I was gonna let this one go but an email prompted me to reconsider. Then, I wasn’t sure how to do it, and pondered either a quick PoSWW or a full-blown post. In the end I decided to handball it to the aether and make it a WitCH. It is a triple bunger of nonsense, and readers can decide which bunger offers the biggest bang.
1. AERO
Amongst AERO‘s five million videos and sermons on explicit teaching, they have a two page At a Glance cheat sheet. The cheat sheet includes a couple of examples or illustrations or whatever, including the thing above.
2. Westwell
Last week, Martin Westwell, long time education academic thingo and current Chief Executive of South Australia’s Department for Education, wrote a short Linked In post, criticising the AERO example/illustration above, and prompting some AI thing to try to improve it.
3. Ashman
A couple days ago, deputy principal Ashman wrote a post, suggesting that “bureaucrat” Westwell’s criticism of the AERO example is selective and unfair, and that Westwell’s purported AI improvements of the AERO thing leave a lot to be desired. Ashman noted that the AERO thing is “far from a lesson plan” and is simply “a quick summary”, that “It is just there to flesh out the definition”. Ashman also noted Westwell’s “obsession with ‘the real world’ “, and Ashman took a whack at Westwell’s “differentiation”.
I won’t go into what I think about AERO’s and Westwell’s and Ashman’s contributions. Readers can give it a go and I am curious how and where they might go. I’ll just note that Ashman closes by suggesting that Westwell is “uncharitable” in focusing on this one AERO resource, thus giving “the impression that [Westwell] has an axe to grind”. Quite possible. But, Ashman complaining about someone else grinding an axe is the funniest thing I’ve read in a long time.
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UPDATE 19/08/26
Following up a remark I made and Potii’s response, below are the K-2 content descriptors on Shape (ugh!). Readers can also check out the optional elaborations, here, here, here, here, here and here.
What this demonstrates, above all else, is that basing any discussion upon the Australian Curriculum is madness, that nothing can remotely be set right until the Australian Curriculum is de-insaned, and that anyone whining about “pedagogy” is doing more harm than.
FOUNDATION
sort, name and create familiar shapes; recognise and describe familiar shapes within objects in the environment, giving reasons (AC9MFSP01)
describe the position and location of themselves and objects in relation to other people and objects within a familiar space (AC9MFSP02)
YEAR 1
make, compare and classify familiar shapes; recognise familiar shapes and objects in the environment, identifying the similarities and differences between them (AC9M1SP01)
give and follow directions to move people and objects to different locations within a space (AC9M1SP02)
YEAR 2
recognise, compare and classify shapes, referencing the number of sides and using spatial terms such as “opposite”, “parallel”, “curved” and “straight” (AC9M2SP01)
locate positions in two-dimensional representations of a familiar space; move positions by following directions and pathways (AC9M2SP02)
Let me add a comment, which is tangential to the above discussion, about geometry and the real world. In Book 1 of “Elements”, Euclid defines a line as a “breadthless length”. I have never seen a breadthless length. I could not draw one. I cannot even imagine one. The definition leads me to conclude that a line exists only an idea, and likewise for all other shapes that use lines.
Euclid includes lots of diagrams in his work, but they are only an aid to assist us in understanding. His work could have been produced without diagrams – but it would be harder to read.
It’s similar in chess. We can record the moves in symbols: 1. e4 e6 2. d4 d5 et cetera or just think about the moves. We don’t really need a chess set – but the chess set makes it easier to follow a game.
Good night and good luck.
Reference: http://aleph0.clarku.edu/~djoyce/java/elements/bookI/bookI.html
Thanks, Terry. It’s not really true that Euclid can be read without the diagrams, for the reason you note: the only formal way we have a sense of what Euclid means by “breadthless length” is by his diagram.
Of course we also have an informal way to know what a line is, which is what is really going on, and I think this is relevant to AERO’s slop. It is not the main issue with their slop, and it is not that one should not try to define “square” in some manner. But AERO’s pseudo-definition only makes sense if you know what “sides” means. Are they gonna then pseudo-define “line”? At some point, you have to accept semantic primitives.
What is implicit (by “implicit” I am guessing something that is not literally present, but seems likely to be intended) in this AERO (whatever “AERO” stands for) example is the hand-waving the teacher will almost certainly be doing. Pointing to the diagram drawn on the whiteboard, waving her hand to direct the students’ attention to “sides”, maybe gesturing with a finger that traces from one end-point to another. Implicitly, this hand-waving helps show what the word “side” means in this context. (Not a football “side”. Not a “side” of bacon. Not a right-hand “side” on a page, … The word “side” means, or possibly does, many things.
Behind this is what Terry Mills points out: the diagrams in Euclid (and elsewhere) and the sketch of this square, are approximations of ideas. Moreover, they are not inherently 2-dimensional or 3-dimensional, or whatever-dimensional ideas. Just ideas.
W.W. Sawyer sometimes talks about trying to teach geometry to a bodiless angel, speaking over the telephone, using words without images. Sawyer says this is difficult, but as a thought-experiment is possible. This leads Sawyer to present the angel’s logic once all the talking has persuaded the angel that Pythagoras’s Theorem is true. A-squared + B-squared = C-squared, for a triangle with end-points a, b, c, and “sides”, A, B and C. That is, a two-dimensional figure — triangle.
The angel then accepts that Pythagoras’s Theorem is true for a three-dimensional object with endpoints a, b, c, d, e, f, g — a rectilinear parallelopiped, a “brick”, and top edges A, B; height-edge C, and long diagonal D.
A-squared + B-squared + C-squared = D-squared.
Then Sawyer produces the angel’s logical next step:
E-squared = A-squared + B-squared + C-squared + D-squared …
And we leave visually-representatable geometry.
(I may not have been clear in my sketch of Sawyer’s thought-experiment with the angel. But Sawyer is an excellent teacher, and should not be forgotten.)
Behind the
The AERO-teacher’s hand-waving, and Terry’s emphasis on concepts that are hinted at by a diagram, we have Marty’s insistence that we rely on undefined terms — NOT that we teach Grade 1 students in this way. But later, maybe around mid-Secondary, we review Geometry — a descriptive, approximate geometry with diagrams and technical terms — and introduce Terry’s, and Euclid’s vaguenesses — “that which has no breadth” … — and then introduce some undefined terms: “point”, “line-segment”, “ray”, line”, “rotation”, … and attempt to make clear that what we UNDERSTAND (the concepts) are implicit in the hand-waving and diagrams.
Meanwhile, back at that AERO-teacher, I am thinking of a RHOMBUS which does not have 90-degree (or quarter-turn) interior angles.
All four sides of these non-rectilinear rhombuses are equal in length.
For one of them to be square, ALL the interior angles must be equal.
That crucial defining statement for “square” was omitted by the AERO-teacher’s half-right lesson.
Thanks, John. I think this is interesting stuff but, in the context of explaining a square to a grade 1 kid, it is overblown. Just as AERO and Westwell and Ashman are overblown. It’s a square, for Christ’s sake, not an inverse trig function.
So you just need four equal sides and 4 corners for something to be a square. Huh.
I wonder how the examples and non-examples part of the lesson would go based off that definition.
It comes off as a very dreary lesson or a thoughtless whipped up example of explicit teaching.
Thanks, Potii. Yes, the supposed definition is the PosSW aspect. And yeah, maybe it’s meant to be more “property of” than definition, but having the kids chant as if it were a definition is pretty damn stupid, and AERO displaying this example in their short cheat sheet is pretty damn stupid. Perhaps Westwell is being uncharitable, but if AERO is gonna highlight something like that, they have to wear it.
But beyond that, as you also note, the entire thing comes across as dreary and thoughtless. None of it, but also Westwell’s supposed AI’s improvements, comes across as a good and human y1 class on shapes.
I wonder how you’d go about teaching a year 1 student what a square is?
One thought that comes to mind is about rotational symmetry. Take a bunch of four sided physical shapes (just rectangles, kites and squares, maybe?), the students make tracings around them and then turn the physical shape over the tracing and counting how many times they match themselves. Then they answer what shape has the highest number of matches? Then property of equal sides follows on. That way you avoid having to talk about types of angles (I remember learning about angle types in year 3, I think). At some point kids will make dubious spinning tops and have a laugh.
Maybe too much abstaction? Maybe just define it through a visual and get them to do drawings, categorising pictures of different sided shapes and tessellating different physical shapes.
Thanks, Potii. I strongly lean with your last paragraph, and I think AERO and Westwell and Ashman are all being ridiculous. They are all pushing their barrows, and the kids be damned.
I have no idea how I would teach “square”, or geometry more generally, to Year 1 kids. BUT, I certainly wouldn’t pretend that the kids don’t already know what a square is, and I wouldn’t be making it their introduction to axiomatic geometry.
There is just something fundamentally nuts about the entire discussion. The nuttiness may be strongly driven by, or at least is permitted by, the vacuous insanity of the AC: read the K-2 CONTENT entries on geometry, and then go weep.
I tried to find the content but trying to navigate the ACARA website was too unwieldy, so I gave up. I’ll save my weeping for another time.
It really does come off as people fighting over scraps.
Yep, they’re scraps. I’ll update the with post the AC drivel tomorrow.
I updated the post with the AC “conent”.
Saw the content in the update. I actually found that page before but I thought they were overviews of the topics covered in year 1 and 2. I didn’t realise they were the actual directives on what to learn (I haven’t paid close attention to the AC since I teach in NSW). That’s incredibly loose. Some kids will get to see good maths, other won’t. Why argue how to build a house if the foundations are already sinking into the mud?
Exactly. AERO’s highlighted thing is ludicrous but the entire discussion is ludicrous.
Just tried this out on my daughter who is in grade one. She laughed at me and said: ‘don’t be silly dad, this is a prep thing’.
Of course, and at most. AERO and Westworld and Ashman are all being ridiculous.