Last week, the New South Wales government came out with the next great plan to Save Mathematics Education: make mathematics compulsory up until the end of high school. Why? According to Premier Gladys Berejiklian, this will “ensure students have the numeracy skills required to succeed in today’s society”.

Yes, of course. In exactly the same way, for example, that compulsory instruction in ethics ensures that lawyers and cops act ethically.

What’s the source for this latest nonsense? Well, it’s kind of, sort of from the Interim Report of the NSW Curriculum Review, which was released a few days earlier, and which is prominent in the Government’s media release. Like all such reports, the NSW Report is barely readable, the predictable mishmosh of pseudoscience, unweighted survey, statistics of undeterminable worth and contradictory motherhoodisms. Thankfully, there’s no reason to read the Report, since the NSW Government hasn’t bothered to read it either; nothing in the Report points to making mathematics compulsory throughout high school.

Still, it was easy enough to find “maths experts” who “applauded the move”. Jordan Baker, the *Sydney Morning Herald*‘s education reporter, quoted four such “experts”, although the only expert appearing to say much of substance was doing anything but applauding. Greg Ashman, who is always worth reading (especially when he is needling nitwits), pointed to the need for specialist teachers in lower years. He is then quoted:

*“You need to move away from the fashion for inquiry learning and problem-based learning and instead focus on high quality, interactive, explicit teaching of mathematics. Do that, and I believe numbers in year 12 would organically grow.”*

In other words, if you stop having shit teachers teaching shit maths in a shit manner in lower years then maybe more kids will choose to stick around a little longer. (Ashman is more collegial than this writer.)

The NSW government’s compulsion will undoubtedly push mathematics in the exact opposite direction, into ever more directionless playing and mathematical trivia dressed up as real world saviour. You know the stuff: figuring out credit cards and, God help us, “how to choose cancer treatment“.

To illustrate the point perfectly, Melbourne’s* Age *has just published one of its fun exam-time pieces. Titled “Are you smarter than a 12th grader?“, the reader was challenged to solve the following problem from yesterday’s Further Mathematics exam:

*A shop sells two types of discs: CDs and DVDs. CDs are sold for $7.00 each and DVDs are sold for $13.00 each. Bonnie bought a total of 16 discs for $178.00. How many DVDS did Bonnie buy?*

The question this problem raises isn’t are you smarter than a 12th grader. The real question is, are you smart enough to realise that making mathematics compulsory to 12th grade will doom way too many students to doing 7th grade mathematics for six years in a row? For the NSW government and their cheer squad of “maths experts”, the answer appears to be “No”.

Why does anyone other than Bonnie need to work this out? In which case, she can just look in her 100% recycled paper bag and see for herself.

Thanks, RF. Yeah, it’s typical of the pseudo-real nonsense you get in Further, which is supposed to be above (below?) such things. It’s also trivial.

We just need to look at English to see the truth of the claim: “If X is made compulsory, then X will end up better taught because more teachers that are good at teaching X will be employed”. Of course, in order to begin addressing the atrocious level of instruction in mathematics on average the department would need to confront too many inconvenient truths, and so I’m not holding my breath.

The whole “basic skills for life” thing is nonsense.

Simultaneous equations are a decent topic and students do seem to remember these in first year — it’s a nice bridge to matrix methods. Of course, it would be nice if they were given the geometric viewpoint and a deeper understanding earlier on, but a lot of things “would be nice”.

Thanks, Glen. Yes, of course simultaneous equations is a good topic, both for what it is and where it leads. These things

aretaught geometrically, at least for two equations and two unknowns, in around Year 9. Notice also the extra triviality of the exam problem. It can be solved more easily with a little rhetorical algebra.The biggest problem is that we now have a generation of primary teachers who don’t know how to calculate anything by hand or – God Forbid, do this in their heads – and therefore don’t know how to teach the basics in a way that solidifies place value and its place in the base ten system. Furthermore, most of them haven’t read a book in years! – Just had to throw that one in!

Hi Valerie. Your comment kind slightly (but only slightly) off-topic, but it’s hard to disagree. But it is worse than many primary teachers not knowing the basics sufficiently to teach them. The teachers are being actively encouraged to

notteach the basics.I think you are right on the money here.

Well, I’m favourably quoting you, so of course you’d say that!

Long long ago, I taught at a university in the US where mathematics was compulsory for all students; this was good for the mathematics department which was paid according to the number of students taking mathematics subjects; however, since mathematics was compulsory, and one would expect that most students would pass it, it was up to the department to design a course that most students could pass.

Thanks, Terry. Yes, I also lectured and tutored such compulsory subjects in the US, though I think my universities were a little less lenient. In fact, I was hugely impressed by many of the (mostly) guys on sports scholarships, gamely fighting through these subjects. It’s a clunky part of the American liberal arts tradition, which got a lot less clunky with the introduction of “Maths for Poets” subjects.

A shop sells two types of discs: CDs and DVDs. CDs are sold for 13.00 each. Bonnie bought a total of 16 discs for $178.00. How many DVDS did Bonnie buy?

x is the number of DVDs.

16-x is the numer of CDs

7(16-x) + 13x = 178

112 -7x +13x =178

6x =178-112 =66

x = 66/6 = 11

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Yes, it’s a pretty basic algebra problem (maybe a year or two later in the States than seventh). The funny thing is I occasionally have some little bit of algebra like this that I need to code into a spreadsheet financial model. And I always need to write it down separately to make sure I get the basic algebra right. Can’t just code it directly. And I worry about screwing it up.

I also find that there’s a cognitive load and that even pretty decent MBAs will freeze up at a McKinsey case interview if at the end, you make them do some little bit of algebra. Or even just multiplying a bunch of ratios for unit conversions….easy to mess up and get one wrong side down.

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I think the average person doesn’t need to do this a lot in daily life. The real benefit is the tools, which need to become a foundation for later problems in higher parts of math or in basic physics and chemistry. Chemistry in particular is like “algebra word problem on steroids”.