The following question appeared on Australia’s Year 9 NAPLAN Numeracy Test in 2009:

*y* = 2*x* – 1

*y* = 3*x* + 2

*Which value of *x* satisfies both of these equations?*

It is a multiple choice question, but unfortunately “The question is completely stuffed” is not one of the available answers.

Of course the fundamental issue with simultaneous equations is the simultaneity. Both equations and both variables must be considered as a whole, and it simply making no sense to talk about solutions for *x* without reference to *y*. Unless *y* = -7 in the above equations, and there is no reason to assume that, then *no* value of *x* satisfies both equations. The NAPLAN question is way beyond bad.

It is always worthwhile pointing out NAPLAN nonsense, as we’ve done before and will continue to do in the future. But what does this have to do with rural Peru?

In a recent post we pointed out an appalling question from a nationwide mathematics exam in New Zealand. We flippantly remarked that one might expect such nonsense in rural Peru but not in a wealthy Western country such as New Zealand. We were then gently slapped in the comments for the Peruvian references: Josh queried whether we knew anything of Peru’s educational system; and, Dennis questioned the purpose of bringing up Peru, since Australia’s NAPLAN demonstrates a “level of stupidity” for all the World to see. These are valid points.

It would have been prudent to have found out a little about Peru before posting, but we seem to be safe. Peru’s economy has been growing rapidly but is not nearly as strong as New Zealand’s or Australia’s. Peruvian school education is weak, and Peru seems to have no universities comparable to the very good universities in New Zealand and Australia. Life and learning in rural Peru appears to be pretty tough.

None of this is surprising, and none of it particularly matters. Our blog post referred to “rural Peru or wherever”. The point was that we can expect poorer education systems to throw up nonsense now and then, or even typically; in particular, lacking ready access to good and unharried mathematicians, it is unsurprising if exams and such are mathematically poor and error-prone.

But what could possibly be New Zealand’s excuse for that idiotic question? Even if the maths ed crowd didn’t know what they were doing, there is simply no way that a competent mathematician would have permitted that question to remain as is, and there are *plenty* of excellent mathematicians in New Zealand. How did a national exam in New Zealand fail to be properly vetted? Where were the mathematicians?

Which brings us to Australia and to NAPLAN. How could the ridiculous problem at the top of this post, or the question discussed here, make it into a nationwide test? Once again: where were the mathematicians?

One more point. When giving NAPLAN a thoroughly deserved whack, Dennis was not referring to blatantly ill-formed problems of the type above, but rather to a systemic and much more worrying issue. Dennis noted that NAPLAN doesn’t offer a mathematics test or an arithmetic test, but rather a *numeracy *test. Numeracy is pedagogical garbage and in the true spirit of numeracy, NAPLAN’s tests include no meaningful evaluation of arithmetic or algebraic skills. And, since we’re doing the Peru thing, it seems worth noting that numeracy is undoubtedly a first world disease. It is difficult to imagine a poorer country, one which must weigh every educational dollar and every educational hour, spending much time on numeracy bullshit.

Finally, a general note about this blog. It would be simple to write amusing little posts about this or that bit of nonsense in, um, rural Peru or wherever. That, however, is not the purpose of this blog. We have no intention of making easy fun of people or institutions honestly struggling in difficult circumstances; that includes the vast majority of Australian teachers, who have to tolerate and attempt to make sense of all manner of nonsense flung at them from on high. Our purpose is to point out the specific idiocies of arrogant, well-funded educational authorities that have no excuse for screwing up in the manner in which they so often do.

Well said Marty.

I suppose the irony of the situation – that a professional body who claims to test literacy has failed at proof-reading on multiple occasions (the internet, and your articles from The Age provide more than enough examples of such) – is not lost on everyone…?

I’ve been a Mathematics teacher for longer than I care to admit and will admit under the condition of anonymity that the concept of numeracy still puzzles me as much as the word “pedagogy” did when I first began teacher-training. Much like the motivation behind the content of certain NAPLAN questions. Maybe it is time to contemplate retirement. Me, not you.

Reply to Number 8:

I have found that replacing the word “pedagogy” with the word “bulldust” makes any relevant article much more understandable. For those of little experience of country roads, bulldust is a fine dust which penetrates even the smallest gaps, and camouflages potholes so they are not seen till too late.

I think you’re being strange here. There is a specific x,y pair for which the two equalities hold. Yes, that means y has a specific value here, also. So what. They could have asked for the pair or just the x or just the y.

I don’t need to ASSUME y has a certain value. That’s already constrained by the two equations themselves! I just need to assume the two equations (which are, are GIVEN).

For that matter, if I solve by subtraction, the y is eliminated. So why do I need an assumption about it? Heck, you liked pushing the .999… proof, which involved a subtraction of two equalities. I don’t see why I get to do that and don’t also get to subtract these two equations.

No, I’m not being strange. The question is plain nuts.

“Hacker is wrong.” 😉

Think about this…

See example 1 in the attached: https://www.chemteam.info/Stoichiometry/Stoichiometry-AP-Examples1-10.html

I don’t need more special assumptions. Just the two functional relationships and solving for the intersection (the one point where both are true). This is a real world example that is analogous. I want to know how much y (Zn) there is. I DON’T need a new piece of information on how much Mg there was.

The two functional relationships are an adequate constraint. There are no degrees of freedom for x (Mg) to run off and be something else, with the two equations (chemical relations) both given.

And this proves Hacker is right?

I was making a funny about the style of flat assertions. Not linking the two topics themselves.

Christ. I wrote a whole goddam article.

Great.

Now howzabout those simultaneous equations? Do I need to tell the kids how much Mg there is? Or is it constrained by the two linear equations. And I can ask for Zn alone? Or Mg alone or both. And I don’t need to give them more information because the problem is adequately constrained? There is a physical reality of a certain amount of Zn and Mg in the sample. The information given constrains the answer.

A, if you can’t see why that question is nuts, I can’t help you. I’m too tired to argue it.