A bit over a week ago, the Australian arm of Oxford University Press, in collaboration with the Australian Maths Trust, released a White Paper: *The knowledge and skills gap in Australian primary mathematics classrooms*. Yeah, it’s in the “well, duh” category of reports, on the massive range of student mathematics levels, which primary school teachers must then manage. But, still, the report can’t be a bad thing, can it? Well, …

OUP’s press release was dutifully stenographed by the media, in this rare instance a positive (in sum, just). Unfortunately, *The Age*‘s Adam Carey attempted to add some value. After noting the horrors flagged in the OUP report, Carey remarks,

*The results follow the development of a new Australian curriculum beginning next year that emphasises greater mastery of maths problems in the early years.*

It is unclear how a statement can be simultaneously irrelevant, meaningless and antipodally wrong but, somehow, Carey has produced it. Carey’s and the others’ reports also quote various OUP-promoted “leaders” saying irrelevant, leadery things. Still, the key message is there: some primary school students know bugger all mathematics in comparison to other primary school students.

OUP’s paper is based on a survey of a couple hundred primary school teachers. A small sample, and there is no clarity or analysis, but the teachers’ message is clear enough. The report notes, for example, that 30% of Year 5 teachers claim a 5+ year range of knowledge/skills of the students in their classroom. There are a number of such statistics, simultaneously horrifying and old news to anyone who has been paying attention.

Such statistics are the Big Message of OUP’s paper, and already there is a problem: referring to such differences as a “gap” hilariously undersells the problem. If, for example, we are told that some of the men in a room are two metres taller than other men there, it doesn’t suggest these other men are short; it suggests these other men are flatworms.

Yeah, sure, you can have tall men, and you can have “accelerated” kids. Asian kids and fellow travellers will commonly be above Australia’s woeful year levels. Nonetheless, the claim – and truth – of a 5+ year gap in a Year 5 class doesn’t imply that some students are way behind; it implies that some students are learning very close to nothing in primary school.

Why this is happening is of course the critical question. The OUP paper acknowledges the question in its conclusion:

*This paper presents several potential reasons why there is a knowledge and skills gap in Australian [primary]* mathematics classrooms …*

Except, OUP’s paper presents nothing of the sort. The paper fleshes out the problem, and considers the difficulty of teachers’ task of dealing with the problem, both of which are reasonable and important. But the paper never considers the much, much more important issue of the source of the problem. The paper never acknowledges the Elephant Truth of a poor curriculum pseudo-taught with poor techniques to students who have not been taught to pay attention, and with no expectation, much less demand, of mastery at even the low levels proffered. Without such acknowledgment, OUP’s report dissolves into meaninglessness. It then becomes meaninglesser.

OUP’s report is “complemented” by four articles, written by “some of Australia’s leading mathematics educators”. These articles are intended to “provide practical implications for teaching mathematics to primary students”, whatever that means.

Pride of place goes to AMT’s Janine Sprakel. Unsurprisingly, Sprakel promotes problem solving, at which AMT excels, and which has absolutely zero relevance to the knowledge and skills gap. Perhaps if AMT hadn’t been so busy playing footsies with ACARA, they could have addressed the reasons for the unpreparedness of students to tackle any but the most trivial of problems. But, such is the cosy way of edu-industry.

The second article, by teacher Annie Facchinetti, is better. Facchinetti offers various suggestions, some good and some bad, on differentiating in the classroom. It is all too vague, and the vapour of wishful thinking hangs thick in the air, but at least Facchinetti is attempting to offer plausible strategies. It gets much worse.

The third article is by teacher and big shot Peter Maher, who writes on the importance of engaging students. Teachers should supposedly do this by presenting the mathematics in “real-world situations”. For example,

*A study of fractions, a topic that can appear dry and rather esoteric to children, can come alive when applied to recipes and the time divisions in games.*

Uh, thanks Peter, but that’s not how anyone learns to be adept with fractions. Students learn to be adept with fractions by doing hundreds of carefully crafted exercises on fractions. Claim it to be “dry” and “esoteric” if you like, although that is highly contestable. It is also necessary.

The final article is by Peter “The Not So Great” Sullivan, who wants to ensure that all students are included in “rich learning activities”, and “open-ended” and so forth. Sullivan’s usual nonsense, with absolutely no bearing on the issue at hand, the non-attainment of fundamental knowledge and skills. Of course, since TNSG was lead writer of ACARA’s current, woeful curriculum, it would be preferable to not hear from TNSG for a while, or ever again.

It seems that Oxford University Press tried to do a good thing, they tried to score a meaningful goal. Their build-up was impressive. And then, with the goalmouth wide open, they did a Lewandowski.

*) The paper refers to “secondary mathematics classrooms”, seemingly a cut and paste error from OUP’s similar 2021 report on secondary schooling.

In case there are those in primary looking for something substantial on “mastery”. (Even the worst primary “official curricula” can be serviced by good texts. Oxford used to market “Inspire Maths”

https://global.oup.com/education/content/primary/series/inspire-maths/?region=uk

but did so as a modification of material under licence from Marshall Cavendish, and the arrangement ceases as from early 2023. However, there is another excellent – in my view much better – carefully structured resource that some might find helpful: see below.)

But first to comment on “The knowledge and skills gap in Australian primary classrooms”:

Sprakel: “take time” (“Take some time to do some mathematics today. I mean really take the time. Do a problem that you are about to set for your students. Stare out the window and ponder. Scratch around with paper and pencil. Draw a sketch, scribble out a table. Look for a problem that really engages you, for it will most likely engage your students. Get to know the problem. Think about how your students will approach it. What will they need to be successful? How can you help them along if they need it? How can you extend the learning for all students? What will the hurdles be? Take the time.” Excellent. But even if I had the time, how do I ensure that my chosen problem for today interlocks with yesterday’s? And tomorrow’s? And last week’s? And …? Isn’t that where educational publishers used to play a role?)

Facchinetti: “differentiation”.

Maher: “Real-world” situations (in primary school!).

Sullivan: “whole-class, rich learning opportunities”.

Is this really going to help?

I would encourage those who find these liberal “add-ons” appealing but insufficient to take a look at:

This scrupulously designed series interprets Sullivan’s “Putting it all together” comments below in a way he seems not to grasp – namely as a coherent six year program in which *all* the parts are interlinked in a way that supports long-term progress:

[Sullivan, p.21: “Note that it is not the individual elements that are critical but the overall approach. By using such a lesson structure consistently all students, especially those who may lack confidence and be unwilling to persist, know the structure and become aware that there are multiple opportunities to engage with tasks and to learn. A key feature of the overall approach is that this structure of lessons, consistently applied, gives students confidence of what is to come and reduces anxiety”.]

Unfortunately, it may not be enough just to “buy the books”: one does need the associated training, so interested schools might like to link up.

The virtue of the genuine mastery approach is that it builds over time in a way that eliminates most of those who currently form the bottom end of the “five year gap in Year 5”, without boring the pants off the top end. However, should the top end need more, I can also recommend(!!) https://mathsnoproblem.com/en/products/mathsteasers/

Thanks very much, Tony.

Readers may wish to correct me, but I know of no comparable programs or resources readily available in Australia. (OUP Australia does not appear to offer the Inspire series.) AMT does some great competition stuff and has some (much less great) books, but as far as I know it is all add-on for the smart/motivated guys, not a regular classroom program for anybody.

Of course, since the majority of Australian primary teachers believe that having students master the multiplication tables is a bridge too far, there’s not a whole lot of momentum for further mastery …

The mathsnoproblem stuff looks excellent, and anyway I’m not gonna second guess Tony Gardiner. However:

*) At the moment the primary series appears to be between editions, with a number of texts/workbooks currently unavailable.

*) While the books themselves seem very cheap, the shipping to Australia is very not cheap (and awkwardly piecewise constant).

I note there are a few used copies of your mathsteasers floating around (and there are now a few fewer).

My copy of Mathsteasers Beta arrived today. It is great. I also now understand the import of Tony’s ‘ “differentiation” ‘.

I read the paper with interest.

I was disappointed that there was no information about how the data for the survey were collected.

I noted that results from PISA, TIMSS, and NAPLAN were all presented in one diagram. This might encourage people to ask: Why are these data so different from each other? What do these three data sets, collectively, tell us? Are they even comparable?

I wondered about the meaning of “relatively no improvement over time” in TIMSS and NAPLAN.

Sprakel from Australian Maths Trust (AMT) discusses problem solving. AMT has produced some on-line modules on how to incorporate problem solving in the classroom with an emphasis on Problemo. I have worked through a couple of them: they were well produced, not long, and useful.

Facchinetti mentions the difficulties faced by generalist teachers in teaching students in a primary school about mathematics. To deal with this raft of issues, mathematics teachers need considerable expertise in the discipline as well as in teaching methods. I wonder if mathematics in primary (and secondary) schools should be taught by specialist mathematics teachers rather than generalist teachers.

Maher emphasises real-world applications. The question that is always in my mind is: Whose world — my world or the world of the students? Often, I might see an interesting application of mathematics, but will my students be as interested? We live in different worlds.

Sullivan is an enthusiastic supporter of open-ended problems in mathematics. Such questions are rarely asked in text books, even though life is full of such questions. I have, from time to time, used such questions and found them illuminating.

I liked Marty’s phrase that the report contains “old news to anyone who has been paying attention”.

On good (or “good”) curriculum materials, the Grattan Institute has just released a report on “How to improve school curriculum planning”. In particular, a friend noted to us that the authors were advocating use of the materials by something called Ark Curriculum Plus (pp 10, 46, 47, 53, 54, 70, 77).

I’ve read nothing of or about the report and know nothing of Ark. If anybody knows anything, I’m curious.

Last year OUP conducted survey investigating the same issue at a high school level. (Vinculum, Volume 58, Number 3, 2021)

At year 7 34% of teachers reported a gap of 5 or more years, which dropped to 27% by year 10.

The “potential reasons” presented for this gap were essentially the same:

The transition from year 6 to 7.

Challenging differentiated teaching (and thus engaging students) with such a large gap, and a lack of resources for said differentiation.

Lack of problem-solving skills for the real world.

“Mathematics anxiety”

Covid / remote learning

96% of teachers surveyed said they did not have enough time to teach, and 50% said they don’t know techniques for “remedial” teaching.

Thanks, Wilba. The announcement of the report is here, the report is here, and the video of the follow-up webinar is here. (People can also register for a follow-up webinar for the current, primary report, here). Note that the 2021 report had articles from (almost) a superset of people.