As noted in a couple quick posts, last week the Grattan Institute released their report, The Maths Guarantee, on primary school mathematics teaching. I’ve now read the thing; here are my thoughts.1
I tend to write long and people tend to read short, so I’ll put the headlines in the headlines. In brief, the report is very good but with a very big bad. The good is that the report is pushing hard all the (one would think) no-brainer aspects of good mathematics teaching: decently long lessons decently often; the necessity of good resources; explicit instruction, particularly for new and fundamental concepts and techniques; the importance of mental skills and automatic recall, and the regular practice needed to attain it;2 engaging in proper mathematics practice rather than idiotic explorations;3 and an expectation of mastery, with frequent testing to monitor progress. I have some large concerns about this “good” – details below – but in sum this good is very good. The very big bad is that the report treats ACARA’s nonsense Curriculum and ACARA’s nonsense NAPLAN testing with way too much respect and way too much as a given. The sum of it is that, while the Grattan report is very good on how to teach primary mathematics, it is way, way too weak on what mathematics should be taught.
One final global comment: I disliked the writing style. As Terry Mills noted in a comment, the report consistently uses the term “maths” rather than “mathematics”. This colloquialism is gauche and distracting and plain bad; everyone is doing it now and everyone should stop. Beyond “maths”, the report is generally written in too casual a manner, and seemingly intentionally so, presumably to make the report friendlier in feel and so more palatable. Fair enough, and the lack of pompous jargon, which typically swamps such reports and makes them unreadable, is a huge plus. Nonetheless, clarity is paramount and such a report should be written in a reasonably formal manner; Grattan somewhat underdoes this aspect. And, again, they employ “maths”.
On to the details.
1) Mini-disclaimer: I’ve had some very brief contact with Grattan-ish people. Probably not sufficient for a disclaimer, but I am so puzzled that Grattan doesn’t hate me, particularly given I’ve written a couple pretty mean things, a disclaimer feels in order.
2) It was very pleasing to see Grattan give Jo Boaler’s nonsense a drive-by slap (p 23).
3) It was similarly pleasing to see Grattan give AAS’s reSolve twaddle a drive-by slap (p 21).
The Recommendations
The body of Grattan’s report is evidence that Australian primary mathematics teaching is stuffed, together with pointers, including a large focus on specific exemplar schools, on how things can be unstuffed. Presumably anybody reading this post at this blog does not have to be convinced that things are stuffed, and we’ll leave that be. As to the exemplar schools and why they are supposedly exemplary, we’ll get to that, at least a little. But the force of the report, if it has any force, is the specific recommendations it makes, to the State and Federal governments and education “leaders”, to unstuff things.
The recommendations are detailed in the prefatory material, thankfully not referred to as an “executive summary” (pp 3-4). In brief:
1. Raise Expectations
2. Provide better guidance
3. Arm schools with high-quality curriculum materials, catch-up interventions, and assessments
4. Improve teaching quality
5. Tighten monitoring and oversight
Listed baldly, this is of course just motherhood, but in the preface Grattan fleshes out what they propose. The body of the report also makes pretty clear what they mean by “high-quality curriculum materials” and “teaching quality” and so forth. We’ll consider each recommendation in turn, what it seems to mean to Grattan, where this is good and where it falls short.
Expectations
There is no more compelling problem in Australian mathematics (and all) education than its poverty of no expectations. There may be some desire that students do well at mathematics, even if “mathematics” is not properly understood, but the desire is not very strong and there is certainly no general expectation. It is therefore excellent that Grattan places this recommendation front and centre, and they hammer it throughout. Grattan’s insistent use of the terms “master/mastery” is great to see.
But how are we to measure on the large scale whether these new-found expectations are being met? Grattan explains (p 4):
Commit to a long-term aspiration of 90 per cent proficiency in NAPLAN numeracy, with an interim target of a 15 percentage point increase over 10 years.
Jesus H Christ.
To be fair to the Grattan authors, I strongly suspect that they are lying through their teeth. I do not for a minute believe that the authors regard NAPLAN as in any sense an adequate measure of whether appropriate expectations have been met.4 But what are the authors to do?
This is the fundamental problem, always, with Grattan-like calls for reform. If if were just one piece of the educational puzzle slightly out of place then the fix would be easy enough: we can see where the piece needs to go and how it should fit. But in Australia all of the pieces of the puzzle are out of place, and more than a few have been lost, eaten by the dog many years ago.
Grattan wants to focus on primary mathematics teaching, which is understandable and, in its way, good. But then, to avoid fighting a larger battle, Grattan must simply pretend that ACARA, with the passive or active support of a plethora of clueless education ministers, has not completely ballsed up national testing. And so, Grattan’s sensible and important recommendation is immediately perverted into Madness As Usual.
It is also much worse than simply the idiotic testing of reasonable expectations, because Grattan must discuss such “expectations” in terms of the Australian Curriculum, which is, to use the technical term, fucked. So, once again and more so, the Grattan authors must simply lie, either by omission or blatantly. Here are four examples I stumbled across in the report.
Commenting on Bentleigh West Primary, one of the exemplar schools, the report notes (p 48),
Bentleigh West has found that students make quick progress thanks to its high expectations that students will master these learning intentions. Students now cover the Foundation and Year 1 curriculum in the first year of school.
All credit to BW, but what does their example suggest are the reasonable expectations for other schools’ Foundation year? Reasonably, it suggests that other schools could do the same. But, exemplar school notwithstanding, in effect Grattan argues that a school’s students should simply be “proficient” in ACARA’s Foundation twaddle.5
In a section of the report hammering the necessity of “fluency”, Grattan notes the importance of automatic recall (p 24):
Students should have automaticity with addition and related subtraction facts up to 10 + 10 by the end of Year 2 (at the latest) [a comma would be nice] and with multiplication and division facts up to 12 × 12 by the end of Year 4 (at the latest).
Excellent. Except, as support for this important and no-brainer directive (better worded in terms of “tables”), Grattan references the Australian Curriculum. Well, let’s see. The addition-subtraction stuff is there, badly, but the multiplication-division stuff simply is not. The relevant Year 4 “algebra” content descriptor is (AC9M4A02),
recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
The wording is terrible, made worse by the elaborations, but also, critically, the AC only goes up to 10 x 10 rather than 12 x 12. This matters, and Grattan simply lied here. Either that, or Grattan is simply unaware of the true awfulness of the AC. I like the Grattan guys, so I will choose to believe that they lied.
For example, imagine a Year 5 lesson in which students are learning the standard method for adding fractions. This is a three-step process that involves finding the lowest common denominators, adding the numerators, and simplifying (where possible). It would be unwise to set, as the first practice question, 7/13 + 8/9 because the lowest common denominator of these fractions is 117 and the answer involves improper fractions. Such questions are best reserved for when students are fluent with the procedure of adding fractions.
This is hilarious. The reality is that the majority of Australian school students will never see a sum such as 7/13 + 8/9, in any year. Many current Year 12 students would piss themselves if they were required to evaluate such a sum without their idiot box at hand. The sum is certainly not going to appear in Year 5 unless the school has declared, “Bugger the AC. You will learn some proper arithmetic”. Which of course the school should do. But for those primary schools gullible or lazy enough to follow the AC, the hardest sums that even their Year 6 students will likely see is of fractions with related denominators: that is, where one denominator is a multiple of the other (Year 6 Achievement Standard).
The final example is a non-example: algorithms. Grattan does not once use the term, which at least means we’ve been spared the nauseating and meaningless phrase “algorithmic thinking”. But it also means that Grattan never makes proper reference to the algorithms for arithmetic and, in particular, the traditional algorithms. Sure, in a sense it is just a word, and Grattan does consider and refer to algorithms in some reasonable if unsystematic and disorganised manner. Still, messages are important, and at least in part Grattan seems to be following ACARA’s anti-algorithmic lead. It also feels as if Grattan may be too open to modern alternatives, those ridiculous multiplication boxes and their kin.
4) Early on, the Grattan report notes that “numeracy” is not (ugh) “maths”, the former characterised as “the application of [ugh] maths to everyday situations” (p 8). Grattan fails, however, to hammer home the perverting aspect of NAPLAN’s and ACARA’s, and everyone’s, micro-minded focus on “numeracy”, and Grattan themselves seem way too willing to shop the silly utilitarian sales pitch (pp 12-13). Eventually (p 66), Grattan notes that NAPLAN, “while important, is not sufficient”, with a brief outlining of the insufficiency. This is way, way too little, and it is way, way too late.
5) The weakness of the AC also appears to confuse Grattan, and perhaps some of Grattan’s exemplary schools, on the proper role of “extension mathematics”. There is a concerning emphasis in the report on “acceleration”, on going faster rather than going deeper (pp 51-53). Given the snail-pace of the AC, this is perfectly understandable, but it remains true that acceleration tends to be done poorly and without clear purpose, and is either done without proper teacher oversight or is distracting the teacher from the larger class. (“Differentiation” is a cup and balls swindle.) More generally, although there is not much to go one, Grattan’s coverage of extension mathematics is unconvincing; again, Grattan does the “how” better than the “what”.
Guidance
By “guidance”, Grattan means guidance for teachers upon “how to teach [ugh] maths well” (p 3). Of course, Grattan already knows how to teach mathematics well, and their entire report is pushing their angle on this. So, what Grattan is really asking for here is documentation backed by governmental clout, to encourage and/or force schools and teachers to pay attention. Go for it.
Curriculum Materials
This one is trickier. The basic problem is clear, that there are currently few if any “high-quality curriculum materials”. Indeed for primary schools there are very few curriculum materials at all, of any quality. The insanity of thousands of primary teachers scrounging here and there for anything that might vaguely fit the intended lesson and be of some marginal use cannot be overstated. Just a few decent primary textbooks would go a long, long way towards improving primary mathematics teaching. It would also go a long, long way towards maintaining primary teachers’ sanity. But, there are issues.
The obvious issue is that it is impossible to produce high-quality materials for a Mariana Trench-quality curriculum. It is even harder when the curriculum is so absurdly vague that no one can know for certain what it contains. It follows that any high-quality resource must, like Bentleigh West, pay only lip service to the Australian Curriculum.
Grattan is calling for “an independent quality assurer” who can “review the quality of externally-created, comprehensive curriculum materials used by schools” (p 4). Fine, and good. That, currently, any fruitcake can publish a textbook or launch a website, and that schools can then use the fruitcake’s stuff without any quality assurance, let alone any formal approval process, is simply mad. But, by what standard is the quality assurer going to assure quality? It is a critical question, and Grattan does not even suggest an answer.
Curriculum debacle aside, there are issues with what Grattan, and others, mean by “curriculum materials”. Their meaning seemingly extends, at least on occasion, beyond good explanations of concepts and techniques, together with a good selection of exercises and harder problems, to fully packaged lessons. This is a real concern.
There is a whole scientific education movement at the moment, with various factions that I cannot be bothered distinguishing, but all seemingly with the message that delivering a mathematics lesson is like an IKEA assembly. Just follow the slides, with Step 1, then Step 2, and so on, and Voilà: you have a bookcase classroom of kids that can do addition. I do not believe it. I am deeply suspicious of pre-packaged lessons, and I am deeply suspicious of packages that look like pre-packaged lessons even if the packers assure me that they are not. Grattan does not appear to share this suspicion (pp 49, 64 -65).6
Grattan also appears to have at least some time for online “materials” and, again, I am suspicious. I have looked at Maths Pathways, which is apparently used by one of Grattan’s exemplar schools, and Maths Pathways seriously sucks.7 Grattan does not appear to realise that Maths Pathways seriously sucks (p 150).8
6) At one point, while discussing “consistency” across classrooms at one of the exemplar schools. Grattan notes that “Teachers added their unique flair to the participation routines”. Grattan doth defend too much, methinks. And not very well. Without disparaging gimmicks, the alternative to (over)consistency is not gimmickiness.
7) As do Essential Assessment and Mathletics. Do any of these online teaching things not suck? it seems unlikely.
8) One online resource that is being pushed by a lot of people, and about which I know essentially nothing, is Ochre. The Grattan report indicates that Ochre provides “comprehensive curriculum resources” (p 46), but one might be able to avoid using Ochre in an IKEA-ish manner. As for the Ochre resources themselves, the Grattan report includes two examples. One is a bread and butter percentages question, with easy, medium and hard versions, which is straight-forward but nicely presented (p 46). The second is a “rich [ugh] maths application task” on percentage discounts, and it is unimaginative and dull and aimless (p 26). It is an example of the kind of “rich mathematics task” that is created by people with an insufficient understanding of what rich mathematics is. I have no idea how typical such a task is of Ochre, and even if so, it may well be the case that Ochre is fine and good with the bread and butter, while being weaker with “rich” material; most such producers are.
Teaching Quality
In effect, Grattan’s recommendation here seems to overlap significantly with their recommendation on guidance. Grattan wants teachers to learn better teaching through “micro-credentials” and through more successful and nearby schools offering assistance and the like (pp 3-4). Fine. Grattan also calls for an emphasis on employing specialist mathematics teachers in schools, which would of course would be excellent (if the teachers can be found). But, Grattan forgot something.
One of the huge reasons for mathematics teaching being so poor is that too many teachers simply know too little mathematics, too weakly. Education faculties rarely provide any suitable content lessons to to-be teachers, and if other faculties do, it is typically more by random luck than considered design. Yet, Grattan’s recommendations do not even mention this gaping hole. Yes, Grattan later considers the issue in decent depth (pp 30-38), including a pleasing note of contempt for LANTITE (p 37). Still, this absolutely critical issue didn’t make Grattan’s headline recommendations.9 Once again, there is too much concern for the “how”, and not nearly enough for the “what”.
9) There is a weird line in the recommendations about updating the “core course content” of ITE programs “as new guidance on effective [ugh] maths is published” (p 4). This is garbled, but in context the “effective maths” would appear to be referring to mathematics teaching.
Monitoring
The main recommendation here is for the introduction of “a national early years screening tool to identify students at risk of falling behind in maths”. That is fine, and good. It is not nearly as important as the teachers’ regular testing, concept by concept, of their student’s understanding, which Grattan also hammers. But, fine.
Overall Assessment
The Grattan report is probably better than I’ve made it out here. More sense is contained in the body than in the summary recommendations. Still, even in the body, there are issues. There are many good notes but, also, some notes are way off-key.
Overall, I’ll give the Grattan report a C+, maybe a B– if they bring me an apple. Yeah, the Grattan report is a hell of a lot better than most. But this blog, like Grattan’s exemplar schools, refuses to grade on a curve.
Thanks, Marty, for you detailed and perceptive comments on the Grattan report. One thing that might be done is to look at school texts from the first half of the twentieth century. Some of them are pretty bad, but the best of them have some fine qualities. (Side comment: the illustrations are made by competent commercial artists and do not use cartoon characters.) The first is that they treat the pupils as people and not some stereotype dreamed up by an educator and the tone is that of a helpful uncle. Sections begin with some everyday situation that the pupils can be related to (albeit, stereotypically, kitchen examples involve girls and workshop examples involve boys). One example that comes to mind is a chapter on decimals that begins with a lad in the front seat of his car and looking at an odometer and asking dad why the last digit is black on white.
There are some worked examples often with an explanation why they work and loads of exercises. My impression of the earlier syllabus that each year of schooling involved sequential mastery of a certain topic — this is the year the kids can multiply multidigit numbers, this is the year they can do arithmetic on fractions; let’s move on to the next stage.
Two things that never seem to be mentioned in teaching the young: they should check their work, preferably by an independent method; they should present their solutions in good order, setting out what is known, the steps and the conclusion. I favour lots of mental arithmetic, because here is where some judgment and strategizing and recall comes in because how it is done often depends on the context and some ways are more efficien than others. At the right level, algebraic manipulation performs the same function.
Thanks, Ed. The suggestion (fact) that old school texts may be much better came up in this post, on which Tony Gardiner commented, wisely as always. But I cannot see old texts as exemplars being of much help. The rot is much deeper than that.
There are also stereotypes in modern texts over here: If Anna says this and Tom says that, and the student is to decide who is right, then the answer is always Anna. Or, in more recent texts, it’s Ayse when her opponent is Dimitry.
We had a couple of very good textbooks up to the 1990s; we’re currently trying to get them scanned and will make them available online. Plus there’s a conference by critics of the current school system coming up; probably we will be completely ignored by the education science people, but we will try hard to make ourselves heard.
Anna and Ayse are very funny. I’m not sure who your “we” is, but keep us informed.
“15 percentage point increase”. In my opinioin, this is where it all started to go wrong: The absolute dogma of the religion that kids are elementary particles whose progress can be measured and weighed exactly. This resulted in a big bang of education science that ripped apart a curriculum that used to work.
Thanks, Franz, although I’m not sure I agree, at least for Australia.
Australian mathematics education began to rot long, long before the measuring fetish came in. I think the measuring was then an attempt to undo the rot. I think it might help to some degree (at least for “proficiency” if not for properly high standards), if the measures were not so appallingly bad.
Claims about the length of the Australian curriculum that differ. IPA versus Akara https://www.theage.com.au/national/counting-controversy-ipa-sticks-to-claim-that-maths-curriculum-is-3500-pages-long-20250422-p5ltgc.html
Thanks, JJ. Post is in progress …