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.

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. 

UPDATE (23/09/22)

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”.

11 Replies to “Not the Volume of a Cone”

  1. Do you think the formula for the volume of a cone is left out because otherwise the \frac{1}{3} causes problems for Year 10 students who don’t know what fractions are?

    I noticed last year that Year 7 students don’t recognise perfect square numbers (small ones like 9, 16, 25 and 36) and worried about preparing them for factoring the difference of two squares in algebra. Now you’ve noted that they are leaving the difference of squares out and I guess the curriculum writers are solving that problem in a similar way.

    Are you making a compilation of things left out of the curriculum too? Like a school mathematics cemetery.

    1. Ah, wst. I see the snark and the cynicism of the blog is starting to work on you.

      Your mathematics cemetery idea is obviously worthwhile, but the curriculum is such a swamp of God-knows-what, it is very difficult to do. I think the better metaphor is of a mathematics leper colony, with topics banished from the general populace, and with the limbs falling off.

    2. Difference of squares could be covered in year 9: “AC9M9A02 simplify algebraic expressions, expand binomial products and factorise monic quadratic expressions” but being limited to monics this could only be done in a limited way.
      I guess that, in the future, students will need to be in yr 11 methods before they get into algebra. Expect the standards to fall for senior school maths.

      1. Thank MW, and no. Difference of two squares is a labelled thing to be learned, by heart, and to be practised, or it is not. In the AC it is not, and the fact that Do2S is somehow permitted by one content elaboration is a country mile short. These people are insane.

  2. What do students learn about Pythagoras’s theorem? Are they told only the result without any proof? (A chestnut on this blog.)

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