New Cur 27: The Proof Is in the Plodding

A month or so ago, we posted on Euclid et al, asking about the proper role of proof in a mathematics curriculum. The question and subsequent discussion was purely theoretical of course, since proof barely exists in the Australian Curriculum. Here’s the proof. Continue reading “New Cur 27: The Proof Is in the Plodding”

PoSWW 37: Squaring the Circles

This one comes courtesy of Mystery Fred. The diagram above is for a Circle Gaps Brainteaser, and appeared online last week as part of Double Helix, CSIRO‘s science magazine for kids. The text for the brainteaser (as if it matters) is as follows:

What is the area of the orange star in the centre? The blue circles each have an area of 3 square centimetres, and the big square has sides that are 4 centimetres long.

A comment on the post makes it clear that the choices of sidelength and area were purposefully made.

Continue reading “PoSWW 37: Squaring the Circles”

Here’s Looking at Euclid

Proof barely exists in the Australian Curriculum. This is nuts, of course, but leave that be. Even when it is accepted that proof should – must – have a significant role in the curriculum, there are questions to be asked:

In which topics should proof be introduced and emphasised, and at what stage(s)?

Should “proof” be more a topic(s), or more an omnipresent concern?

How proofy should teacher-presented or students’ proofs be? Continue reading “Here’s Looking at Euclid”

Right-Angles and Wrong Angles

It hit the news last week, that two high school kids had come up with a new proof of Pythagoras’s Theorem:

Two New Orleans high school seniors who say they have proven Pythagoras’s theorem by using trigonometry – which academics for two millennia have thought to be impossible – are being encouraged by a prominent US mathematical research organization to submit their work to a peer-reviewed journal.

I had decided to leave it alone. I had figured out enough of the story, that the two kids had done something very cool, which had then been way over-egged by the predictably clueless, Homerically lazy media. I’ve done these stories, and they can be tiring and tricky.

My friend Grant Cairns,* however, tipped it over the line, by pointing out an MAV tweet:

Good ‘ol MAV.

How a right-angled triangle is any more about “the world around us” than the number 3, God only knows. Grant summarised it as the MAV being “totally grounded in reality”. More accurately, the MAV is totally grounded by reality. To an earthbound hammer, everything is an earthbound nail. Continue reading “Right-Angles and Wrong Angles”

New Cur 16: The Decimation of ACARA’s Elaborations

One of the black humour aspects of ACARA’s promotion of its new curriculum, and the draft that preceded it, was ACARA declaring ad nauseum that the curriculum had been “refined” and “decluttered”. ACARA’s claim was then repeated ad more nauseum by education reporters stenographers. Continue reading “New Cur 16: The Decimation of ACARA’s Elaborations”

New Cur 15: The Vastness of Space

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:

Continue reading “New Cur 15: The Vastness of Space”

New Cur 12: A Futile Quad Wrangle

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:

Continue reading “New Cur 12: A Futile Quad Wrangle”

New Cur 11: Circling Reason

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.

Continue reading “New Cur 11: Circling Reason”