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.

# Tag: Specialist Mathematics

## The New Report on the VCE Exams is Out

The report of the VCE exam review conducted by Dr. John Bennett has been handed down. The media release is below and the Executive Summary of the report is here (and in Word). Presumably, there is no intention to release the full report. **(23/03/24.** And my presumption was wrong. See the update below.) I haven’t yet had a chance to look at anything, and I may update this post later.

## UPDATE (20/02/24)

VCAA’s acting CEO, Kylie White, gave a lengthy ABC interview this afternoon. There are also reports in the *Age*, *Herald Sun *and EducationHQ.

I’ll leave off writing any detailed thoughts about the report until the dust and my brain have somewhat settled. In brief, while there are significant nits to pick the report is very good on some important recommendations. In particular: employ competent mathematicians; and report in a timely manner. These are not magic wands, but they would be big and important steps.

## 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.

## 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.)

## WitCH 117: The Roots of Disunity

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”

## 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 *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”

## The Complex Roots of VCAA’s Defence

### 1. Introduction

Sometimes VCAA is their own worst enemy. Well, no: we all know the identity of VCAA’s worst enemy. But on occasion VCAA places runner up. Maybe third.

I’ve been pondering VCAA’s major 2022 errors, how they could have occurred and how VCAA could continue to defend the flawed questions for so long, against all reason. Yes, “VCAA is nuts” springs to mind. But that’s not enough. VCAA being nuts is necessary but not sufficient to explain this extended episode of madness. Continue reading “The Complex Roots of VCAA’s Defence”

## 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”