How we've begun using Cuisenaire rods

Kassia Wedekind tweeted:

@Simon_Gregg Group of Ts and Ss new to Cuisenaire rods want to explore, investigate. Besides open exploration, what else would u start w?

— Kassia Wedekind (@kassiaowedekind) October 14, 2016

Knowing Kassia as a writer and blogger with a lot of understanding about young children's explorations of mathematics, I'm a little daunted trying to answer. But I'll have a go anyway.

First of all I'm impressed with just open exploration. My K3 class show no sign of losing enthusiasm for it. At first, when I asked them, they had no idea that the rods were linked with numbers or measurements, but there is so much implicit maths in what they do, and just doing it extends their understanding of it. It's an aesthetic enterprise as much or more than a mathematical one, but that seems right. After all, mature mathematicians often describe their motivation as a kind of aesthetic pleasure they find in it.

I document a lot by taking photos. This makes it easier to break up our creations at the end of a session, because they are not "lost", but more importantly we look again at what we've made, and I refer back to particular ones as starting points for new departures.

Students need a lot of rods. This is true for any material you use where students like either a large scale or want to continue a pattern. The little sets that people usually buy are not enough.

One of the things the teacher can then do is to say, did you see the way Ana made that wall? Do you think you could all make a wall of some kind?

And they have been so creative, there's enough for many sessions of this kind of return. You can see it right from our first meeting.

For instance, there's been lots of rectangles and surrounded rectangles:

I've used Cuisenaire trays in sessions after this:

Other things that have appeared are plans, maps really, of roads and carparks, models of houses with walls and chairs of different sizes. All of which could be followed up. Helen Williams suggested using different-sized rods to represent the three bears as the story is told, with students choosing their three sizes of rods, and holding the right one up at the right time. There could be three different chairs made, beds...

Using narrative seems is a great way in. We've been reading and writing stories about rockets, aliens and going to the moon, and T created several beautiful rocket images, which also showed one of the first examples of a staircase. So it got returned to twice. Once for a, "let's all try to make that kind of pattern in some way" session, and once for a "show a way to get to the moon" session!

We've just been making some faces within squares with sides as long as the orange rod - which was challenging but also delightful.

Alongside this, we play games. Rods behind backs, can you take out the red rod? Together and with partners. Or, here's the sandwich with something missing, what  needs to go in to finish it off.

And we're just beginning writing.

What trains have you found?#Cuisenairerods@nrichmaths @mathhombre @mburnsmath pic.twitter.com/TIf2OkZtKL

— Simon Gregg (@Simon_Gregg) October 6, 2016

As you can imagine, there's been some great opportunities for sitting with students and listening to them talk about what they're doing. But here I think I've go a lot more to learn form Kassia and her colleagues and their students... 

Writing!

All our individual work in K3 has been with manipulatives and orally so far, with lots of play and games. Today I tried them with a bit of recording in their books.

"What trains can you make that are the same length as the yellow rod?"

Following Madeleine Goutard's lead, I'm leaning towards - and today I asked for - writing rather than drawing as a way of recording, which I would have gone for more in the past, but I was happy to see the drawing too. The rationale here is that symbols are a quicker and simpler way of recording and so they can allow you to think further.

We talked through using the first letter for the rods:

Impressively, just about everyone got it. (One child who doesn't have much English didn't quite understand what I was asking for. I did sit with him for a while and do one example, but he followed up by drawing around rods in various patterns.)

It was interesting to see the different ways the children demarcated their different trains. We should look together at how they managed that.

Although I'd shown them the + sign before, when on the carpet at first with their whiteboards I asked them to write down a train I showed, that wasn't how children recorded, so we went with a list of letters. One boy did add the +s. He wrote

y+p+w

I suggested that to show p+w was the same as y, he wrote

y=p+w

but this was evidently confusing as he then switched to

y=p=w

Maybe I should have just left it!

Where would you go next with this?

I think they need to do something similar a few more times, look at each other's pages, see how to show what they want to say really clearly.

Any thoughts, suggestions? I'm feeling my way through this...