Yes, we have tons of overdue homework for this blog, and we will start hacking into it. Really. But we’ll also try to keep the new posts ticking along.
The following, long WitCH comes from the Cambridge text Mathematical Methods 3 & 4 (including an exercise solution from the online version of the text).
UPDATE (07/02/21)
Commenter John Friend has noted a related question from the 2011 Methods Exam 1. We’ve added that question below, along with the discussion from the assessment report.
The following question appeared on Australia’s Year 9 NAPLAN Numeracy Test in 2009:
y = 2x – 1
y = 3x + 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.