Explicit Objections

The New South Wales Department of Education is cajoling, and possibly commanding, teachers to engage in “explicit teaching”. What does that mean? According to the Department,

Explicit teaching practices involve teachers clearly showing students what to do and how to do it, rather than having students discover that information themselves.

Yeah, what dinosaurs. Continue reading “Explicit Objections”

Do You Gotta Get a Gimmick?

It is possible that the lessons to be had from burlesque for the teaching of mathematics have not been so fully appreciated. To help rectify this, here is a number from the musical Gypsy.

And the question: when teaching mathematics, do you gotta get a gimmick? Do gimmicks help? Or, do they simply give the illusion of helping?

I’m honestly not sure. I’m not even sure if my own teaching is gimmicky (although at times it has been described as burlesque).

Selling Teachers Short

A few days a ago, an occasional commenter told us about the teacher shortage at their school. They suggested the shortage was going to “play havoc” with their teaching load. We’re not quite sure how that works, since we thought there were strong and weird restrictions on what could be demanded of teachers, but we’re not doubting the reality on the ground. Our teacher correspondent also offered tentative reasons for the shortage: boomer teachers retiring, both naturally and motivated by covid; little incentive for people become new teachers; new teachers not lasting.

Continue reading “Selling Teachers Short”

Marty Talk – Not Quite The Prime Number Theorem

Having foolishly ventured out to Monash Uni last Tuesday to see the Evil Mathologre give a Lunchmaths talk, I found myself roped in to giving the next one. So, anyone who is around Monash next Tuesday and has nothing better to do is welcome to attend. Details below, and here. Continue reading “Marty Talk – Not Quite The Prime Number Theorem”

MAV’s Valuing of Mathematics

The MAV have started the engines for their 2022 Annual Conference. The organisers have already lined up an impressive list of speakers and, as always, the MAV have put out the call for anyone and everyone to present, at a cost of only $500 or so for the two-day extravaganza.

Of course, if planning to attend or present, one should keep in mind the theme and sub-themes of the conference: Continue reading “MAV’s Valuing of Mathematics”

Mr. McRae’s Triple Gift

This is a story from long, long ago. It is about Mr. McRae, who was our grade 4 teacher, at Macleod State School. We have written about Macleod before, and we have written, briefly, about Mr. McRae before, in regard to the moon landing:

I still have vivid-grainy memories of watching Armstrong’s first steps. A random few students from each class in Macleod State School were selected to go to the library to watch the event on the school’s one TV. I was not one of the lucky few. But Mr. Macrae, our wonderful Grade 4 teacher, just declared “Bugger it!”, determined which student in our class lived closest to the school, and sent out a posse to haul back the kid’s 2-ton TV. We then all watched the moon landing, enthralled and eternally grateful to Mr. Macrae.

He was that kind of guy. No-nonsense and intelligent and cultured.

The year he taught us, Mr. McRae was new to Macleod. He had just appeared on the playground before the first class of the year, tall and commanding. Rumour had it that he had played Under 19s for the Richmond Football Club, making Mr. McRae just shy of a Greek god. (The actual Greek god was, of course, Carl Ditterich.) He was a standard and excellent teacher. Firm, disciplined and disciplining, but kind, and with a calm and intelligent air of bemusement. He was the boss, but a thoughtful and unpredictable boss. Hence, our class getting to watch the moon landing. And, how else to explain the boxing match?

One day, Mr. McRae inadvertently started a harmless play-scuffle between two students. He then decided the dispute should be settled by a proper boxing match in front of the class. Once, of course, a kid had been sent home to fetch a couple pairs of boxing gloves. We can’t remember whether we lost, although we remember we didn’t win. In any case, neither of us had a clue how to box, and so the match was followed by Mr. McRae giving the class an impromptu lesson on technique. This was, to explain it a little, the era of Lionel Rose and Johnny Famechon and TV Ringside.

That’s all by way of background. The story we want to tell is of a mathematics lesson.

One Friday afternoon, Mr. McRae introduced his grade 4 class to Pythagoras’s theorem. Or, at least, to Pythagorean triples; we can’t specifically remember the triangles, or anything, but undoubtedly \boldsymbol{3^2 + 4^2 = 5^2} made an appearance. Why he showed us this, God only knows, but Mr. McRae ended the class with a challenge: find more triples. Our memory is that the specific challenge was to find a certain number of triples, maybe three, maybe five.

We have no idea what Mr. McRae hoped to achieve with this challenge, but we remember pondering, aimlessly, hoping to find triples. Eventually, by smart persistence and dumb luck, we stumbled upon the trick: doubling a triple gives a new triple. So, \boldsymbol{6^2 + 8^2 = 10^2}, and so on. With this kid-Eureka insight, we then happily spent the week-end doubling away.

Come Monday morning, Mr. McRae asked for the class’s triples. We proudly went to the blackboard and wrote up our largest creation. By memory, it was something in the millions. So,

    \[\boldsymbol{1572864^2 + 2096152^2 = 2621440^2}\]

or thereabouts. And then Mr. McRae uttered the fateful words:

“Let’s check it!”

There were the inevitable groans from the class, and the little Archimedes hero of the story was more popular than ever. But, Mr. McRae was the boss, and so we all set down to multiplying, including Mr. McRae himself. And, ten or so minutes later, the class collectively started to conclude … the equation was wrong. Yep, Little Archimedes had stuffed up. Which led to more fateful words:

“Let’s find the mistake!”

More groans, more multiplying, and eventually the error was found. By memory, after quite a few doubles, somewhere in the mid thousands. And, satisfied, Mr. McRae led the class on to whatever he had been planned for that day.

What is the moral? We have a reason for telling the story, beyond a simple tribute to a great, memorable teacher. We think there are morals there. We’ll leave it for the reader to ponder.

The Past is a Foreign Country

We’ll fill one more gap from our presentation. Our previous gap-fill was on Professor E. R. Love and the disappearing art of lecturing. The past is a foreign country and, indeed, they do things differently there. This post is about the past and that foreign country. The country is called China.

The above photo is of a Nanjing school, the sister to our daughters’ school here in Melbourne. It is considered a good public school, but no more than that, and the photo is of a Year 5 class. What does one notice? What does one notice, that is, apart from the algebra and the general formulae, material that Australia typically covers, thinly and badly, in around Year 8?

There is no colour. The room is dressed in drab tiles and off-white walls. There are no posters. There’s just rows of students at their desks, and a teacher up front with nothing but an overhead projector and a blackboard. What a Hell.

It’s a Hell we would kill for.

The photo is of a class, of a teacher teaching, of students learning. The students are respectful and attentive. They are undistracted, in no small part because there is nothing to invite distraction. It may not be apparent from the photo but was obvious from our observations, the students also enjoyed and appreciated the class. They were happy and engaged, and the teacher was engaged with them. The students presented their work and asked questions, and the teacher responded and, when need be, corrected. She was kind, and she was firm. The class had a purpose and everyone clearly understood and appreciated that purpose.

The Nanjing school is not just a Hell we would kill for, it’s a Hell we know very well. The Nanjing class reminded us of nothing as much as our primary school from the 60s. Macleod State School was completely ordinary, just another cheap, flung-up middle class Melbourne school. It had grey walls and desks in rows, and hilariously bad heating. It also had bullies and authoritarian assholes and corporal punishment, and the worst teacher we ever experienced or ever witnessed.

Macleod State School also had classes where the teacher was the boss and was, properly, respected. There was a clear and meaningful curriculum. The teachers were expected to, and generally wished to, teach the curriculum. The students were expected to and generally wished to, learn the curriculum. The students also had very little say in the matter. The school had a purpose, a proper purpose, and in general everyone went about that purpose in a thoughtless and efficient manner.

The past is a foreign country.

Video: Mathematics in Hell

Below is the video of our recent LunchMaths talk. You can comment/correct below and/or at the YouTube link.

A big thanks to Lawrence and Emma-Jane for arranging the talk, and for making the zooming as painless as possible. A couple of aspects that I intended to talk about, and some probably valuable clarification, were only covered in the Q and A. I’ll leave it be except in reply to comments, except for one aspect that I really regret not getting to and which I’ll cover in a separate post ASAP.

Zooming into Friday: Mathematics in Hell

Because we’re so in love with technology, and because we’re so short of things to do and, mainly, because we’re so, so stupid, we’ve agreed to give a LunchMaths/MUMS talk via Zoom this Friday.

The details are below, and this link is supposed to work. Attempt to enter at your own risk.

UPDATE (24/08) 

The video of the talk has been uploaded and can be viewed on YouTube and/or on this post.