Bernie’s Valiant Effort

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”

Witch 112: Cooking Induction

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).

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Witch 111: Positively Contra

Almost there. This is a continuation of the previous WitCHes, here and here and here, on the Logic and Proof chapter of VicMaths, Nelson’s Specialist Mathematics Year 12 text. It is the penultimate section, Proof by contrapositive and contradiction. Most of the worked examples are OK (including Example 18, a correct and reasonably well-written proof “by contrapositive” that if n2 is divisible by 3 then n is divisible by 3). But, there are issues, notably in the exercises.

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Witch 109: Bad Language

This is a continuation of a previous WitCH (and PoSWW) on the Logic and Proof chapter of VicMaths, Nelson’s Specialist Mathematics Year 12 text. The previous WitCH comprised the first part of Section 3.1, titled Conjectures, together with some associated exercises. The remainder of 3.1 covered conjectures proper, including examples and counterexamples and the like:

Yes …

On to 3.2, titled The Language of Proof. Below are the, um, highlights from this section. We’ve restrained ourselves and not included associated exercises.

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Witch 107: Infer a Pounding

This has a lot in it: it’s more of a coven than a WitCH. We couldn’t see what else to do.

As with our recent PoSWW, this WitCH comes from the Logic and Proof chapter of VicMaths, Nelson’s Specialist Mathematics Year 12 text. This is a new VCE topic, for which the summary from VCAA’s study design (Word, idiots) is,

This summary is also given as the prompt of Nelson’s chapter. Then, the extended excerpt here is Nelson’s introduction to the chapter, together with a few of the associated exercises + answers. (The textbook then continues with its coverage of “conjecture” and so forth.)

Readers who lose sight of land may wish to refer to a solid introduction to argument to get their bearings.

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You Can Lead a Horse to Textbooks

Or a mule, maybe. You can lead a mule to textbooks.

About a month ago, there appeared a Conversation article by Rachel Marks, a researcher in primary education at the University of Brighton, in England. Based upon research for which she was the Principal Investigator, Marks’s article was about a UK government program, launched in 2016, where primary schools were offered matching funds to purchase mathematics textbooks. Marks and her colleagues concluded that schools substantially rejected the program: few schools took up the offer of subsidised texts, and fewer stuck with it. Continue reading “You Can Lead a Horse to Textbooks”

Witch 106: Plane Silly

We’re snowed, and we have a couple posts in the works that simply won’t behave. So, we’ll just keep the ball rolling with a WitCH, and have you commenters do the work for now. The following is the introduction to planes (a new VCE topic) in VicMaths, Nelson’s Specialist Mathematics Year 12 text.

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