What a month. It’s raining mendacity.

Today, the ridiculous AMSI-AAMT-MERGA statement received further press coverage, this time in a report from education stenographer, Suzan Delibasic (paywalled, Murdoch):

*“Leading experts are calling for a maths curriculum overhaul, with a major review set to focus on fixing declining academic results.”*

Once the stage has been set with straight-faced paraphrasing of AMSI-AAMT-MERGA nonsense, Delbonis’s report consists of quotes from three of these “leading experts”, beginning with AAMT‘s CEO, Allan Dougan:

*“The whole idea of a maths class where the teacher teaches the content and the students practise it 300 times, that’s what we’re moving away from.” *

300 times? If a kid is assigned *30 exercises *as practice, the school will call Child Services. 3 times is much closer to the current mark, particularly in primary school, where the real damage is being done.

We have no idea where Dougan dredged up his Dickensian dream, but of course it has nothing to do with reality. The reality is that decades of “leading experts” killing the teaching of technique, of denigrating proper practice is a huge part of why Australian mathematics education is currently a disaster. Dougan apparently imagines the cure is *less* practice than the trivial amounts that currently exist.

To illustrate the point, Dougan provides his own, striking example:

*“[Dougan] said one problem-solving task could involve year 6 students taking part in an activity called It All Adds Up, where each letter of the alphabet is given a dollar value” *

*“Letter A is $1 to Z being $26. You can start asking students open questions such as finding a four-letter word that costs $50 —the success of this task is how they approach it and how they think about problem solving.” *

Looks like a fun game. How about VOID? Or CLOT? Do I win?

Seriously, Year 6? As an add-on activity for Year 2, maybe Year 3, sure. But if you imagine it reasonable to expect *Year 6* students to gain anything from such an addition game, then your sense of appropriate skill level bears no relation to reality. And even for Year 2 or Year 3 students, it’s a *game*, which by definition cannot be the main game. You learn addition by practising addition – the carefully structured 30 times thing – *not *by the occasional random sum in the middle of a game.

Our second Leading Expert is AMSI‘s Director, Tim Marchant:

*“Australian Mathematical Sciences Institute director Professor Tim Marchant said he was concerned by the shortage of qualified maths teachers.”*

*“The data shows about 50 per cent of schools have maths classes taught by teachers that aren’t qualified in maths,”*

Well, it wouldn’t be AMSI if they weren’t punching down, whining about unqualified teachers. But Professor Marchant also considers classroom activities:

*Prof Marchant said group activities in the classroom helped learning and made maths “fun” … He suggested hands-on learning experiences including using Rubik’s cubes to help with problem solving.*

Rubik’s cubes. Not enough games, not enough “fun”, that’s the problem.

Once upon a time, we had hope that AMSI would be a genuine force for improving Australian mathematics education. Now, we’d be happy if AMSI would just shut up, stop signing ridiculous statements and go away.

Our final Leading Expert is Peter Sullivan, Emeritus Professor of Education at Monash University:

*“The revised curriculum needs to be simply written so teachers can understand and comprehend it; we want the big ideas clearly articulated,” *

That’s Peter the Great there, the guy who led the writing of the *current *Australian mathematics curriculum.

Leading Experts. The “experts” part is debatable, but the “leading” is absolutely clear. These people are leading Australia to an even deeper level of educational Hell.

I recall helping a student with Year 12 mathematics. In the section he was studying there were some exercises to do. Q1 had 10 parts. He started to do them – but by the time he had done 5, I figured that he knew what he was doing. I suggested that 5 is enough – you understand this point, let’s move on. “But this is fun!” he said. Well, who am I to argue?

You mean a student might actually enjoy the mastery of a technique? Who would have thought?

I know you know this, but I agree with Terry that a lot of students really do seem to enjoy doing work that they know how to do. Based on my admittedly brief experience teaching, students who tune out of mathematics seem to do it because they feel like they can’t do it, not because they don’t want to. They seem thrilled at the idea of simply memorising (“I can do that!”) or practising simple things until they are easy. And it’s not boring, because often the patterns in the numbers speak for themselves – like when you notice dividing by 9 often gives you repeated decimals and you think about why. Too much time selling how mathematics is interesting can be a trite distraction from the actual interesting stuff right in front of you.

100% yes. The idea that getting kids to practise and master technique is somehow child abuse is insane. And this insanity is at the heart of all modern education. *Of course* kids want to be good at things.

Coming back to this a bit late, but I’ve also found that a lot of students take the view Terry initially mentioned: “I’ve got the gist of this after doing a couple of examples, so why do I need to do a dozen exercises as practice?” And then later on (or in future years) when encountering questions which assume that basic skills are transparent and automatic, these students will complain about how the question is too complicated or has too many steps or that they should be able to use a calculator, etc.

Although I wonder if they’ve developed this attitude because in their primary / junior years, they haven’t been drilled enough, or encountered sufficiently complicated algebra / arithmetic questions, to appreciate the value of mastery…

And here, at Radio KAOS, the hits just keep on coming… Seriously, a four-letter word that adds-up to fifty dollars? How short-sighted! Why not a twelve-letter one like, for example, SCHEISSDRECK which, coincidentally, neatly summarises both the current state of education in Ozbekistan and the quality of said ‘leadership’.

It was shortsighted of them not to allow six-letter words.

The really sad reality is that there are still a few Mathematics teachers in the system that I would classify as truly great, but I cannot think of one under the age of 45 (and even then I can only think of one under 50). For a point of reference, I’m 40 and have been teaching for 17 years and have had one, maybe two colleagues (long retired now) that I would call truly great. I’ll never be their level of brilliant which makes me appreciate their brilliance all the more.

One of the things I envy most about them is their ability to ignore a lot of this nonsense; to quietly, calmly but very publicly question it in staff meetings and then continue doing what they know is best, comfortable in the knowledge that no school leader will dare to ask them to do otherwise.

Whilst one or two of these teachers have been mentors to me when I was a pre-service teacher, I don’t see them passing on their wisdom much and I don’t see their greatness spoken about at all. The Eddie Woo’s of this world (disclaimer: I’m still not 100% sure how I feel about Eddie himself as a teacher – the commentary about him I detest, but his teaching itself… I’m yet to be convinced either way) have perhaps started the odd conversation about some other great teacher someone had once, but by and large they retire and get forgotten and their schools move on.

So… what am I trying to say? Not much, I just wish these “experts” would go away. The great teachers of this world will achieve their greatness in spite of, not because of your “revolutions”.

Thanks, RF. You raise an excellent and really depressing point: the loss of memory. Yours is another aspect of what I was discussing here. Implicit in my post above (and I hope to write on it explicitly soon) is that the very idea of a curriculum is being lost. You are noting that the art of teaching is being lost. Indeed, *everything* is being lost.

The general point is this: any movement that fetishises the present cannot possibly have appropriate respect for the past.

And therein lies the problem. This obsession with teaching being a “profession” (thanks VIT… for really pushing this in obscure directions) and the “science of teaching” will always and forever ignore the basic fact that good teaching (and lecturing even more so) is an artform.

A pre-service English teacher I watched a few years ago came out of a classroom and summed up their feedback experience quite succinctly: “they want me to be more boring”.

So, this is what “good teaching” means to those who decide who gets to become a teacher in Australia at the moment…

Please do not feed or annoy the animals.

RF: “Learning science” is the new phrase. Get with it!

Thanks Terry – to quote Abe Simpson (my source of wisdom in this world I struggle to comprehend):

“I used to be with it.

Then they changed what it was.

Now what I’m with isn’t it

and what’s it seems weird and scary…”

The trouble with that quote is the revolutionaries see traditionalist objectors exactly as Abe Simpson, as old men yelling at clouds.

Really? People can voice that expression without vomiting?

Tim. I know Tim. Let me dig a bit.

Glen, good luck and forgive my pessimism. I’ve seen this movie many times.

Let’s see what he says, I’m not going to rule out the possibility that he was misquoted. I mean, I’ve seen games etc being used to great effect.

BTW on topic to the post, I’d say 300 times is not out of the question for several things. The number of times they have repeated the 7 times table in a two year period for instance.

Glen, Glen, Glen.

Hey! I’d rather have hope and be wrong than not have any hope at all. I’m going forward in good faith… you do not need to share my faith :D.

Tim seems to be quite interested in getting feedback from people and seeing if AMSI can indeed do anything to help. I gave him my 2c.

Glen, I judge AMSI from what I see them do. What I’ve seen them do recently is sign an idiotic statement, whine with a very weird statistic for the fifteenth time about unqualified teachers (which is an issue but a fifth order issue), and be quoted about fucking games.

Tim wants feedback? Stop AMSI doing dumb stuff. Start AMSI addressing and taking a proper stand on what is screwing up education.

Not gonna happen.

Recently I had a CRT experience of watching another teacher offer a lesson in problem solving to Year 10 students. These problems would not be routine exercises, but something to stretch the students. Sounds fair enough.

A handout with these problems was distributed to the students and off they went. My role was to wander around and assist.

One of the problems boiled down to finding a formula for 1+2+…+n although it was not stated so bluntly. I asked the teacher “How do you expect that Year 10 students will be able to do this?” He was not sure but, in case I needed it, he told me the answer – which he found it on the internet.

Naturally the students did not get very far; after some time, most just gave up and chatted to each other for the rest of the lesson. Eventually we were saved by the bell.

I wondered what benefit this was for the students.

In reality, of course you’re not in the slightest wondering what the benefit might have been.

Do it spatially – arrange dots in a triangular pattern:

1, 1+2, 1+2+3… but do it in a right-angled triangle pattern.

At any point, copy the “triangle” with different colored dots and put these two triangles together in a rectangle.

Then the formula is just half a rectangle whose length is 1 more than its width…

Of course, a certain level of pre-planning on behalf of the teacher (and I do not consider looking up an answer online as planning) is required to make a success out of this.

Right! I’ve taught it this way to primary school kids.

I’ve never (sadly, I think it could be amazing, if tiring…) taught primary but I can see this activity working there with a suitably skilled teacher who is prepared to plan, trial, reflect, plan again and try again.

Of course… time.

Kids can pick up a lot of these Proofs Without Words things very easily, and very early. It’s valuable. It’s not the main game.

Sure. I’m not questioning the activity, but rather the way a teacher left it as an exercise seemingly without thinking it through. I guess the bit that worries me is that a (assumedly experienced) teacher of Mathematics thought this was a good activity to leave for a CRT and then didn’t seem to want (or perhaps know how) to debrief with the learners afterwards.

In isolation, good ideas can become very bad ideas.

And also agreed that it is not the main game, but I think it far from trivial.

I question the activity. See my reply to Terry below.

My point was that teaching students about problem solving is easier said than done. The students should experience that “Ah-Ha” moment, and learn to enjoy thinking. Chess problems are good examples.

Terry, I agree that problem-solving is easier said than done, but I’m not sure you made the point very clearly. Was the 1 + 2 + 3 + … + n problem supposedly presented as a “problem-solving” exercise? From your description, it seems unlikely, and unlikely that the problem was presented with any “what is this for?” thought whatsoever.

There are various reasons to show kids 1 + 2 + 3 + … + n , and either the algebraic proof of the sum, or a visual version of that proof, or both. But I don’t see that it makes for a good problem-solving exercise.

To be fair to the problem-solver fanatics, I think some people are putting a lot of thought into such things, and there are much better examples than 1 + 2 + 3 + … + n and Dougan’s Scrabble. There’s Harradine’s MathsCraft, and the Australian Maths Trust.

But I am still generally sceptical. I am not sure I know what “learn to enjoy thinking” means, or how I would teach that. I am not convinced that most of those “aha!” moments during “problem-solving” aren’t fundamentally contrived, aren’t more manufactured than genuine. To the extent it is genuine, I’m not sure it differs from well-chosen “difficult problems”, that have always been part of a decent teaching plan.

I am certainly convinced that none of this problem-solving should come before the prior attainment of appropriate knowledge and technique, that none of it supports the idiot revolution underway. I can imagine that MathsCraft and AMT and the like may ride this constructivist wave to greater glory. Alas, I very much doubt that they will take a principled and properly visible stand against the idiot forces that are, at the moment, benefiting them. And if so, I am not sure that, in sum, such groups, even the intrinsically good groups, are not doing more harm than good.

The bits I agree with from the opinions above:

1. Teaching problem-solving as a skill is difficult.

2. Giving students a problem to solve before they have learned a sufficient toolbox of skills with which to approach the problem is going to, more than likely, do more harm than good.

3. There is probably a bit too much focus on problem solving over skill mastery in a lot of curriculum documents.

4. There is definitely too much in pre-service teacher education and at these “PD sessions” teachers occasionally attend.

5. The majority of “revolutions” in education are idiotic.

And here are the bits I don’t agree with:

Chess problems are good examples. Willing to be persuaded, but what I’ve seen in books and online so far has yet to persuade me.

To the extent that one wishes to use doing chess problems as a means to improve at chess, I think most chess teachers / students / players would agree that unstructured solving is not effective. More effective are things like (i) grouping problems by type (ie. capture defender), and studying many problems of the same type, (ii) completing many “easy” problems under short time pressure, to improve pattern recognition and automaticity, (iii) keeping track of which problem types one finds difficult, and returning to those more regularly, (iv) once greater expertise has been achieved, mixing up problem types to further improve one’s ability to identify which sort of tactic / motif is most relevant, etc.

More or less, the same thing required for how to use problem sets / exercises to improve at mathematics…

SRK, a really excellent summary of the situation.

I won’t try to persuade anyone of the value of chess problems in problem solving. I agree with SRK that there is an art in using them in the classroom. However, G.H. Hardy wrote “a chess problem is simply an exercise in pure mathematics” (A mathematician’s apology, p. 15). And, it is not surprising that many key figures in the world of chess problems have a background in mathematics (e.g. John Nunn, Raymond Smullyan (1919-2017)). Anyway, I am obsessed with them.

Having had a nice meal out, I wonder if we should distinguish “problem solving” from “problem solving in mathematics”. The term “problem solving” is often used in the context of mathematics, but placing problem solving in a broader context might be useful. Problems that we encounter that need solving are not necessarily mathematical problems. They may be personal problems, or political problems, or financial problems, or problems confronting society.

Terry, this is getting the cart before the horse, and before anyone, at least anyone here, has agreed that we want that particular cart.

The question is, what do you want to teach in school? Then, the question is, how do you teach it?

Problem-solving is not the goal: it is only, at best, a method to reach that goal. Unless, that is, you have a revolutionary – and idiotic – sense of schooling, where you give up the idea of traditional disciplines and you have, instead, de facto subjects such as “Problem Solving”.

Assuming we are not so idiotic to give up traditional disciplines, “problem solving” offers little, at least for the first many years of schooling. On the other hand, “problem solving in mathematics” may have a role, although there is deserved scepticism: if PSIM does not just amount to traditional hard problems, it is not so obvious how much it offers, and it seems clear that it is being way oversold.

Even supposing we agree that an aim of school education is to improve the ability to answer / solve problems that are unfamiliar / open-ended / etc., my understanding of the cog-sci / cog-psych literature is that performance at such tasks is strongly correlated with domain-specific knowledge / skills. The idea that we can effectively learn (much less teach!) domain-general / content-neutral knowledge or skills is a fantasy.

I don’t think it helps the defenders of problem solving to retreat to the idea that we just want to teach “problem-solving-in-mathematics” because I thought that the main motivation for their view is that improving at “problem-solving-in-mathematics” causes improvement at “problem-solving-in-general”.

Obviously the surname of every kid in the class was Gauss.

Problem solving is not a bad thing. The bad thing is idiots that want students to construct their base knowledge by problem solving, rather than use problem solving as a way consolidating and extending what’s already been explicitly taught. Imagine the coach of a football team ‘teaching’ his players by getting them to run around with a ball and explore.

And don’t get me started on the whole group-work thing and the sucker (smart kid) that ends up doing everything.

As Marty has put it: These idiots think all the students will be Lewis and Clarke when the reality is Bourke and Wills.

What I don’t understand is the following: Listening to all these idiots is what’s got education into the mess it’s in. But apparently the solution to the mess is to continue listening to these idiots.

Here is an example from Martin Gardener:

Organisation is important in VCE. At a more basic level, students should learn how to be well organised. They should bring what they need to class. Any suggestions on how to get the message across?

Hi,

If you like “proof without words” then QED would be one possibility (;-)

https://www.bookdepository.com/QED-Burkard-Polster/9781904263500?redirected=true&selectCurrency=AUD&w=AF45AU96ZUQUMHA8VRJ7&pdg=pla-295092701166:cmp-6919946397:adg-82581721111:crv-389775188388:pos-:dev-c&gclid=EAIaIQobChMI75i–KuR8AIVy8KWCh3LqA-qEAQYASABEgKi2fD_BwE

Steve R

If the answer is 42, what is the Question?

Let’s take a punt on AMSI = 42…

Are the AMSI now just a bunch of

Zugzwanged Woolaroo Wombat Worrying

…. ….?

So then, what are the two missing four letter words (both prime) and 30 or 60 apart from the (ZWWW = 101) prime example above – that aptly completes the phrase describing the bunch of “experts” attempting to come up with fresh ideas for the Australian Mathematics Curriculum…

Hitchhikers Guide to the Galaxy – as if you didn’t know – was the source of the answer…

For what it’s worth, I am an unqualified teacher…

I have no idea what happened to AMSI. They’ve had a habit of being Silly and Useless, but they appear to have graduated to Really Stupid.

ACARA are – judging from the WitCH60 – equally amusing…My wee example with AMSI=42 would be the sort of question I’d fire at pupils (those old enough to follow your ever so slightly profane Blogs)…Much as I respect Teaching and Teachers, I fear that not enough is given over to puzzles that allow students to figure the answers out for themselves…Just for your WitCH60 – the answer to Fermat’s Last Theorem undoubtedly lies buried in Pythagoras Theorem…Of course – as that is just my own “marginalised” opinion – it is then, asking a hell of a lot for students to fully understand it…

I’ve thought about toning down my blog, so that more students might be sent to it, and decided “Fuck it”. If teachers think the occasional bad (schoolyard) language here is worse than their students’ corruption by idiocy, then that’s the teachers’ choice. I just can’t be concerned.

I’m sure students have ways of hearing about and then finding your blogs … Teachers who think that the language used or opinions expressed at your blogs are not fit for student consumption, particularly VCE student consumption, can …