Tony Gardiner on Problem Solving

This is our final excerpt from Teaching Mathematics at Secondary Level Tony Gardiner’s 2016 commentary and guide to the English Mathematics Curriculum. (The first two excerpts are here and here.) It is a long and beautifully clear discussion of the nature of problem-solving, and its proper place in a mathematics curriculum (pp 63-73). (For Australia’s demonstration of improper placement, see here, here and here.)

Continue reading “Tony Gardiner on Problem Solving”

Tony Gardiner on Financial Mathematics

Our first excerpt from Tony Gardiner’s Teaching Mathematics at Secondary Level is here. Our second excerpt is a short remark on “financial mathematics” in a mathematics curriculum (p 75). The relevance to Australia’s draft curriculum is obvious.

Continue reading “Tony Gardiner on Financial Mathematics”

Tony Gardiner on Exactness and Approximation

It’s been a while. We’ve been trying hard to get out a long, long post on ACARA and the draft curriculum. (Working title: Moby Albatross). We also had a great WitCH planned, but that was torpedoed by Simon the Likeable. For now, we’ll keep readers occupied with some excerpts from the writing of Tony Gardiner.

Gardiner is an English icon, sort of a one-man AMT, but without the foot-shooting. Previously, we wrote about Gardiner’s and Alenxandre Borovik’s beautiful (and free) book, The Essence of Mathematics Through Elementary Problems. Then a few weeks ago, we posted a “puzzle” from Gardiner’s book, Teaching Mathematics at Secondary Level.

Written in 2016, TMSL is Gardiner’s commentary and guide to the English Mathematics Curriculum, with a particular focus early secondary school (Key Stage 3). Although framed around a specific curriculum, much of  TMSL is written from a more general perspective. In particular, Chapter 2.3 of  TMSL is on problem solving and the manner in which problem solving can fit, or misfit, in a mathematics curriculum. We shall excerpt this chapter in three posts, beginning with two short passages and concluding with the main content of the chapter. Our first excerpt is on the importance of exactness in a mathematics curriculum (pp 73-75).

Continue reading “Tony Gardiner on Exactness and Approximation”

Obsessive Compulsion

Last week, the New South Wales government came out with the next great plan to Save Mathematics Education: make mathematics compulsory up until the end of high school. Why? According to Premier Gladys Berejiklian, this will “ensure students have the numeracy skills required to succeed in today’s society”.

Yes, of course. In exactly the same way, for example, that compulsory instruction in ethics ensures that lawyers and cops act ethically.

What’s the source for this latest nonsense? Well, it’s kind of, sort of from the Interim Report of the NSW Curriculum Review, which was released a few days earlier, and which is prominent in the Government’s media release. Like all such reports, the NSW Report is barely readable, the predictable mishmosh of pseudoscience, unweighted survey, statistics of undeterminable worth and contradictory motherhoodisms. Thankfully, there’s no reason to read the Report, since the NSW Government hasn’t bothered to read it either; nothing in the Report points to making mathematics compulsory throughout high school.

Still, it was easy enough to find “maths experts” who “applauded the move”. Jordan Baker, the Sydney Morning Herald‘s education reporter, quoted four such “experts”, although the only expert appearing to say much of substance was doing anything but applauding. Greg Ashman, who is always worth reading (especially when he is needling nitwits), pointed to the need for specialist teachers in lower years. He is then quoted:

“You need to move away from the fashion for inquiry learning and problem-based learning and instead focus on high quality, interactive, explicit teaching of mathematics. Do that, and I believe numbers in year 12 would organically grow.”

In other words, if you stop having shit teachers teaching shit maths in a shit manner in lower years then maybe more kids will choose to stick around a little longer. (Ashman is more collegial than this writer.)

The NSW government’s compulsion will undoubtedly push mathematics in the exact opposite direction, into ever more directionless playing and mathematical trivia dressed up as real world saviour. You know the stuff: figuring out credit cards and, God help us, “how to choose cancer treatment“.

To illustrate the point perfectly, Melbourne’s Age has just published one of its fun exam-time pieces. Titled “Are you smarter than a 12th grader?“, the reader was challenged to solve the following problem from yesterday’s Further Mathematics exam:

A shop sells two types of discs: CDs and DVDs. CDs are sold for $7.00 each and DVDs are sold for $13.00 each. Bonnie bought a total of 16 discs for $178.00. How many DVDS did Bonnie buy?

The question this problem raises isn’t are you smarter than a 12th grader. The real question is, are you smart enough to realise that making mathematics compulsory to 12th grade will doom way too many students to doing 7th grade mathematics for six years in a row? For the NSW government and their cheer squad of “maths experts”, the answer appears to be “No”.