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.
Not that one should expect much, of course. Even in the current curriculum, cones only appear in the “advanced” 10A material, where the volume formula is simply treated as a fact to be applied.* So, there couldn’t be much less. But, less there is.
The following, a Year 3 Measurement elaboration, is the one and only reference to cones in the new mathematics curriculum:
identifying, classifying and comparing common objects found on Country/Place as cubes, rectangular prisms, cylinders, cones and spheres (AC9M3SP01)
That is crazy. It gets crazier.
The general capabilities is another “dimension” to the Australian curriculum, comprising the general knowledge and skills and stuff that students are expected to gain through the Australian curriculum as a whole. One of the seven general capabilities is numeracy. And, in the Measurement and Geometry subsection of numeracy, there is listed the following knowledge/skill/whatever to be learned:
uses metric units formulas to calculate the volume and surface area of right prisms, cylinders, cones and pyramids
To be fair, this is a general capability, meaning it can be developed in any and all subjects. So, presumably ACARA envisions kids learning about the volume of cones in an Aboriginal Studies class, or something.
*) A derivation of the volume formula is implicit in the solids of revolution topic, in Specialist Mathematics. One can argue what might be presented earlier, at least to a strong class. It is is worth noting, however, that the difference of two cubes, which is the kind of tool you’d want, appears nowhere in the current or new Curriculum, F-10 or senior. While we’re at it, it is worth noting that the difference of two squares appears nowhere in the new curriculum.
An anonymous commentator has noted that spheres are in the same sinking boat. Previously, the volume and surface area of spheres was in the 10A material. Now there are just two references to spheres in the new curriculum: the elaboration above, and a second look-at-things elaboration in the same spot:
classifying a collection of geometric objects, including cylinders, spheres, prisms and pyramids according to key features such as the shape and number of faces and/or surfaces, edges and vertices (AC9M3SP01)
Notably, the numeracy capability ostensibly requires the learning of the volume and surface area of prisms and cones and pyramids, but requires no understanding of spheres other than that they are “round like a ball”.
We’ve updated the title, to fit in with a new series of posts.