Time for another competition. This one is sort of a localised version of a previous competition, and the motivation is similar.

The Mathematics Education Research Group of Australasia is currently holding their annual conference. The list of scheduled talks is here, and the draft proceedings is here. The competition is to name, and to briefly argue for, the MERGA paper-talk that provides the *genuinely* greatest benefit/insight/whatever into mathematics education. So, the question is, what of genuine worth can people find. And, the best and best-argued answer, as determined by our unesteemed judge,* will win the competition.

The winner will win a signed copy of the best-selling** book, *Putting Two and Two Together*.

Happy hunting.

*) Me.

**) In Poster and Ross households.

Talk about trying to find a needle in a haystack. It’s more like trying to find a grain of rice on the beach (or perhaps in a sewerage farm) …

Numeracy ≠ Mathematics: Numeracy and the General Public by Helen Forgasz looked promising and the first few lines looked even more promising. But then it fell down a cliff. Avoid.

Then I thought

Comparative Effectiveness of Example-based Instruction and van

Hiele Teaching Phases on Mathematics Learning by Saidat Morenike Adeniji and Penelope Baker

might be the grain of rice I was looking for. This is my nomination for the following – in no particular order – reasons:

1) I can’t be bothered wading through a further 550 pages of crap.

2) It contains the least amount of jargon.

3) The data analysis seems OK. (OK, I haven’t checked it thoroughly, but it look more OK than the usual mumbo-jumbo).

4) It made sense and made me think.

5) The context of the experiment was solving simultaneous equations.

6) The word “numeracy” is not mentioned.

You’re currently winning.

In a one horse race (so far) it would be extremely dire if I was losing!

I think the other competitors have gotten too many pages into it and asphyxiated. But I think Terry M has eternal optimism and extraordinary staying power, so watch this space …

… if I

werelosing …Thanks, John. I’ll look at both.

John, what do you see as the Forgasz cliff?

It started off promising one thing: Numeracy ≠ Mathematics. I thought it would discuss the differences and that teaching numeracy and testing numeracy is not the same as teaching and testing mathematics. But then it just turned into another numeracy advertisement and mathematics got no further mention.

To me, it was a classic bait and switch. I don’t even see the relevance of the title. And at the end it seems that she’s mixing the two up anyway.

Yeah, a good point about the title, although I think the subtitle makes it clear enough. Given Forgasz’s thing is just an introduction to a “round table”, it’s difficult to make much of it, good or bad. But, it smells pretty bad.

Not clear enough! – The subtitle fooled me too. I thought it was alluding too how the general public are continually fooled into thinking that numeracy and mathematics are the same thing. Forgasz’s name attached to it should have been the clear warning.

Huh. I’ve now looked at the Adeniji-Baker paper. It is a weird grain of rice.

The paper is the report of the authors’ experiment, on the teaching of “solving complex mathematical problems using … simultaneous equations”. The authors compare a Cognitive Load Theory approach with a constructivism approach, and argue with the stats that constructivism was the winner.

However, there is no indication precisely what was taught, nor how it was taught with either approach, nor how it was assessed. As such, the conclusions are meaningless.Perhaps the MERGA talk itself had some detail, and thus some meaning. But, and although one can only conjecture, the whole thing smells to me. The introduction of the paper frames the whole discussion on the perceived importance of PISA-like skills in real-world scenarios, and thus it’s reasonable to conjecture that the mathematics and its assessment had this flavour. So, I’d

reallywant to see plenty of details before giving the study any credence whatsoever.I asked Greg Ashman about the paper, since Greg is

~~Mr.~~Dr. CLT. While noting the absence of detail, Greg seemed pleased that an apparently genuine attempt had been made to compare CLT and constructivist approaches. He also noted that the two groups of students were taught by different teachers, which was unavoidable (because of Covid constraints) but not optimal.It’s perhaps a small insight, and not one I can apply (too late by high school), but I think the abstract called

Beyond the Arithmetic Operation: How an Equal Sign is Introduced in the Chinese Classroomby Jiqing Sun sounds interesting.It says they’re going to describe how the equals sign is introduced in China (where it is relatively well-understood) vs in Australia (where it isn’t). The first part: the equals sign is introduced separately before arithmetic operations. That’s interesting. I guess there

maybe confounding factors explaining Chinese students’ superior understanding of the equals sign, but I like the idea of paying attention to details and making sure students understand the symbols they use.(Admittedly I just skimmed through and didn’t look very hard. These are just abstracts though? It seems like we can’t judge without seeing the talk?)

Thanks, wst, and good point. It would appear that some entries in the “proceedings” are full papers, and some are only abstracts. I’m not sure we can glean much from the Jiqing abstract, except that it sounds interesting. That still puts it high on the list.

As far as I recall, authors of papers to be presented can submit abstracts or full papers. Full papers get a more thorough review than abstracts.

Sun’s paper (or at least some version of the paper) can be downloaded here. It seems Sun also presented the paper at an MAV conference, presumably in 2019.

Thank you. I think he makes a pretty good case for introducing the equals sign in the first year of school.

I had a look at ACARA’s curriculum, and they do lots of comparing but leave out the case of equality – except in the case of “sharing equally”. Perhaps they could add it to “using counting to compare the size of two or more collections of like items to justify which collection contains more or less items”. Would that be cluttering the curriculum though? I can’t judge.

Thanks, wst. I hope to look at the paper soon.

Clearly, generally in primary school, the importance of equality is not made sufficiently clear. It’s not obvious to me when and how it should be introduced and taught. I’m not suggesting this is hard (or easy), I just haven’t thought about it.

Thanks, wst. I had a look at the paper. It’s not rocket science, and I’m far from sure I agree with the conclusions. (I don’t know what I’m comfortable with equating six carrots with 6, even temporarily.) But, yes, it is interesting.

There is no question that Australian primary schools undersell the importance of equality. So, some earlier introduction of the concept of and the symbolism for equality may well be helpful. But I wonder if the late introduction is the main cause. It seems to me the more natural and larger culprit might be the simple lack of sufficient, and sufficiently difficult, arithmetic problems, and written arithmetic in particular.

In any case, you’re now winning.

Education ‘experts’ like to get as much mileage as possible from a single paper. So one paper will get presented at ten different conferences – maximum exposure is the name of the game. MERGA Conference: tick. MAV Conference: tick …. And it will bob up in at least half a dozen different mathematics education journals too.

All aboard! … The gravy train is about to depart.

John, many mathematicians do this as well. Maybe not as brazenly, but they do it.

Yeah, I know. Most academics do it. But you’re right. Not as brazenly. And it’s not stuff that gets shoved down your throat as the golden elixir. And there’s generally a more robust peer review process.

Often I have heard talks at academic conferences begin with “I apologise to those of you who have heard this before, but …”

It is OK to present the same paper (maybe with some tinkering) to different audiences *where there will be almost no overlap*; the talk improves after each presentation – up to a point – then it stops improving, at which time, the author should write it up for a journal article or start something new; obviously I have done this.

On the other hand, I have known academics who, on principle, never repeat a presentation.

If you were to look through the abstracts of a mathematical conference or journal, would you find articles that stand out as articles of great benefit to mathematics? Here is an example:

https://www.ams.org/journals/proc/2022-150-09/

I don’t understand even the titles!

Terry, we can argue this is you really wish. You’ll lose.

Terry, I’ll bet London to a brick that most of those articles are of more benefit to mathematics than most of the MERGA articles are to mathematics education.

Hi Terry. I’d argue the much stronger statement that every single one of those articles have some value. I browsed through the list briefly and some are even quite interesting (IMO).

(BTW PAMS is a journal, despite the name, just to be clear.)

I know that PAMS is a journal.

However, advances in research are often made through the cumulative effect of small advances which, in themselves, may not be particularly significant.

At one stage, I suggested to MERGA that they could have a special issue of their journal devoted to the most important problems in mathematics education. Although their reply indicated that they liked the idea, it was not followed up.

BTW, another mathematics education journal in Australia is the Australian Mathematics Education Journal. Attached is a paper that I submitted to AMEJ.

2020-MillsSacrez

The suggestion that MERGA would have any sense of the most important problems in mathematics education is absolutely hilarious.

Hi Terry. I think it is very easy to play semantics with the word “significant” here. Again, I’ll just reiterate that I think all of those papers published in PAMS are significant, and several of them I think are very interesting. I could pick any of those papers at random and be quite sure that there is a good motivation and some nice mathematics in there, that advances the field.

Having some value at all is I believe the point of this post (sorry for continuing to derail it), so the amount of significance larger than zero, measured by whatever metric, is beside the point.

Really? So many words, so little information. I vote for this paper: Only real problem : it wasn’t there.

Planning for Growth by V Helpful and F Useful.

Recent graduates and teachers who are not trained to teach mathematics are often asked to teach lower secondary mathematics classes. They often find that the teacher that they are replacing has left the school taking with them their plans and resources, leaving these new, or new to the subject teachers under resourced and under supported. We asked schools whose students consistently show more than 1 years growth per year in standardised tests of mathematics [What would that be? Naplan? Pat-M? Something else?] to participate in this research by sharing their learning and assessment plans and week by week programs for year 7, 8 and 9 classes. Twenty schools were generous enough to participate. These schools were then matched to other schools that had much poorer growth but similar socioeconomics, remoteness, etc and these other schools were also asked to provide planning documents. The documents of the two groups were analysed. We found that the more successful schools had more complete documentation of their planning and … Examples of LAPs … Examples of programs …

@M Ware: Good idea! There are a few issues that need to be resolved before progressing further.

What is the evidence for saying that teachers being replaced do not leave plans or resources for the replacement teacher? My experience is the opposite. When I have filled in for other teachers, there have always been resources provided. And when I was replaced recently (flu – my first sick leave this century), I left detailed resources for the replacement teachers.

Schools volunteered to be involved in the project. This restricts the capacity for generalisation to a broader population of all schools.

How would one analyse planning documents?

Only questions – but a good idea all the same. Thank you.