We really want to get on to other things, but this needs to be done. Below is pretty much a complete cataloging of Nelson‘s use of the adjective “complex” in the five recent WitCHes (here, here, here, here and here). To be clear, there is tons more wrong, and bad, in the selected excerpts in the WitCHes: the proper WitCH updating, currently scheduled for late 2029, will be long and painful. But the use of “complex” warrants particular attention. It reflects VCAA’s complex madness, and we doubt that it is a coincidence. Continue reading “A Sum of “Complex” Numbers”
Last one. These are excerpts from the final section of Nelson‘s complex numbers chapter. Similar to the previous WitCHes, I’ve tried to not be manipulative material in selecting the material except, of course, in selecting the worst bits: the worked examples not indicated are standard, and in general the working is tedious but ok; a monotonous but essentially correct proof of the conjugate root theorem is included in the text.
I was gonna go with The Sot-Weed Factor, but that was too cute a title, even for me.
We’re now getting to the VCAA-related material, which prompted this whole series. The last two sections of Nelson‘s complex numbers chapter are on factors and roots of polynomials. Below are excerpts on factorisation. (For the sake of interpretation, note that: the factor and remainder theorems are stated reasonably clearly, but of course with no hint of a proof; these two theorems are followed by two standard “worked examples”; the working of all the worked examples is painfully earnest and slow, but is close enough to correct.)
There is still a big issue in the previous WitCH that I believe no one has noted, but let’s continue. Here are excerpts from the next subchapter of Nelson‘s chapter on complex numbers. Continue reading “WitCH 117: The Roots of Disunity”
This is our second WitCH on Nelson‘s chapter on complex numbers. As with our first WitCH, we have not excluded any definitions or arguments or explanations from the text that would fill apparent (and actual) gaps in the selected material; the rest of the subchapter consists of routine examples and less problematic (but far from unproblematic) exposition. Continue reading “WitCH 116: Polar Bare”
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. Continue reading “WitCH 115: Not So Complex”
We’ve been pondering VCAA’s weird defence of their 2022 exam questions, and we decided to investigate a little. We’ll write more on this soon, but for now just a quick post on something very unsurprising that we stumbled upon in the Year 12 Specialist texts. The following is an exercise that appears in both Jacaranda and Nelson (but not in Cambridge): Continue reading “The Stability of Stupidity”
I have a heavy post coming very soon, but it seems worthwhile first getting in this quick, light one.
Once upon a time, before going off the rails, I was a (semi)regular mathematician. I proved theorems and stuff like that. I was a committed lecturer and, with all due humility, a very good lecturer, but I had no specific interest in “mathematics education” and I knew nothing about school mathematics. That began to change around twenty years ago when, back in Melbourne, I somewhat randomly began talking to mathematics teachers. I soon realised that most Victorian mathematics teachers, even very dedicated ones, knew little mathematics and understood less. I began giving talks to teachers and then public talks, and I discovered the obvious about myself: I am significantly better at telling jokes than proving theorems. Burkard then appeared and it all took off, first with the popularisation, which Burkard has continued, and now with my gadflying. Some years earlier, however, before all this began, I bumped into my future occupation, and into a maths ed titan. This is the story of that bump. Continue reading “A Maths Ed Lecture From Long Ago”
As some relief from the heavy lunacy of the AMT debacle, here is a light little story, a lead-in to a second little story to come soon. A couple weeks ago, we were contacted by Simon the Likeable, asking if we had any “old (or new) texts” containing an introduction to matrices suitable for not-so-strong Year 10 students. Simon wanted to avoid using the school’s current Year 11 text, which the students would use next year, but also his inclination was to use an older text. Continue reading “Bernie’s Valiant Effort”
Last one. This is the final in our sequence of WitCHes on the Logic and Proof chapter of VicMaths, Nelson’s Specialist Mathematics Year 12 text; the previous WitCHes are here and here and here and here (and a PoSSW here). This WitCH is on the final section, Proof by mathematical induction. The worked examples are all similar in form to that given below. The exercises seem ok except for one, which is almost almost good, but which definitely isn’t good (and for which no solution is provided).