WitCH 138: Second Rate

Not counting the Witchfests on Nelson‘s Proof and Complex chapters, I don’t think we’ve had a textbook WitCH for quite a while. This one is hardly in the same league but it’s been on my to do list for a long time and it’s definitely a source of irritation. The topic came up in discussions with a colleague today, and I’m too busy and too tired to do the posts I should be doing, so this’ll do for now. It is an example from the differential equations chapter of Cambridge’s Specialist Mathematics 3 & 4, and it is related to this previous WitCH from the same text and chapter. As was the case with the previous WitCH, it is a representative, one of a type.

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A Sum of “Complex” Numbers

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”

WitCH 119: Poly Want a Cracker?

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.

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WitCH 118: The Chaos Factor

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.)

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WitCH 116: Polar Bare

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”

WitCH 115: Not So Complex

Last year we took a multiwhack at VICmaths, Nelson’s Year 12 Specialist Mathematics textbook, specifically at Nelsons 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 Nelsons chapter on complex numbers. Continue reading “WitCH 115: Not So Complex”

The Stability of Stupidity

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”

A Maths Ed Lecture From Long Ago

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”