ACARA’s draft mathematics curriculum contained innumerable head-slappers, including the following content and elaboration from Year 8 Number (which we posted upon here):
recognise and investigate irrational numbers in applied contexts including certain square roots and π (old AC9M8N01)
investigate the Golden ratio as applied to art, flowers (seeds) and architecture
That has changed. In its stead, ACARA’s approved Curriculum has
recognise irrational numbers in applied contexts, including square roots and π (new AC9M8N01)
investigating the golden ratio in art and design, and historical approximations to π in different societies
Yep, pretty much perfect now. And, as it happens, expanded.
The following is a content and elaboration from the draft Year 7 Measurement:
explore the use of ratios to compare quantities. Model situations (including investigating ‘best buys’) using ratios and solve practical problems, interpreting results in terms of the situation (old AC9M7M04)
solving practical problems involving ratios of length, capacity or mass such as in construction, design, food or textile production
This has also been adjusted:
use mathematical modelling to solve practical problems involving ratios; formulate problems, interpret and communicate solutions in terms of the situation, justifying choices made about the representation (new AC9M7M06)
modelling and solving practical problems involving ratios of length, capacity or mass, such as in construction, design, food or textile production; for example, mixing concrete, the golden ratio in design, mixing a salad dressing
Thank God ACARA eventually undertook all that consultation with mathematicians. If they hadn’t, who knows what nonsense we might have ended up with.
I would replace mixing a salad dressing with mixing a drink, to be honest.
I wish I’d made that joke.
A reminder: avoid personalising ACARA’s curriculum. I’m tired of commenters wilfully ignoring the boundaries, and I now have a hair trigger for deleting comments.
Noone can make sense of elementary mathematics unless they realise:
* There are no irrational numbers in applied contexts.
* There are no negative numbers in applied contexts.
* There is not even (exact) “equality” in applied contexts.
These are all inventions, ideas, imagined idealisations – things that just happen to be “unreasonably effective” in allowing us to make sense of precisely those “applied contexts” (as Euclid, Archimedes, Galileo, etc. – and Eugene Wigner) realised.
Thanks very much, Tony. I doubt that ACARA’s writers thought more than three seconds about what “irrational numbers in applied contexts” might mean.
The same can be said about straight lines, triangles, and other geometric shapes: e.g. Euclid defines a line as a breadthless length. The diagrams that we draw in geometric proofs are simply aids to help us understand the argument; they are not necessarily part of the argument. Similarly, you can discuss a game of chess without a chess board or even a diagram – and experts do just this.
Do we need applied contexts though?
In a game, such as chess, clearly we do. But in Mathematics? I don’t see how these “applied contexts” do anything of benefit and I can see the potential for great harm.