naturally ingenious combining

I'm rereading some of the chapters in Madeleine Goutard's Experiences With Numbers in Colour. Something jumped out at me. It was written in 1964, but in a way it's better suited to now, to 2016. The destiny of many if not most sets of Cuisenaire rods around in the 60s was to end up in the bottom of cupboards, along with the Dienes apparatus and Geoboards. What was not there, the ingredient that was needed to make the pedagogy work, was the idea and practice of number talks. Even now this is maybe not that widespread, but at least it's out there, with wonderful books like Intentional Talk leading the way. Now that we are using quick dot images, asking children to look at groups of dots and tell us how they see the total, we understand better the importance of what Goutard below calls "naturally ingenious combining".

I won't be using this particular part for a while as my five year olds will be doing a lot of playing and other things before we get to this stage. But you'll see what's happening. The class is motivated to explore something together, they are creative and playful in the way they find solutions. The emphasis is on doing and trying out rather than having remembered (although they evidently have a lot of experience with rectangles as products of two numbers).

The passage starts with Goutard introducing some rods:

She then introduced a black rod (7 white rods long)...

And not just flexibility of mental calculation. Flexibility in thinking. And also comfort with manipulating numbers. These days too it's easy enough to take photos of what the kids have made , get them up on the whiteboard, and come together to talk about the different representations together.

Meeting my new class

So, last week we all met our new classes for 45 minutes. Mine will be all five years old in September, what up until now we've called Year 1, but come September, we're calling Kindergarten 3 because 1. we're being less British, and 2. we're being much more play-based.

So, after an introduction ("Do you want to call me Mr Gregg, or Simon?") and a song, I introduced - of course - the Cuisenaire rods. I asked them what they thought they were for, and they said making pictures of various kinds, not a mention of maths. I said they were sometimes used for patterns and numbers, and one boy counted to twenty in response.

So - of course - I said, "Make anything you like out of them, pictures, patterns, whatever you like!"

And they did!

a blue-black pattern

We'll return to this, and explore lots more patterns.

a gate

A lot of people made things in 3D, like for instance this house:

a house with a chair

 I wonder what other-size chairs we can make...?

a face - we know where this leads

 And here's an interesting rectangle...

 Here is the beginning of lining things up, measuring them up against each other neatly. We're going to follow up with a lot of this.

a sun shining!

When I look at these pictures, and all the others, I see the kind of things the children are interested in. They like houses, and roads, car parks and castles. Some made abstract patterns of rectangles, or spelled out their name. And I see lots of starting points for further exploration.

(The next day a couple of the girls came to me with a home-made envelope with some nice messages and pictures inside, like this one of that first meeting. Those yellow trays on the tables are the ones with the Cuisenaire rods in.)