As was our previous post, this one concerns a very small but very telling detail of the new mathematics curriculum. A minor perversion of the curriculum is the renaming of the study of geometry as “Space”. This stupidity was noted by AMSI last year, in their submission on the draft curriculum:
This one comes courtesy of commenter jono, who pointed out the absence of quadrilaterals in the f-6 part of the new Curriculum. jono noted that the terms “rhombus” and “kite” and “parallelogram” and Trapezium” are not once mentioned, and that the single mention of “quadrilateral” is in a Year 1 Space elaboration:
Just for a change, this post will be about a good aspect of new Curriculum. Just kidding. Sort of.
The following is an elaboration and associated content descriptor from Year 8 Measurement:
solve problems involving the circumference and area of a circle using formulas and appropriate units (AC9M8M03)
deducing that the area of a circle is between 2 radius squares and 4 radius squares, and using 3 × radius2 as a rough estimate for the area of a circle
There are two ways one might react to this elaboration. First, one might justifiably have no idea what is the meaning or intent of the elaboration, and then conclude that the curriculum was written by idiots. Or, one could recognise that the elaboration is at least attempting something good but that the attempt was an abject failure, and then conclude that the curriculum was written by idiots. All roads lead to Rome.
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.
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.
Yeah, it’s been a while. We’ve been busy. But, hopefully we’re now back with normal transmission, and we’ll start with an easy one, courtesy of Mysterious Michael. It is an exercise and solution from Cambridge Essentials Year 10/10A.