Last year we took a multiwhack at VICmaths, Nelson’s Year 12 Specialist Mathematics textbook, specifically at Nelson‘s chapter on logic and proof: see here, here, here, here, here and here. This post is the beginning of a second multiwhack, this time at Nelson‘s chapter on complex numbers.
Why do this? Do we particularly have it in for Nelson? Not really, although the temptation is there. It is a very bad text, every chapter deserving of a multiwhack. But Nelson is hardly alone in this regard. Cambridge, for example, is also very bad and, being the respected textbook of record, is a much more important target. Indeed, we have already taken a double–whack at the first part of Cambridge‘s complex numbers chapter, and we could have productively extended that whack to the entire chapter. But Nelson‘s complex chapter, while not as fantastically bad as their chapter on proof, is plenty bad, and is bad in specific and seemingly important ways.
Regular readers of this blog know well the back story. In 2021, VCAA stuffed up a complex numbers question on the Specialist Mathematics Exam 2, a stuff up which, still, VCAA refuses to acknowledge or to correct in their exam report. VCAA’s inexcusable failures resulted in their stuff up being repeated verbatim in Nelson (and Jacaranda). Then, in 2022, VCAA stuffed up again, in an almost identical manner, and once again, and still, VCAA refuses to acknowledge the stuff up or to correct their exam report (Word, idiots). VCAA’s subsequent defence of their 2022 question was completely mad.
This post, however, is not about VCAA’s lack of professionalism. Nor is it about VCAA’s incompetence. Nor is it about VCAA’s arrogance. Nor is it about VCAA’s cowardice. Nor is it about VCAA’s dishonesty. Nor is it about VCAA’s disconnect from reality. These are all givens. This post is about Nelson.
The madness of VCAA’s complex question defence, and the madness of the complex exam errors having occurred at all, seems to us very much in synch with the madness of Nelson‘s chapter on complex numbers. We have no idea why the two are in synch but that it is the case seems unquestionable to us. Thus, an understanding of all that is wrong with Nelson‘s complex chapter may provide an understanding of some that is wrong with VCAA. In doing this, we could have focussed more directly on specific wrongnesses in Nelson, and left alone the general wrongness and badness. But to do so would have arguably missed, or at least minimised, a broader point. In any case, these things are work and we get tired; WitCHes are easier.
Here, then and finally, is the first WitCH, on the first section of Nelson‘s chapter on complex numbers. Since Nelson launches the chapter with some presumed understanding, the first two snapshots are from Nelson’s companion Year 11 text, which introduces complex numbers from scratch, and which covers (very badly) the basic algebra and geometry. And just a quick note in self defence: we have tried very hard to be fair and to not cherrypick. Yes, we have selected the worst aspects and we will not reproduced some routine and less flawed material. But we will not intentionally exclude any meaningful explanations that somehow justify or mitigate the selected material. On the flip side, we will also not reproduce any of Nelson‘s nauseating CAS instruction, which is badly perverting and butt-ugly, but which is off the point of the WitCH(es).