Thread by @edsouthall

This was so interesting (says me), so ... thread time... #tmwyk

https://twitter.com/edsouthall/status/1356963960126324739

I was discussing with primary trainees how important mathematical conversations were, and play, and moving towards a "thought provocation through prompts" model of teaching. So the boy (6) seemed like an apt guinea pig (bribed with strawberry laces).

So I asked hiim to select the shape with the most sides from a box of shapes, and he selected this. How many sides I ask? He counts, "five, so pentagon"

Watching him count I spotted he just stopped before he got all the way around the shape (pointing at the sides as he went), so I just put my finger in place to help him get back to the start. He gets it right this time. Next I ask if he can find a shape that fits on a side ...

He makes this, and explains that these are triangles 'because tri means 3 and it has 3 sides' - it becomes very clear this boy is without doubt, 'ed's son'. Precocious little soul😂

First big surprise : I asked him :Is this still a hexagon? He says no and says 'there's 12 sides'. Bamboozled me there. He says ' there's 2 sides for each side now, so i can count in 2's". I was absolutely not expecting him to do that. He also says it's a star.

Next I ask if he can fit any shapes in the gaps to make a new shape. So he makes this:
I ask 'do you like this shape?' he says 'no, because it's not finished' (referring to the concave bits).
'What could fit in those gaps then?'

He makes this, and says it's a new triangle. We count the sides and he says 'oh, it's not a triangle, i don't know what it is'. I ask if it's a hexagon? He says no, and compares the two (2nd pic). We count up the sides for both.

"Well, it has the same number of sides, but this one has short sides and long sides so it's not a hexagon". This is exactly the sort of thing I talked to trainees about previously: more representations help children reinterpret, and reinterpret again.

To him, a hexagon has 'a look' as well as six sides. This notion begins to be unpicked through this activity, but it's even more striking in the book activity next...

Book activity: I ask 'which of these are triangles?". He says all of them, but interestingly adds "but only one of them is correct". Can you guess which one he points to?

'because it's flat on the bottom'.
"None of the others are finished because they aren't flat on the bottom... but..."
*turns page*
"if you do this, now they're ok"

I ask which is his favourite triangle, he points to the bottom left "it's the right way, and it's the best size". He then points out that "all of them make a square too". Bit puzzled, but he shows me with his finger what he means...

This is his square.

Finally, we look at this page. He spots quickly that the circle looks 'cut out' from the annulus (no, he didn't call it that), but also eventually notices that the triangle is cut out from the dart too.

But the triangle is 'not a good triangle', because it's 'kind of squashed' compared to his favourite triangle from before. He calls the dart a triangle so we count up the sides. He concludes it's not a triangle, but hasn't got a name for it because ...

"a four sided shape is a rectangle or a square and they don't look like that" (amazing, i love this!).

Then after some thought he concludes the dart *is* a triangle, because if you put the squashed triangle at the bottom, it's a triangle.

So there you have it. Talk maths with your kids #tmwyk it's such a valuable low stakes opportunity to see their thinking, unpick misconceptions & learn from one another.
If you're interested, the blocks are these:
amazon.co.uk/Wissner-Gmbh_0…

& book is me:
members.m-a.org.uk/Shop/product/1…