ACARA’s Not an Option

“Boy, the food at this place is really terrible.”

“Yeah, I know. And such small portions.”

“And they won’t even serve it to us.”

Yep, ACARA is even worse than Woody Allen’s Catskills resort. This charmingly insidious aspect of ACARA’s appalling mathematics curriculum was pointed out to me by blog-commenter Storyteller, while discussing my Cones Don’t Exist post. Continue reading “ACARA’s Not an Option”

Not the Volume of a Cone

ACARA is why we can’t have nice things.

Yesterday I decided to be a good guy for a change, and went about writing up Alfred Lodge’s derivation of the volume of a cone. While doing so, however, I thought to take a quick peek at how cones are covered in the new mathematics F-10 curriculum. Big mistake.

Continue reading “Not the Volume of a Cone”

The Volume of a Cone

A few days ago, we pulled on a historical thread and wound up browsing the early volumes of The Mathematical Gazette. Doing so, we stumbled across a “mathematical note” from 1896 by Alfred Lodge, the first president of the Mathematical Association. Lodge’s note provides a simple derivation for the volume of a cone. Such arguments don’t vary all that much but, however we missed it, we’d never seen the derivation in the very elegant form presented by Lodge. Here is Lodge’s argument, slightly reworded.

Continue reading “The Volume of a Cone”

The Awfullest Australian Curriculum Number Lines

As regular readers will know, and have been ignoring, we’ve been steadily working through ACARA’s new mathematics curriculum, compiling the annoying-or-way-worse 1-liner content descriptions and elaborations. No one is reading it of course, because that would be nuts. Or, it would cause the reader to go nuts. But, we’ll continue. In for a penny, in for a pounding. Continue reading “The Awfullest Australian Curriculum Number Lines”

Applied Mathematics is Bad Mathematics

Yes, the the title is clickbait, but it is not our clickbait. It’s the title of an interesting and semi-provocative 1981 article by Paul Halmos. Halmos’s article came to mind after a brief conversation recently, about applied mathematics in Australia. As with pretty much everything Halmos wrote, it seemed worth sharing.* Continue reading “Applied Mathematics is Bad Mathematics”

Funny Numbers

The leadership of my high school in the early 70s was, I presume, pretty typical for a suburban Melbourne school. It was not unkind, but it was authoritative and distant. Except for one guy, a deputy principal or something, who was a complete asshole. This one guy was always angry, always yelling at some kid for something, and forever stomping down the hallways. He also always held his head at a weird and pronounced tilt. And so, the students’ name for this asshole was 43 Degrees. Continue reading “Funny Numbers”

David de Carvalho and the Annoying Taco Kids

Last week we wrote about the mushy Australian puff piece on PISA clown, Andreas Schleicher. Readers may recall that Schleicher was critical of “Australia’s shallow Curriculum”. Schleicher says nothing of substance, simply advocating, ad nauseam,

“teaching fewer things at greater depth”.

The Australian piece also briefly quoted Ben Jensen and Mailie Ross, from some consultancy group called Learning First. In the same issue of The Australian, Jensen and Ross had an opinion piece strongly criticising the Australian Curriculum in the opposite direction:

“The Australian curriculum, however, is not a high-quality, knowledge-rich curriculum. It doesn’t guarantee the knowledge students are supposed to learn … Instead, it is a skills-based curriculum; the standards for students to achieve are skills-based. A skills-based curriculum includes knowledge but isn’t specific about what knowledge should be taught, so there is no guarantee of what will be taught in each year level, let alone across the curriculum.

[The Curriculum should] make it clear what knowledge and skills students have the right to learn in order to participate productively in life. Be honest and acknowledge that the Australian curriculum does not offer this clarity.”

Jensen and Ross’s piece is not great, in particular arguing too loosely on the basis of vague generalities. But, notwithstanding the vagueness of both pieces, there is a clear conflict about what the Australian Curriculum is, and what it should be. Luckily, we have ACARA’s CEO, the all-wise David de Carvalho, to resolve the conflict. Continue reading “David de Carvalho and the Annoying Taco Kids”

The CAS Betrayal

This post will take the form of Betrayal, with a sequence of five stories going backwards in time.


Last year, I was asked by an acquaintance, let’s call him Rob, to take a look at the draft of a mathematics article he was writing. Rob’s article was in rough form but it was interesting, a nice application of trigonometry and calculus, suitable and good reading for a strong senior school student. One line, however, grabbed my attention. Having wound up with a vicious trig integral, Rob confidently proclaimed,

“This is definitely a case for CAS”.

It wasn’t. Continue reading “The CAS Betrayal”