Polynomialy Perverse

What, with its stupid curriculastupid texts and really monumentally stupid exams, it’s difficult to imagine a wealthy Western country with worse mathematics education than Australia. Which is why God gave us New Zealand.

Earlier this year we wrote about the first question on New Zealand’s 2016 Level 1 algebra exam:

A rectangle has an area of  \bf x^2+5x-36. What are the lengths of the sides of the rectangle in terms of  \bf x.

Obviously, the expectation was for the students to declare the side lengths to be the linear factors x – 4 and x + 9, and just as obviously this is mathematical crap. (Just to hammer the point, set x = 5, giving an area of 14, and think about what the side lengths “must” be.)

One might hope that, having inflicted this mathematical garbage on a nation of students, the New Zealand Qualifications Authority would have been gently slapped around by a mathematician or two, and that the error would not be repeated. One might hope this, but, in these idiot times, it would be very foolish to expect it.

A few weeks ago, New Zealand maths education was in the news (again). There was lots of whining about “disastrous” exams, with “impossible” questions, culminating in a pompous petition, and ministerial strutting and general hand-wringing. Most of the complaints, however, appear to be pretty trivial; sure, the exams were clunky in certain ways, but nothing that we could find was overly awful, and nothing that warranted the subsequent calls for blood.

What makes this recent whining so funny is the comparison with the deafening silence in September. That’s when the 2017 Level 1 Algebra Exams appeared, containing the exact same rectangle crap as in 2016 (Question 3(a)(i) and Question 2(a)(i)). And, as in 2016, there is no evidence that anyone in New Zealand had the slightest concern.

People like to make fun of all the sheep in New Zealand, but there’s many more sheep there than anyone suspects.

Factoring in the Stupidity

It is very brave to claim that one has found the stupidest maths exam question of all time. And the claim is probably never going to be true: there will always be some poor education system, in rural Peru or wherever, doing something dumber than anything ever done before. For mainstream exams in wealthy Western countries, however, New Zealand has come up with something truly exceptional.

Last year, New Zealand students at Year 11 sat one of two algebra exams administered by the New Zealand Qualifications Authority. The very first question on the second exam reads:

A rectangle has an area of  \bf x^2+5x-36. What are the lengths of the sides of the rectangle in terms of  \bf x.

The real problem here is to choose the best answer, which we can probably all agree is sides of length \pi and (x^2+5x-36)/\pi.

OK, clearly what was intended was for students to factorise the quadratic and to declare the factors as the sidelengths of the rectangle. Which is mathematical lunacy. It is simply wrong.

Indeed, the question would arguably still have been wrong, and would definitely still have been awful, even if it had been declared that x has a unit of length: who wants students to be thinking that the area of a rectangle uniquely determines its sidelengths? But, even that tiny sliver of sense was missing.

So, what did students do with this question? (An equivalent question, 3(a)(i), appeared on the first exam.) We’re guessing that, seeing no alternative, the majority did exactly what was intended and factorised the quadratic. So, no harm done? Hah! It is incredible that such a question could make it onto a national exam, but it gets worse.

The two algebra exams were widely and strongly criticised, by students and teachers and the media. People complained that the exams were too difficult and too different in style from what students and teachers had been led to expect. Both types of criticism may well have been valid. For all of the public criticism of the exams, however, we could find no evidence of the above question or its Exam 1 companion being flagged. Plenty of complaining about hard questions, plenty of complaining about unexpected questions, but not a word about straight out mathematical crap.

So, not only do questions devoid of mathematical sense appear on a nationwide exam. It then appears that the entire nation of students is being left to accept that this is what mathematics is: meaningless autopilot calculation. Well done, New Zealand. You’ve made the education authorities in rural Peru feel very much better about themselves.