There is another contribution from the Education community:
How to do the sums for an excellent maths curriculum
This one does not directly address the open letter, although, given the framing and the links, it is difficult to not see the article as an intended rebuttal. Again, we know little of the authors, and we have not read the article with any attention. We’ll be interested in what commenters think. (Ball-not-man rules still apply.)
UPDATE (10/06/21)
Glen has pointed out that the article is from April 21. So, it is definitely not in response to the open letter. However, the article came out soon after the ridiculous, pre-emptive strike statement from AMSI, AAS and others, and in its first sentence the article links to the reporting of this statement. Whatever merits it might have, the article is not an innocent reflection on educational method.
UPDATE (10/06/21)
As indicated by SRK, there is now (in effect) a response from John Sweller.
I feel as though there are so many strawmen being built that I am about ready to just drown. I don’t like it. For instance, the article implies that critics are against:
That’s just ridiculous.
I ask honestly: do the authors of these articles honestly not understand what the criticisms consist of, or do they deliberately misinterpret and misrepresent the position of the critics, so that they can easily make them appear ridiculous?
Sorry Marty I’m not really up to tearing both of these apart at this moment, but from a quick look they are both overflowing with issues.
Sorry, just to add: we are going to have another article to look at soon. Did you see this?
“Tomorrow Emeritus Professor of Educational Psychology at UNSW John Sweller adds to the debate.”
Sweller’s reply: https://www.aare.edu.au/blog/?p=9210
I liked the previous article better, because it was clear what they were saying. Reading this one reminded me of talking to someone who puts their fingers in their ears and says “nananananannananaa, I can’t hear you.” I guess that means I found it disingenuous?
For instance:
“The TIMSS data tells us that more positive attitudes, in terms of valuing, liking and confidence with mathematics are related to higher achievement. So teaching approaches that support the development of positive attitudes are vitally important…”
completely ignoring the other way you might interpret that first sentence.
My third comment on a post and I still am not engaging properly with it.
Let me say two things:
1. This is from April 2021 (thus why it is not referencing recent things)
2. There is a “thought” at the bottom of the article (comments are closed, so I don’t know what this “thought” actually is, perhaps a remark from the editorial board or a referee… or perhaps it is simply that the article is too “old” to have any further “thoughts” added to it) that I don’t hate. Here it is in full for your convenience:
By Daniel
April 21, 2021 at 9:10 am
I wonder what the authors define “traditional explicit teaching” as? I feel their argument about turning students off mathematics because of it would be clearer if they did.
From my experience as a mathematics teacher, it seems to be more because of poor teaching of arithmetic (i.e. teaching that doesn’t develop confidence and speed in it) is to blame for turning students off mathematics. The authors touch on this, “Students need sound content knowledge in order to draw on that knowledge to solve problems”, but fail to see it its meaning – even with such title for their article.
So many aspects of mathematics build on a strong foundation of arithmetic – algebra, a generalisation of arithmetic, being the obvious one. How can students solve problems, let alone ones they have never seen before, without algebra? It is such a powerful concept/tool. To do without it would slow students down and over encumber their thought process (cognitive overload).
Being confident with arithmetic supports students to tackle the challenges of mathematics (whether it is exams or problem solving). They will have resilience to survive exams through being built up to have arithmetic as almost second nature; and be unphased by the complexities of the problems they need to solve since arithmetic is almost second nature.
Regardless of teaching style, a curriculum that fails to emphasis the importance of arithmetic fails to guide well meaning teaching and consequently fails to support student achievement in mathematics.
The “thoughts” are comments from the public and they were open at the time of publishing the article. The lone comment is my one and guess no one else commented before they closed it. It’s good you don’t hate it.
Huh. How odd.
Ah, maybe you can post it as a comment here, and then I can delete mine — if you want, of course.
Nah, it’s fine where it is.
Just had this pop-up on my FB feed. Worth a read (no paywall). 🙂
https://www.theage.com.au/national/there-s-a-lot-at-stake-as-the-maths-wars-erupt-20210611-p580a3.html
Thanks, Sir H. It’s a pretty good piece. The open letter seems to have inspired a number of reports and opinion pieces. In general, I’ve decided against linking them, since I’m not sure they’d add much new. I decided to post on the last two articles, since they were in opposition, and figured it would be interesting to see what people made of them.
OK, one (and only one this time) thought:
The authors seem to be arguing that the big problem is students begin to identify themselves as “non-maths” students in early secondary school. The solution (again, I’m guessing as to the authors’ argument) is to make the subject MORE complex…?!?
As a person who has been known to teach mathematics at high schools when I have to (OK, I’ve taught nothing but for over a decade – that brief foray into Physics was just… not right) I know that the authors are making a statement that appears to be true – students, very early in secondary school (or actually much, much earlier) have a fixed attitude that they can’t do maths.
Now if that was not the end of the story I would not be angry. Similar to solving any sort of puzzle, learning any sort of skill, if there was more to the story (such as – I can’t do this YET, I’m going to find some way to practice more, or god forbid there was a mandated minimum level of practice as there now is for learner drivers…) then maybe there would be hope that we can turn this ship around.
Sadly, we are now fighting a battle on three, if not four fronts: the student who says they can’t do it, the parent who shrugs and says that they “never really got it” themselves (whether you consider that one front or two is up to interpretation), the school “managers” (public and private) who think spending billions of dollars on new facilities is a great idea but when anyone suggests that spending 1% of that on improving the skills of their own teachers is flatly ignored and finally the curriculum and assessment authorities who instead of listening to the grievances of teachers and doing something (anything) to help, they dig their heels in and insist that they are right, we are wrong.
As more and more brilliant mathematics teachers ride off into the sunset, there is no second wave coming to replace them (or if there is, such teachers are nabbed immediately by the private schools who know what a rarity such talent will be in the very near future).
So… what to do?
No idea.
RF, there’s nothing to do. One can, and should, fight the battles, such as over this draft curriculum. One can, and should, ridicule the idiocy behind it. But the war against stupidity has been lost.
Part of me hopes you are wrong on this final point; the proof is pretty irrefutable though!
On the other hand, I too have fixed attitudes. For many years I did not like beetroot because of the colour – I had never eaten it. I don’t like movies that involve divorce or submarines. I don’t like people telling me stories about broken bones. I don’t like 20th century fiction. These attitudes are not rational.
I now like beetroot – so my fixed attitude did change but it took a long time – more than 70 years. So I understand that some students will have fixed ideas about all sorts of things.
Unfortunately, it is a fact of life that many parents and teachers share this dislike of mathematics, and should a student seek advice from such a person then this dislike of mathematics will be reinforced. (I recall one student telling me, with some pride, that his father not read a book since he left school.)
I have just proposed a paper for the MAV conference on how society should view mathematics – but I doubt that it will get accepted.
It is foolish to not recognise that students will be stubborn with their ideas, typically reinforced by foolish teachers and foolish parents and a foolish society. It is also foolish to regard students’ ideas as “fixed”.
What makes you suspect the MAV will reject your paper? Yes, they’re ideologically-driven clowns, but they’re also clowns with no standards. They’ll accept pretty much anything as a conference paper, unless it’s too mathsy.
Last year I offered a paper on games, specifically on the game “paddocks”, sometimes called “dots and boxes”. I used games of strategy, and in particular, paddocks, in teaching VCAL students. Students enjoyed it of course, but the issue was to convince them that thinking about strategy is a mathematical activity. Interestingly, the game was developed by a French mathematician (Lucas) in the 19th century. More interestingly, it seems that there is still no known strategy for playing the game. We went from numeracy in VCAL to the edge of knowledge in one double lesson. I thought it was a good story. But evidently the reviewers did not. They don’t give reasons. As someone advised me later, “Interesting – but it’s not in the curriculum”.
My new submitted paper on how we should view mathematics is even further removed from the curriculum. It’s based on the work of Kant.
So, last night I proposed a second paper on chess problems. Maybe one will get accepted; at least problem solving is in vogue.
Attached is a good problem. White to move and mate in 200. True! I have not got to the bottom of it yet – but I am on the way with the help of a published partial solution – except that this afternoon, the cat sat on my chess set which was set up at about move 180, so I have to start again.
Just to be clear, the MAV rejected your paper last year?
Yes; and also, just to be clear, the person who told me that the topic was not on the curriculum was not associated with the conference; it was just an opinion that he offered when I told him about my paper.
Was your paddocks paper accepted or rejected by the MAV?
One submits only abstracts for consideration. A full paper may be written later. My proposed abstract on paddocks was not accepted. It’s quite possible that there were too many submissions for the time available.
Without reason? So why don’t I write about this?
Please don’t write about it.
They may have said something like “Due to the large number of proposals …”. I don’t really remember.
But just let it rest, please.
Thanks.
Of course I won’t write about it. It’s your (wrong) move.