TNDOT 3: The Remainders of the Day

Here’s a third entry in our Teaching New Dogs Old Trigs Tricks series: the first three questions from the 1907 Victorian Matric Algebra exam.* As well as the computational aspects, readers might be interested in contemplating what was expected for the proof parts, as well as how one might fruitfully present such results to students now, a century later.

*) TNDOT 2 is also in the process of being updated. Stay tuned.

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Misinformation and the Eulering Of Nate Silver

Sometimes it seems that there is no choice but to write a post.

Last week, Australia’s censorship asshole was back in the news. Julie Inman Grant and her team of goons have a new report out, which Inman Grant announced with a predictable warning of “a perfect storm” of online hate. Fair enough: I, for one, loathe this woman and am happy to declare it online. Or in person. Or by post. Or by carrier pigeon, if that’s all that’s going. Inman Grant’s hysterical message never really changes, however, and my loathing for her never really changes, so I decided to spare readers a new post. But then I stumbled upon a Twitter battle between Nate Silver and a misinformation guru. Still no reason to post: Twitter clowns are in plague proportions, of course. But then then I saw that the misinformation clown had decided to go in for a little Eulering. That was too much, and here we are. Continue reading “Misinformation and the Eulering Of Nate Silver”

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”

Can a Maths Ed Theory Give Back More Than It Takes?

A year or so ago, a decades-long friend and colleague reappeared. My friend also has a strong interest in maths ed, although she takes the “Let’s all be friends” approach. Readers of this blog know well that I’ve given up on that, but still my friend and I can argue amicably about this and that. In particular, she took some issue with my “all modern maths ed sucks” post. While conceding that most educational research is bad, she was unwilling to write off the discipline entirely and she suggested a few things for me to read. I gave them a semi-decent try, and my response was “meh”. While the stuff she suggested was mostly reasonable, or even good, I felt it was, at best, addressing third order issues. One article, however, has had me pondering a little, and I thought it may be worth sharing.

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