Dear Primary Schools,
If your students are not learning their multiplication tables, up to 12, by heart, then you are fucking up.
If you think giving your students a grab-bag of tricks replaces multiplication tables, then you are fucking up.
If you think orchestrating play-based, student-centred theatricalities replaces multiplication tables, then you are fucking up.
If you think quoting the Australian Curriculum gives you license to not teach multiplication tables, then you are fucking up.
If you think quoting some education twat gives you license to not teach multiplication tables, then you are fucking up.
Thank you for your attention.
So, multiplication table is a such good idea?
Was I too subtle?
nah, you are good. i see the answer in another comment. thanks.
Something I have always wondered…
Why do multiplication tables stop at 12? Why do they go to 12?
Why not 10? Why not 15?
And yes, Marty, your key point here is as valid as it was in the 1960’s or whenever the “New Math” almost (?) destroyed education.
Well, they do often stop at 10. Because, you know, who ever uses multiples of 12?
As for why one doesn’t go further, in the early 19th century at least some school districts went to 20. Given 13 and 14 are of relatively less use, stopping at 12 is reasonable.
For all its sins, I don’t know that New Math killed multiplication tables.
Yeah, I was using “New Math” as a title for a range of “initiatives” which have, over time, killed many tried and proven ideas.
I just remember Harold Jacobs writing about “New Math” when he said something along the lines of a poor teacher is not at risk of doing harm with Old Math, but anyone other than a skilled teacher in New Math will undoubtedly do damage. My immediate thought was times tables.
I wonder if it is a hang-over to the imperial units, perhaps?
You mean hangover relics like seconds and minutes and hours?
In a way.
At the end of the day, they are all pretty arbitrary choices that make sense in one context or another.
360 degrees in a circle is another one that makes at least some sense, works and so we use it.
It is a pragmatic approach. I’m not saying it is perfect, nor that is the best approach, but it sort of works.
Times tables though, up to 10 I totally get. 11 is pretty easy, so sure. 12 is not too hard either, I guess… I would argue strongly though for learning powers of 2, 3 and 5 as well as square numbers up to 15 squared as well as the regular times tables, but that is also a very arbitrary preference.
Up to 12. It is not negotiable.
I personally hate the idea of rote learning – but do accept the need to have a basis for numeracy and literacy – Primary school kids do have to start with this form of learning…Without knowing your alphabet or your “times tables”, civilised life as we know it, could become very difficult indeed…The downside of rote learning is that some people develop “thinking” habits that stay with them for life…Saw this – here on a local “Ripon Blow your horn” Facebook site – evidently sent out by a Melburnian…
I don’t know who to give credit to, but this is hilarious.
So we Melburnians are now into 2.0 of defeating COVID-19. These words made me laugh 🤣 But there’s a lot of truth mixed in to consider. . .
1. So let me get this straight, there’s no cure for a virus that can be killed by sanitizer and hand soap?
2. Is it too early to put up the Christmas tree yet? I have run out of things to do.
3. When this virus thing is over, I still want some of you to stay away from me.
4. If these last months have taught us anything, it’s that stupidity travels faster than any virus on the planet.
5. Just wait a second – so what you’re telling me is that my chance of surviving all this is directly linked to the common sense of others? You’re kidding, right?
6. If you believe all this will end and we will get back to normal just because we reopen everything, raise your hand. Now slap yourself with it.
7. Another Saturday night in the house and I just realized the trash goes out more than me.
8. Whoever decided a liquor store is more essential than a hair salon is obviously a bald-headed alcoholic.
9. Remember when you were little and all your underwear had the days of the week on them. Those would be helpful right now.
10. The spread of Covid-19 is based on two factors: 1. How dense the population is and 2. How dense the population is.
11. Remember all those times when you wished the weekend would last forever? Well, wish granted. Happy now?
12. It may take a village to raise a child, but I swear it’s going to take a whole vineyard to home school one.
13. Did a big load of pajamas so I would have enough clean work clothes for this week.
It’s a lot funnier than the fact – as reported many moons ago – that our Prime Minister’s “Herd Immunity” strategy – has now “conveniently” been swept under the carpet…
Though Clearly “well educated” – I would contest item 10 in the above list – as IMHO “rote learning” has him believe that his “superior Private and Oxbridge University education” and position – affords him the luxury of making crappy, mindless, thoughtless decisions with impunity…His policy has killed off so many of our aged population that we are the laughing stock of Europe, if not the World – but the good news (for him) is that it has largely gone unnoticed by his very own public – the disadvantaged “Hoi Polloi”…
Thanks, Ewen. In reply,
Don’t use the word “numeracy”. Ever. Except in the form “fucking numeracy”. If you mean “arithmetic”, then say “arithmetic”.
As I replied to Marc, I am open-minded about how the tables are taught/learned, just not whether.
I don’t quite understand what “rote learning” means, but whatever it is, you are wrong to hate it. There is nothing wrong with chanting, and much right with it.
If hating rote learning also means hating speed testing and rapid, thoughtless recall and the like, then you are very, very wrong.
No one is suggesting, or has ever suggested, that rote learning, whatever it means, is all there is to learning mathematics. No one’s thinking is harmed by the inclusion of automatic facts and automated techniques.
Couldn’t agree more! I’ve seen kids in Year 11 (well, adults too 🙁 ) who still can’t do their multiplication tables, and resort to using (and not understanding!) a calculator for basic products and arithmetic.
Aside from the ‘IRL’ benefits of memorising one’s tables, as one progresses in maths, one doesn’t want to have to spare cognitive effort in trying to calculate (by hand or calculator) simple arithmetic – you want to be focusing on the real learning at hand.
Thanks, Tau. It is indeed a no-brainer. Unfortunately, the majority of maths ed creatures have fewer than no brains.
I believe that times 12 was taught because some things (used to) come in dozens.
I think I have already told Marty of when I realised we are in trouble. It was a bar/restaurant and I had ordered 2 meals. They were about $18 each ( it was in the days before GST). When I went to pay the waitress pressed a few buttons on a calculator and asked for sixty something dollars. After I asked her to check again, she pressed some more buttons and then asked for twenty something dollars. When I again challenged she was rather peeved and said “well how much would you like to pay?”.
We keep hearing that governments and employers want all students to learn some “numeracy” and we get worried that they will replace algebra with trivia. But employers do have a genuine problem with employees lacking an elementary feeling for numbers. “Times tables” are just one aspect of this.
Before the lockdown I was volunteering at a homework club. It seemed the only students who knew their tables were those drilled by their parents, I found it difficult to teach algebra to Year 9 students lacking such knowledge. I pushed them to learn tables, even made some interactive computer games, but they thought tables were for babies. So secondary school is probably too late. And I suspect that primary teachers are too embarrassed to chant tables with their charges?
Tom, it is much, much worse than you think.
The majority of primary teachers would regard the real, by heart, teaching of multiplication tables as not only unnecessary, but useless or worse. Such an emphasis on automaticity is considered an anathema to the “higher order thinking” that pretty much every professorial demon-priest won’t shut up about.
As for learning tables by chanting, that would typically be regarded as straight out child abuse. It’s not a question of those few uninfected teachers being embarrassed to do it: I doubt there’s more than a handful of schools in the country in which they would be permitted to do it.
Recently I saw a Japanese language teacher describe having students write Hiragana characters 15 times each as a mindfulness activity. Perhaps they are onto something? Could teachers spin this around and promote chanting times tables as a well-being activity?
I think when Jo Boaler claims that memorizing times tables is stressful, she’s conflating the memorizing with being tested. The chanting itself is not stressful, is it?
Appeal to authority is not always the logical fallacy that people claim, but in this case it is, and it is addressed in my post. Why the fuck should I, or you, or anyone, give a flying fuck what Jo Fucking Boaler claims?
In this case, it is just because other people do – I thought she is a major proponent of anti-times-tables sentiment?
I wasn’t appealing to her authority but rather trying to say how I disagree with her. In her book Mathematical Mindsets (one of about three books on the shelf at my local library about maths) she seems to make a leap from “testing times tables makes people cry” to “no one should teach times tables”. I think we can teach people to memorize times tables and not make them cry.
And actually chanting times tables can be fun, so her reason (concern for students’ well-being) can be flipped around. I’ve heard some people even make up dance actions to go with them. I can’t imagine what they are though.
s-t, I know you weren’t supporting what ever idiot claim Boaler was making. My point is, I don’t care what idiot claim she was making, and neither should anyone. I don’t give a fuck what she thinks about tables, and I don’t give a fuck what sense one might try to make of her bullshit.
As for teaching tables without tears, yes of course it is possible. It is trivial.
“As for teaching tables without tears, yes of course it is possible. It is trivial.”
On the other hand, a lot of people have cried. I burst into tears during a times tables activity in primary school, in front of the whole class. It was a memorable experience. I think that sort of thing is perhaps worth avoiding because some people say it puts them off maths.
Yes, s-t. It clearly had a huge effect on you, creating a lifelong hatred of mathematics. Who knows? Without that you might have gone on to do a PhD in mathematics or something. Oh, wait …
In case you’re interested – I’ve helped develop an online times tables teaching tool that works for all kids. We designed it originally for children with dyscalculia, so it teaches with fun animations and stories. More suitable for 6 years +. We also teach division at the same time as multiplication, number bonds and how to tell the time. Anyone who would like to sign up can use code ‘marni’ to receive £20 (or their currencies equivalent) on a 6/12 month subscription. We have tried to give our tool to schools for free, but because we don’t teach in a mathematical way and they don’t have time in their curriculum to teach tables, they are for the most part, not interested. Website is http://www.tablefables.net
I had no trouble learning the times tables up to 10 when I was 8 years old. But, as a teacher, I did have trouble distinguishing between two identical twins who were colleagues at a school faculty that I had joined. When I passed one of them in the hallway, I couldn’t tell if I was passing Rick or Bob. I didn’t learn how to tell them apart until I had lunch with them and could focus on subtle differences. I thought that something similar might help students who have trouble learning their times tables. For example, if you multiply two consecutive numbers like 7 and 8, the answer will be 2 larger than multiplying 6 and 9, where the smaller number 7 is diminished by 1 and the larger number 8 is increased by 1. In both cases, you are multiplying an even and an odd, and the answer will be even. One could then use Cuisenaire Rods to investigate why that pattern occurs.
Hi Marc. I though the punchline to your twins anecdote was going to be that one of them knew their times tables and the other didn’t, so you began greeting them with “7 9’s are …?” and waited for the response.
I never understood why these muppet educators say that rote learning is bad but button pressing is good. A rote learnt knowledge base is essential for competency in any discipline but these muppets want students to exclusively be explorers using discovery- and problem-based learning. It’s a very simple equation – good teachers understand and use many different teaching techniques (rote learning, problem-based learning, didactic learning etc.) Just like a good carpenter, a good teacher picks the right tool for the job. Sometimes you need the screw driver, sometimes you need the saw. But you need to be willing and able to use both as required.
The problem is that these educators often lack any real understanding of what they’re training others to teach.
I agree with you, John.
Marc, I am open-minded as to how multiplication tables are taught, just not whether. As you note, there are all manner of patterns within the patterns. These are interesting, fun to spot and can be helpful in learning the tables by heart. A corollary of your point is that every primary classroom, at every level, should have a BIG multiplication tables poster prominently displayed.
Marc Roth
I also recommend learning the first 40 or so perfect squares by heart. This is useful for working with quadratics. Marty, please be civil with Jo Boaler. She is a nice, sensitive person who is sincere and means well. However, I had my best success as a teacher in a Juvenile Justice Center using a lot of individualized drill and practice. It was not empty drill but used visualization and historical topics such as quadratic functions, Pythagorean triples, the harmonic mean, hand calculating square roots, and some number theory to teach pre-algebra and algebra simultaneously. We did some collaborative problem solving as well. I agree that some followers of Jo Boaler would dismiss my approach out of hand and dismiss my claims as anecdotal.
Anonymous, I would be delighted to leave Boaler out of this discussion. Not because she may be nice and sensitive, neither of which I believe, and not because she may be sincere and mean well, both of which are irrelevant, but because what Boaler thinks about the multiplication tables has no bearing on the fact. The fact is that multiplication tables by heart are necessary.
I agree with you on the squares. They are underrated.
There’s a whole bunch of facts and formulas (as opposed to techniques) I expect students to have memorised in Methods and Specialist Units 3&4. A sample:
Times tables up to 12×12. Perfect squares to 15^2 (and then simple higher squares such as 20^2, 25^2 etc.)
Pi to 2 decimal places, e to 1 decimal place, sqrt[2] and sqrt[3] to 3 decimal places.
Exact values of sine and cosine of special angles in the first quadrant.
Quadratic formula, Pythaogras’ theorem, sine and cosine rules, sum (Specialist) and difference of two squares, sum and difference of two cubes.
(I’ll hold off mentioning more in case anyone else wants to contribute)
Then there’s memorisation of techniques which is a whole new ball-game.
I’ve never understood where anti-rote learning proponents draw the line or why, surely there are some things they agree should be rote learnt …? I know they all agree that students should rote learn how to press buttons. Where is their line in the sand and why?
JF: I’m curious about root(2) and root(3) – why to 3 decimal places? The trick I tell my students is that root(2) is approximately equal to root(49/25) = 1.4, and root(3) is approximately equal to root(49/16) = 1.75. (Cue comment about how students need to know their perfect squares – yes). Why would you like more accuracy than that?
To your list, I would add:
All of the standard symmetries and complementary angle identities for sine and cosine.
Basic geometrical facts about special quadrilaterals, angles formed by transversals & parallel lines, angles in circles and tangents to circles.
Formulas for the areas, surface areas, and volumes of common shapes and solids.
The location of key features of conic sections (parabolas, circles, ellipses, hyperbolae) given an equation in a standard form.
Domain and range of a collection of standard functions.
Index & logarithm laws.
Aside from polemics about the value of rote-learning these things, I think it’s helpful to have such a list to give to students coming into Specialist 3&4, to say: this is what you need to be able to recall automatically, so if you can’t, work on it over the summer.
Also, I’m unsure if I should add to the list, or at least these are things that I’m not sure should be expected to be automatically recalled at the beginning of Year 12 Specialist:
Table of standard derivatives and anti-derivatives
Chain, product, quotient rules.
Velocity is time-derivative of position, acceleration is time-derivative of velocity.
Hi SRK.
Re: Sqrt[2] and Sqrt[3].
No particular reason except that it helps with decimal approximations of values of sine and cosine for special angles.
The other stuff you mention is interesting.
Re: Formulas for the areas, surface areas, and volumes of common shapes and solids.
For area I only insist on circle, triangle and rectangle. For volume I only insist on sphere and objects with constant cross-sectional area. The rest I’m happy for them to know that such formulae exist and to look them up as required on the Formula Sheet.
Re: All of the standard symmetries and complementary angle identities for sine and cosine.
This falls under techniques that I insist be memorised. Using the symmetry of the unit circle (and yes I insist they have memorised sin is the y-coord and cos is the x-coord).
Re: The location of key features of conic sections (parabolas, circles, ellipses, hyperbolae) given an equation in a standard form.
I only insist on the memorising the standard form of a circle and how to get centre and radius.
Re: Index & logarithm laws. I totally agree.
Re: Domain and range of a collection of standard functions.
Again, this falls under techniques that I insist be memorised.
And Re: Specialist. Yes, a = dv/dt and v = dx/dt must be memorised (and then techniques to be memorised).
Marti,
I recall a math class detention in year 6 to list the first 100 squares. It didn’t take long to find the inductive formula for the sum of the first n odd numbers
Visual proofs using dots are also useful IMO
eg https://qph.fs.quoracdn.net/main-qimg-4258e49c1688f01fea6009c5d87d512b
Steve R
Hi Anonymous. All educational research is essentially anecdotal evidence. The difference between your anecdotal evidence and that of these so-called educational experts is that you’re not trying to justify your existence or trying to publish in order not to perish.
I would trust your anecdotal evidence any day of the week, not so the anecdotal evidence (aka ‘research’) of these these so-called educational experts.
‘Educational experts’ are constantly trying to either re-brand ‘old fashioned’ approaches or discredit an ‘old-fashioned’ approach in favour of some new-age bullshit. Either way it is to fulfil a self-serving agenda. Rote learning currently lies in the latter category. But it’s only a matter of time before it comes back in favour under some new buzz-worded name. Neuro-plasticity imprinting (NPI), anyone?
Hi Marty. Bloody love your site! Cuttin through the BS. Not many people do that anymore! I added a little post above – not sure it will get shown – check out http://www.tablefables.net when you get a chance. My mate and I created it and it teaches all kids their times tables and more. Thank you for your time – if you bother to read this!
Thanks, Marni. Both of your comments appeared, and i’ll leave them up. I don’t have the energy to try out your site, with free trial or discounts or otherwise, but perhaps others will take a look.
To paraphrase Monty Python in Life of Brian, methinks that the sun shines out o’ your arses. Over here in Germany I start teaching how to work with numbers up to 10 when I get 8-graders. And don’t bother asking me how they can work with fractions when the can’t do 6:3 in less than 10 seconds.
I can’t even begin to say how much I hate the educationists who came up with the idea that factoring numbers larger than 15 is best left to computers. Tars and feathers, if I had my way . . . .
Thanks, Franz. Yes, I know this disease is worldwide, except, perhaps, for some “backward” Asian countries.
If you can’t teach, teach teachers.
If you can’t teach teachers, do “educational research”
If you can’t do educational research, become the minister for education.
It seems irrefutable that “mathematics education” as a whole is doing way, way more harm than good.
Our young kids are spoiled by too many idealist educators in the field.
They need more basics training, yes, them (both students and many teachers).
Instead of teaching them too many fancy or glamorous activities,
I would rather teach them the chalky-talky way, with authoritative spirits and assertiveness.
I recall that 20+ years ago, my father forced me to practice hundreds of multiplication and division questions, as well as memorising multiplication tables up to 20. Today, I am deeply appreciative of that.
There is only one attitude I can not appreciate.
The attitude of a teacher who believes that even if a student can (happily, even) learn their tables and provide results from them ‘automatically’, that they are better off not doing it.
Storyteller, is there a person on the planet who believes that a person is better off not doing the tables? I’m not sure even Boaler is that clueless.
Let’s commission a survey to find out. 🙂
Given that is unlikely and that maybe semantics are coming into play here (or my lack of ability to write what I am thinking) I will re-phrase a little.
There is only one aspect of this I can not appreciate.
The actions of a teacher who believes a student/group of students could (happily, even) learn their tables, and provide results from them ‘automatically’, but don’t do what is required to make that possible.
In such a case, why does the teacher take such a course?
Do they believe:
• the student will be fine without that skill? (Just as fine? Or, less well off, but fine?)
• the other students (who the teacher does not believe can … ) will be better off, because ….
• the time spent doing this is better spent doing …
• there is a better way to go about this stuff than just memorising …
I am sure there are more.
Re the last dot point.
A relatively prominent advocate for change made the following series of tweets, taken from a thread which he started with the first tweet quoted below. The tweets are in order, but the in-between tweets of other folks are not shown.
“I see that back-to-basics movement still relishes in disparaging math educators like Jo Boaler to prop up their sterile, factory-produced, Dickensian model of math ed. I am beginning to wonder if these people even like math, because they certainly don’t want kids to like it.”
“I explore primes and composites with my kids. Times tables is low-hanging fruit. The whole back-to-basics could make enough pies to feed a small country…”
“My kids didn’t learn times tables, but they know how to multiply, and more importantly, like to multiply. They played games like
@AlbertsInsomnia, Prime Climb, Yahtzee, etc.
Times Tables is not a gateway to anything but more tedium.”
“My kids learned how to multiply. Do they know the answers on the cliched 12 x 12 times tables? Yes. But, that was NEVER their reference/motivation. My goal was to want them to multiply, not just merely remember facts.”
Following the tweet immediately above, someone asked:
“Multiplication has to be thought about. Would they have to think about what 4 × 8 was, or would they know?
He replied:
“Sometimes they think about them and sometimes they know them. I don’t sweat it. They love math. Don’t sweat the small stuff.”
What does it mean to think about 4 x 8?
I am sure that anyone close to primary schools right now will be able to answer that.
Most often, in my experience, teachers are given information by experts in short bursts. (Never has there been some many experts.)
Whether it is via eduTwitter, at conferences within a 1 hour workshop, in staff meetings (at the end of a long day), … – the expert comes, reads the gospel (so many gospels) and it is then left to the teacher to interpret what they have heard. Often what they hear is from a 2nd, 3rd, 4th or maybe 10th-hand expert – Chinese whispers …
Rarely do they have the time to properly take in what was said, read about it from the actual source, evaluate it given their own situation, …
Seems we might even be now tuned to taking on new ideas from this sort of input. A quick Twitter read for a new idea, give it a go, if it fails, not to worry, plenty of more things to try. New is always better.
Perhaps even more difficult for teachers (possibly damaging in general?) is when, even if the teacher has evaluated and decided that something is not for them, a Principal or leader at their school makes the decision about what is going to happen. Ye all shall …
I love the emotional language used by the “relatively prominent advocate for change”. S/he should be in advertising because s/he clearly knows some of the simple parlour tricks.
It sounds to me that s/he has taught his/her kids the timetables anyway, perhaps without even intending to …
Re: “even if the teacher has evaluated and decided that something is not for them, a Principal or leader at their school makes the decision about what is going to happen. Ye all shall …”
In my experience this often happens because some young idiot bucking for a Leading Teacher position gets into the Principal’s ear (the young idiot needs to have led a ‘school-wide initiative‘ to meet one of the criteria for being appointed a Leading Teacher). I’ve seen absolute shit rolled out because of some young idiot that a Principal has decided to groom into leadership (so that the Principal can tick his/her box of ‘building capacity‘ in the education system).
Let’s see how much that child likes maths when they start to do more complicated problems which – in order to complete in any reasonably efficient way – require automatic recall of basic multiplication facts….
Yep, that works a treat.
Thank, storyteller. I think this correctly puts the burden of proof and responsibility on the teachers, and the maths ed creatures. The students either have their tables memorised or they don’t, and the teachers either regard this as critically important or they don’t.
Anyone who blithely writes “Sometimes they think about [4 x 8] and sometimes they know [it]” is fucking up. And, any maths ed demon-priest who cannot come out and say explicitly that the tables must be memorised can go fuck themselves. That is, unless they are nice and sensitive and sincere and well-meaning and anointed by multiple gods, in which case they can still go fuck themselves.
Hi,
For those who have not read Feynman’s lucky number story it provides another example why one shouldn’t rely on an abacus for understanding but better to “know numbers” ,cubes and linear approximations instead
https://www.ee.ryerson.ca/~elf/abacus/feynman.html
Steve R
More homework here
Click to access linear-approx.pdf
Thanks, Steve. I’d forgotten that story. Very apt.
After grade 2, I was to move and go to a Christian Brothers school in Sydney. There was a preliminary interview. For the final interview, I was expected to know my multiplication tables up to 13. That was my task for Summer. Fortunately I got in, and had a wonderful education for the rest of my schooling.
Often I have asked people “What is
?” I don’t know why this particular question stumps so many people.
I once asked an expert in mathematics education, “Should students know
by the time they finish primary school?” He told me that they should be able to work it out. He said “It’s pretty easy. You just work out 
and double the answer.”
On the other hand, people in ancient Egypt knew that for any multiplication of integers, all you need to know is how to multiply by 2 and add. C’est tout. How they knew this, I have no idea.
Terry, look up Russian peasant multiplication to see how to multiply and divide by 2 and addition to multiply positive integers.
Thanks; I see the connection; however, I do not understand how they knew this 3500 years ago in Egypt.
Maybe ancient Egypt had some Russian Jews who had fled pogroms.
Of course you’re too polite to name the “expert” you questioned. He gave the standard idiot answer, he is a twat, and he should not be permitted near teachers.
Hi Marty. I’ve just discovered your website and really enjoy the no b.s. approach. Times tables are the mathematical equivalent of inhaling air to survive: you won’t last long without it. Agree with learning up to 12 x tables. Not hard, only have to memorise 48 combinations since 1 x anything is trivial, 10 x anything is also trivial, m x n = n x m so that wipes-out half of the 144 possibilities and 11 x anything is trivial from 1 through to 10. In primary school, our teacher had us do times table ‘races’ on the blackboard until we all could recall instantly but I suppose that, these days, that would be considered as some bizarre infringement of the children’s human rights and an affront to their positive well-being. Personally, I think that children arriving into high school without such a fundamental grasp is essentially an affront to their human rights and well-being, let alone to their prospects of a decent education. As a general thought: I’m always amazed about the number of people who try to make themselves look impressive, or seek differentiation (pun very much intended) in a crowded marketplace, by intentionally over-complicating things and presenting themselves as the saviour. And don’t get me started on high school text books… I’m mean, why on earth present something in 12 pages when you could do it in 700..?
Hi, Rixter, and welcome to the Dark Side.
I agree totally with your point about the perversion of over-complication. That was a main theme of my recent talk.
Well when you go to a shop and ask for a Dozen?
Are you getting 10 or 15?
If it’s a NAPLAN question, they’ll ask for the closest.