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.

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New Cur 10: Positively Disposing of Mastery

This post will be about the new Curriculum, of course, but first a bit about the draft curriculum that preceded it.

In August last year, there was a Zoom meeting between representatives of ACARA and AMSI (and of member organisations) to discuss the draft mathematics curriculum, a delayed response to AMSI’s submission calling for a halt of ACARA’s curriculum review. ACARA was under political pressure to consult with mathematicians, but the meeting was a farce. ACARA’s first and foremost concern was to defend their draft curriculum. ACARA did not want to listen.

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New Cur 6: Necessity is the Mother of Convention

ACARA’s draft mathematics curriculum contained the following elaboration from Year 8 Number:

using expressions such as \color{RawSienna}\boldsymbol{\frac{3^4}{3^4} =1}, and \color{RawSienna}\boldsymbol{{3^{4-4}}=3^0} to illustrate the convention that for any natural number 𝑛, \color{RawSienna}\boldsymbol{{n^0}=1}, for example, \color{RawSienna}\boldsymbol{{10^0}=1} (old AC9M8N02)

This has been changed for the approved curriculum:

using examples such as \color{OliveGreen}\boldsymbol{\frac{3^4}{3^4} =1}, and \color{OliveGreen}\boldsymbol{{3^{4-4}}=3^0} to illustrate the necessity that for any non-zero natural number 𝑛, \color{OliveGreen}\boldsymbol{{n^0}=1} (new AC9M8N02)

Give ’em another few years and ACARA just might land upon proper wording. And the proper use of commas. And brackets. And logic.

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New Cur 5: Non-Reoccuring Decimals

Last year, we held a competition: What Are the Arguments FOR the Draft Mathematics Curriculum. The winner was officially no one, partly because everyone was too cynical to take the competition seriously, and partly because everyone’s cynicism was very largely justified. Still, we decided to declare John Friend the winner, for his suggestion in a different competition. John’s suggestion was an elaboration from Year 8 Number:

investigating the use of pronumerals to represent recurring decimals as their equivalent fractions, for example, let \color{RawSienna}\boldsymbol{x = 0.\bar7} then \color{RawSienna}\boldsymbol{x = 0.77777..} and \color{RawSienna}\boldsymbol{10x = 7.77777...} therefore  \color{RawSienna}\boldsymbol{10x \mbox{ \bf - } x = 7} and 9x = 7 so \color{RawSienna}\boldsymbol{x = \frac79} (old AC9M8N03)

This elaboration has been removed for the approved curriculum.

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New Cur 4: Golden Moments

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
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New Cur 3: ACARA’s Not an Option

“Boy, the food at this place is really terrible.”

“Yeah, I know. And such small portions.”

“And they won’t even serve it to us.”

Yep, ACARA is even worse than Woody Allen’s Catskills resort. This charmingly insidious aspect of ACARA’s appalling mathematics curriculum was pointed out to me by blog-commenter Storyteller, while discussing my Cones Don’t Exist post. Continue reading “New Cur 3: ACARA’s Not an Option”

New Cur 2: 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.

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