Friday, 14 July 2017

Going Sideways

A problem with the metaphor of 'progress' in learning is that the 'journey' becomes roughly linear:
If that's extended to an individual lesson, students will be making 'progress' through the lesson. They won't all make as much 'progress' as each other.
Some of them have shot forwards, others are tarrying back nearer where they started.

And what to do with them then, in the next lesson? Put those three shoot-aheaders in a separate group? Ask them to hang around for a bit? Teach them and hope the tarriers will keep up?

This is a real challenge for us all, and I don't claim to have the answer. But I do recommend Going Sideways.
Take a detour, a road less travelled, follow a student's deviation, make room for the unfamiliar embodiment, for variation and investigation. After the number lines, try hopscotch.
Read a story about a hundred ants.
Look at a strange picture:
Solve an unusual problem.
Because maths isn't just forwards, it's sideways too. Maybe it's like this:
Or perhaps it's like this:

But whatever it's like, it's not in a straight line. So when the students go sideways,
make sure to show the ones on the left what the ones on the right did. And the ones on the right should see what the ones on the left did too.

Friday, 19 May 2017

Grids: inquiry and risk-taking

DW says he was playing noughts and crosses in the car, and then wrote numbers on the paper. He brought it in to me, a 10 cm square:
It lay on my desk for a day or two, then we showed it to the class. I asked them what they noticed about it. We wondered about the 17. We counted it through. Then I did what I often do when someone originates something - I asked the children, on similar-sized pieces of paper, to make their own, but different grids. There was a variety, lots with the grids continuing on the reverse side:
I was impressed with how careful the children had been, lots of them choosing to use rulers (I hadn't mentioned them). It seemed like the few that still needed to practice writing their numbers could get on with that, and the others could decide on a layout, a pattern, decide how far to go.

It took a few days for it to really sink into my head that all the children seemed to be enjoying doing this. There was an element of play, of choice. Grids could be large or small. They could even be different, like Bianca's even number one. In the Primary Years Program of the International Baccalaureate, inquiry is one of the key learner attributes we're looking for. For 5 and 6 year olds, this playful exploration is inquiry. There was a constraint, it should be a grid, but otherwise the field was open.

I felt like we needed to be celebratory, high-spirited in this play, so next time, I had large paper squares.

Another important learner attribute in the PYP is being a risk taker. When we looked at what had been done so far, I took a little more time on the ones that had been more different - the ones where the numbers weren't simply in counting order. If people were going to go new places, divergence would help. 'You can start in a different place, or from a different number, or try a different pattern of numbers.'
 A lot of children wanted to get up to big numbers. It took more than one session. So, while next day some finished, I sat with the others in front of the whiteboard. I drew a 4x4 grid and invited ways of filling it in. There were these:
We all contributed to the "random" one.
Then I asked the students to draw a 4x4 grid on little whiteboards and fill it in somehow:
These last two amazed me, capturing something I'd wanted to explore with the students. I'd just read What comes after nine? by  in the latest Mathematics Teaching issue, which looks at how this kind of table gives an enormous amount of naming power to students. Modifying it slightly, I put it together with 3 others to make a #wodb:
which we duly answered:
With the big grids, I was really impressed that the students who are sometimes the least confident in maths kept going on their own and went much further with numbers than I'd seen them go before. And of course there's the variety. (I wonder if our hopscotch work helped with this?) They're up on the wall now:
And the other K3 class is getting going too:
We've given them a middle-sized piece of paper and asked them to make one more grid at home.

And the K2 children have caught the grid bug: