he was friendly and gentle and a very good lecturer. Jim was a showman, and a bit of a salesmen, and I had mixed feelings about him, but Jim also provided an interesting and genuinely worthwhile real-world spin to Bob and Sandy’s more pure material. All three attended all lectures, and they would tease and challenge each other, in an entertaining and educational manner. A taste of it appears here (pp 90-91).
Perhaps unsurprisingly, I thought Bob was the star of the show. Undoubtedly I was biased, but Bob really seemed to be that good, grabbing ideas and approaches from everywhere, and presenting it all in a remarkably clear and engaging manner. I simply loved watching Bob in action and I was honoured to be his tutor and gofer.
Given my strong affection for NMST, I was very puzzled when, in the Department tea room one day, a few mathematicians were talking about the subject and dismissing it as a passing fad. I asked:
“Why?”
“Because it’s Bob. Only Bob can teach [the maths part of] that subject, and once he gets onto other things, it will die.”
They were absolutely correct.
Bob, and I think also Sandy and Jim, stopped teaching the subject after a few years, inevitably having other big projects on their plates. Other lecturers took over, and the maths guy at least was no slouch, but the subject didn’t survive. Whether it was the chemistry between the original lecturers or their individual talents, NMST didn’t work without them.
And so NMST died. There had been plans to write a book based on the subject but it never eventuated. Bob Osserman wrote a lovely little book, Poetry of the Universe, on some of the geometric and topological aspects of NMST. The book was well-received and I’m sure had not more than a thousandth of the sales of whatever crap Eugenia Cheng has just spat out.
A decade later, I was a post-doc or something at the University of Melbourne, when the mathematics department somehow got the idea in their head to offer a Nature of Mathematics subject. Of course I was thrilled with the idea, and I knew stuff. And of course no one listened to Junior Marty. I soon gave up and just listened, while the Established Guys assembled their camel of a subject. I then gave up even listening, when they hit upon the big problem, that “we’re all male and we need a woman lecturer as well”. The camel was subsequently born and was soon after euthanised, putting the poor thing out of its and everyone’s misery.
A further decade later I was a lecturer or something at Monash University, and I was given the opportunity to launch a Nature of Mathematics subject. Thus was born The Nature and Beauty of Mathematics, very much stolen from modelled on NMST. The subject is still alive, and thriving, in the safe and brilliant hands of Burkard Polster, who has made it his own. And once Burkard finishes up, NBM will die. Yeah, the subject might live on as a zombie thing, because Monash doesn’t give a stuff what subjects are offered as long as the students pass and thus continue to pay their fees. But NBM will be dead.
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Do an English teacher from the 1970s and a mathematics professor from the 1980s tell us anything about what mathematic teaching might be in 2024? It’s a stretch but I’ll argue the case, with Andrew as evidence for the argument.
Andrew is not wildly radical like Jamie Bradbeer but he is radical enough. Or at least reactionary enough. Andrew is an old-timer, intent on teaching solid and meaningful mathematics, based on solid grounding in knowledge and technique. He has a low tolerance for teaching crap, which means if the curriculum guidance is crap, as it so often is, or if the textbook chapter is crap, as it so often is, then Andrew will declare “bugger this” and work himself to the bone creating lessons to cover the material properly and deeply and well. Andrew does this for all his students, of all shapes and sizes, to the extent of his students’ abilities. Andrew is a legend.
Andrew is at a good enough school and he has enough respect/clout within the school to get away with this. So what’s the problem? As Greg writes, of those not enamoured of Clarendon’s approach,
But it’s not for everyone. And that’s fine. We cannot be certain our approach is better because nobody has run a controlled experiment. …
In the meantime, if you don’t like what we do, don’t worry about it. Carry on.
Live and let live. But not exactly.
It is not as simple as Clarendon quietly going about its stuff, each to their owning. Greg Ashman is anything but quiet. Greg is one of the most prominent educational psychology guys in the country, seemingly on speed dial of a dozen journalists and constantly being offered a free hit to pronounce on his stuff. Which is fine in principle and helpful in practice, at least for now. Greg and his fellow explicit instruction guys are a counterforce to the current and appalling Boaler-Sullivan-ACARA orthodoxy, and if that is the choice then there is no choice: more power to Greg and his team. But the fact is that Greg and his kindred spirits are gaining in power, are having a significant effect well beyond the gates of Clarendon. It is not so simple for everyone to just “carry on”.
Given that Greg et al are beginning to be a force, their stuff had better be good. I think their stuff is good. I don’t think it is that good.
Things are a godawful mess: the curriculum is awful; the textbooks are awful; the suggestion to sit kids still in a quiet room and having them concentrate on straight solid mathematics is regarded as a heresy; there are snake oilers and techno-saviours as far as the eye can see. Mathematics education is a swampland of meaninglessness. Given this swampland, Clarendon and their approach offer some very welcome solid ground. They know what they want to teach and they seem to teach it very well. Their goals are clear and attainable, and they seem to attain them. But it seems to me that Clarendon’s goals, or at least their dreams, are too modest.
Does Clarendon offer what Andrew offers? I cannot see it. I cannot see that Clarendon could offer what Andrew offers. I can see no way that what Andrew offers can be provided in anything like a programmatic manner. Clarendon offers the solid grounding, and that is definitely not to be sneezed at; it is a hundred miles ahead of most schools. But I don’t see that they offer more, or even attempt to. I don’t see how they could teach decently for the AMC, or for the 70s HSC. I don’t see the depth. It may be there, but I don’t see it, it is inconceivable to me that deep mathematical teaching can be reduced to a bunch of PowerPoint slides.
Of course Clarendon could hire Andrew, except that Andrew couldn’t tolerate Clarendon for a minute, and vice versa. Clarendon wants a system, and Andrew is not part of a system. Andrew is Andrew, and Andrew is the only Andrew. Just as Jamie was the only Jamie and Bob was the only Bob.
That is the problem, of course, and the counterargument. Andrew may be Andrew and that may be great, but when he goes, he’s gone. Bob and Jim and Sandy moved on and their subject died. Clarendon is seeking something more solid and sustainable, less person-dependent. This makes all the more sense, since there are so few Andrew-like teachers out there. They were probably always uncommon and now they are hen’s teeth. But I find it really depressing to not have that dream, to preclude even the possibility of an Andrew, which it seems to me is what Clarendon does, by deliberate design. As Greg wrote,
A suboptimal curriculum that everyone follows is better than an optimal one that is understood and deployed only by some.
I can see why Greg argues this, I can see the benefits, but I cannot agree. Which brings me to the final point.
Andrew is the only Andrew, and mutatis for the others. But while they are there they are there, and that is hugely meaningful for many, many students. And even once they’re gone, they’re not exactly gone.
Other teachers work with Andrew and talk to Andrew and then they move on. Andrew’s approach and his spirit is then part of other schools. These teachers will probably never be Andrew but they are much more than would have been without him. Mr. Bradbeer and Bob had their effect on me and, with all due modesty, I think they were a big part of making me a very good teacher. I see people I taught who are now teachers, and I am proud of them; they have Mr. Bradbeer and Bob in them without ever having heard of them.
I don’t know if such a folklore tradition is the only way or the best way to do this, but it seems important. It is also getting much harder. Such connecting now seems less folkish and more Fahrenheit 451, with the surreptitious passing on of wisdom away from the prying eyes of the firemen.
Clarendon seems determined to preclude even the possibility of this. I have little doubt that a young teacher at Clarendon will learn well. They will become a solid and good teacher, and God how we need them. But I do not see how they could become a great teacher. I do not see how they could learn what a great teacher is.
Maybe that is the best choice in a very bad era. I don’t think so, but maybe. Either way, I find it deeply depressing.
It is possible this could go the other way. Having collaborative prepared plans leaves more time for all things including innovation on the current plans and new ones that are orthogonal.
Having a good starting point could make people more confident in trying something new.
It can also make people complacent or have them view the status quo as written in stone received wisdom. But it doesn’t need to. Keeping the collaboration at a level where there are different things being tried that get compared occasionally would be better that central planning.
Of course. You want some solid common ground, and then on the basis of that common ground shared resources and plans are obviously good in many ways. But, as you note, this collaboration has to be kept “at a level”. The lock-step thing is too much.
The underlying problems, as readers know, or at least know that I claim, are:
(a) the lack of a coherent and solid curriculum, laid out in well-written textbooks containing very good exercises and harder problems;
(b) a teacher workforce that knows what mathematics is and thus what it means to teach mathematics.
It means that mathematics teaching is, must be, by and large absurd. Clarendon seems to be dealing with this absurdity in one, extreme but understandable, manner. They have some solid ground in a sea of absurdity, and there is a clear argument for that. But I don’t see any peaks in Clarendon’s map of things.
Long time listener first time caller.
When you wrote “the suggestion to sit kids still in a quiet room and having them concentrate on straight solid mathematics is a heresy,” did you mean that the fact that it IS considered heresy to make this suggestion is the problem (and therefore that the suggestion is a good one?) or are you yourself saying that this suggestion is a heresy? If the latter, is this just because it may be unrealistic advice in some contexts where good behaviour and well intentioned students are not a given or for some other reason?
Also you’ve written “Andrew couldn’t tolerate Andrew for a minute,” where I assume you meant to substitute Clarendon in for one of those Andrews. Poor Andrew!
Thanks rt, and welcome.
Actually, I have it on good authority that Andrew can’t tolerate Andrew: he drives himself nuts. But, yes, I intended to write that Andrew couldn’t tolerate Clarendon. Corrected now, and thanks.
And sorry for the “heresy” confusion. Your first interpretation is correct. I’ve added a “regarded as” in the post to unmuddy it a little.
All kids, and more than a few adults, must learn to sit still and pay attention, which is not an easy thing to learn at the best of times. It is really not easy when a parade of clowns is advocating play-based whatever.
Thank you for writing these couple of posts, Marty.
I loved reading them and the subsequent thinking they prompted.
Everything dies, but bit of it is almost always left behind; in some cases people are enriched by that, and in others …
I have thunk 1000 thoughts since reading the posts a few days ago.
I wanted to write them all down and write the king of replies, but time, and the difficulty of making a coherent written artefact of all those thoughts, stopped me.
FWIW, and mainly for myself, here is a shortish attempt to share some of the thoughts.
I thought mostly about Jamie, Bob and Andrew.
I have been too lucky, it seems. I have had numerous of these types of people in my life, even one called Bob. He was the first person I could clearly see taught through storytelling.
Bob was such a great teller, who had expert level knowledge of:
• the what,
• the how,
• the why, and
• the how to apply,
of the content of his stories.
He was truly inspirational.
Others followed, we will call them Roger, Garth, Neville, Martin and Angela. I may have even omitted one or two. Each was a different type of teller, but all had an expert level knowledge of the what, the how, the why, and the how to apply, of the content of their stories.
Teaching is simply story telling to me.
The best teaching of this type happens when the story is:
a) engaging and
b) make sense to the listener.
Seems easy enough to me, but it turns not be so.
To make it the best, the story teller needs to have a decent-enough level of knowledge of the what, the how, the why, and the how to apply, of the content of the story and they must know how the story can be told so it will make sense to the audience.
Sequencing, pacing and linking to what is already known by the listeners are three critical factors.
How does one become a teacher of this type?
I can only tell you that from my own experience.
Bob inspired me to be like Bob (I have to tell you I am rather emotional as I type this, such was the impact Bob had on my life). The impact he had on learners was profound, and I wanted to be such a teacher. Why, at that stage, I had no idea! Truth be told, I had already started on the journey, as a Science/Physics teacher. People like Banger (my first ever boss as a science teacher) had planted some early seeds, and Paul Hewitt had done the same.
Somehow I came to know the basic ingredients, but also knew I did not have them all.
So I set about getting them; it became my life.
If you are reading this, I wonder if you happened to have the thought that this person (me) must not have had a life? Or was/is some sort of social misfit, who had no friends, can’t play golf, share a beer, …
I have had such thoughts far too often over the years. And then, at some point, I realised something.
In the most basic of senses, life is just time.
One’s life is simply the compilation of things they choose to spend their time doing.
Bob was the kind of guy who could do it all, he was both a social animal and great storytelling type of teacher. He was a gifted guy.
Me, on the other hand, not so gifted, also not so social. I found myself spending time getting the stuff I needed to be a great teacher of the Bob-type; which was mainly the a decent enough level of knowledge of the what, the how, the why, and the how to apply, of the content of the story. Turns out I could naturally spin a tale well enough. It took me decades to realise that I did this as a way of gaining some level of inner peace/satisfaction/… – or in slightly darker terms, the way I chose to spend my time stopped me reaching for a gun.
I never talked to Bob about why he was like he was, nor Roger, Garth, Martin, Neville and Angela.
As a younger person I wondered why there are not more Bob-like teachers.
I wonder about that less now that I understand myself a little better and what is needed to be this type of teacher.
More than three decades after I first met Bob, based on my own measurements (which could be problematic), I am a decent Bob-like teacher. I wish Bob was still here to see me tell. I am not sure how long it took me to become decent, but it took a while. It was a process.
There are other measures, outside of my own, that suggest how I operate does the job well.
There is also plenty of evidence to suggest that you do not need to be Bob-like, nor teaching in the Claredon way to be a great teacher whose student learn swimmingly. So do not despair.
How does all this drivel tie back to the Lesson Lottery.
It seems simple to me.
There is content to be taught by a teacher, that is to be learned by a group of students.
The teacher teaches, in whatever way they can (within reason) – teachers are humans they vary.
The students being taught by that teacher learn, and are assessed.
If the assessment shows that the learning was successful – happy days.
If the assessment shows that the learning was unsuccessful – unhappy days – action required.
But.
It is of course no longer so simple (it once was, or at least a lot simpler than now).
Why not?
Because it is the action required bit that too rarely happens.
And why is that?
Possibly because the content is not common in all teachers minds and so …
Possibly because the assessment is unlikely to be of a “standard” that allows comparison and so …
Possibly, …
So, what to do then?
Option 1:
Write a simplified, clear and common sense curriculum document for the teachers at your school.
Pick the best text-book (one from 1984 might be the winner … 😂) and supplement with well crafted support activities – make these available to all.
Provide examples of the standard of assessment required of teachers.
Cultivate plenty of dialogue between teachers about teaching, learning and the doing of mathematics.
Hire the best teachers you can, no matter their style (hopefully a Bob-like or two, to inspire those there that wish to be inspired), let them loose, monitor, and act if the learning is not taking place.
Option 2:
Take a Clarendon-like approach.
Option 3:
“Sit on the deck with a gin and tonic, resignedly watching the waters rise”.
After all, everything dies, and it would be nice to do this for a while before that time comes, preferably without the waters rising.
If you read this far, well done. Or maybe you need to get a life … 😂
Happy Sunday. 🙂
Thanks storyteller, a lovely reply. Still tossing up the options, but #3 is looking attractive.
Here’s a hypothesis – the education ‘debate’ boils down to an argument between semantics and character. We’re all probably a mix of both approaches, but most people tend towards one end of the spectrum.
Those who advocate for semantics advocate for the transmission of meanings. Semantic content is, in their view, the foundation of rigorous and clear thinking, writing and talking, which are seen as the core purposes of academic education. For the most part, they are drawn to explicit instruction and tests, since these are probably the best ways of transmitting and then assessing the acquisition of meanings.
Their opponents advocate for the building of character (they have huge disputes between them about what constitutes a good character – a ‘Christian’, a ‘Liberal’, a ‘Democrat’ a ‘Socialist’ etc etc). Since no single item or even related set of items of meaning are essential to having a character of a certain sort (you don’t need to know trig to have a liberal character, you don’t need to know what a tragedy is to have a Christian character etc etc), semantic transmission is much less interesting to them. They are more interested in the culture of a school, in the character of teachers, and in how those interact and support each other. These are the factors which they feel are most important in the likely success of building character of the right sort.
When this post appeals to the notion of a ‘great teacher’ it is crossing the boundary between semantics and character. The two ‘great’ teachers mentioned are remembered mostly as character exemplars (passion, generosity, curiosity etc) rather than for any content that was successfully conveyed. The descriptions of the teachers appeal to me personally, because in so far as I value character, I think I’m broadly liberal, and these teachers sound to me like liberal figure (small ‘l’ liberal obviously).
Having worked at Clarendon I can say that they do a great job of semantics (at least for the upper-middle section of the national cohort who are the majority of their students), but that this doesn’t stop them from addressing character. On the other hand, schools that go down this direction (and Clarendon were certainly guilty of this to some degree) often put the ‘liberal’ character at risk in their pursuit of technical semantic success. This may be through suppressing teacher variation and creativity, or through excessive exam-cynicism (I think every school is entitled to a certain serving of cynicism with regard to exams, but it can also be taken too far…)
For me, the quasi-marketization of the school system has brought out the worst of both sides of the debate. The semantics crew have been pushed into exam-fanaticism. The character crew into ‘higher-order-skills’ mysticism. At the root of both tendencies are the dreadful two ‘m’s: managerialism, and marketing…
No.