One of the movies that didn’t make it into Math Goes to the Movies, appearing just too late, is the 2011 Korean drama, Unbowed. The movie is a legal drama about a mathematics professor and contains almost no mathematics. But mathematics underlies the story, which begins with the professor finding an error in his university’s entrance exam, and with his mathematics department’s reaction: Continue reading “Unbowed”

Tips and Tricks for Specialist Mathematics

I just received the following email from Mystery Student, Alex:

Hi marty,

I’m currently taking Spec 3&4 and just had a couple of questions reading this post.

For testing linear dependence, you recommended using a ‘3×3 determinant’. I was just a bit confused, and I’m always looking for areas to improve my knowledge, blah blah blah.

Do you have any other areas that make questions more efficient that are glossed over by VCAA or textbooks?

Thanks a bunch 🙂

I answered Alex briefly on the determinant question, but there are obviously readers much better informed than me about helpful tips and tricks for Specialist. And, in any case, such questions are best replied to by the crowd.

So, please make your suggestions in the comments below, including answering Alex’s specific question.

If the post takes off then I’ll perhaps try to categorise and summarise the suggestions in updates to the post. Also, if people think a companion Methods Tips post is worthwhile I’m happy to do that (although the worth of that is less obvious to me).

Quick Notes on the Herald Sun’s Exam Errors Article

There is report today in The Herald Sun (Murdoch, paywalled), titled,

Mistake-riddled VCE maths exams robbing students

Regular readers will know pretty much the lay of the land. However, there may be some non-regular readers in the next few days. So, a few clarifying remarks are probably worthwhile. (This is quick: I’ll adjust as I can through the day.)

First of all, without reflecting at all on the accuracy or the merits of the report, I want to make clear that I had no role in the creation of the report. 

Secondly, at one point the report makes quick reference to this blog:

A Bad Mathematics blog run by a professional mathematician with a PhD in maths has identified more than 90 serious problems with specialist maths exams and 77 in maths methods, including sample exams and Northern Hemisphere exams going back to 2006.

More specifically, this appears to refer to the Specialist and Methods (and there’s also Further) error list posts (and the subsequent links included there). The report refers to “serious errors”. Without rejecting that language, the language I use on these posts is of “major” and “minor” errors:

To be as clear as possible, by “error”, we mean a definite mistake, something more directly wrong than pointlessness or poor wording or stupid modelling. The mistake can be intrinsic to the question, or in the solution as indicated in the examination report; examples of the latter could include an insufficient or incomplete solution, or a solution that goes beyond the curriculum. Minor errors are still errors and will be listed.

With each error, we shall also indicate whether the error is (in our opinion) major or minor, and we’ll indicate whether the examination report acknowledges the error, updating as appropriate. Of course there will be judgment calls, and we’re the boss. But, we’ll happily argue the tosses in the comments.

In recording and characterising such errors, I have made no attempt to determine or guess the effect of such errors on students’ scores. That seems to me to be a very difficult thing to do, for anyone.

Thirdly the report refers specifically to three questions in error on the 2022 Specialist Exam 2. That exam is discussed generally here. (The other 2022 exams are discussed here and here and here and here and here.) The specific questions are discussed here and here and here. These three questions (and others on the 2022 exams) appear to me to be unquestionably in error.

Fourthly, and finally for now, for me the prevalence of errors on the VCE exams is simply the tip of the iceberg. The many posts on this blog concerning VCE and VCAA indicate my more general concerns with VCE mathematics. (My broader maths ed concerns are probably best captured by this post.)

That’s it for now. I’ll update this post if something occurs to me, or if someone suggests in the comments that I somehow should.

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).

Continue reading “Witch 112: Cooking Induction”

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.

Continue reading “Witch 111: Positively Contra”

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.

Continue reading “Witch 109: Bad Language”

Witch 108: A Mean Trig

This one, which has been discussed a bit here, comes from the 2023 NHT Methods Exam 2. It is a little strange. There are aspects of the question we like, or at least there are some interesting ideas underlying the question. Nonetheless there is no shortage of crap, and so here we are.

Continue reading “Witch 108: A Mean Trig”