"a dialogue with students which involves meta cognition (thinking about their own thinking) and meta-conceptions (students thinking about their own knowledge and understanding of concepts)"earlier posts:
meta-dialogues are hard to establish
initiating a meta-dialogue
In my last blog I said:
What happens next? Focus Question: What do the other students find hard about fractions?I did ask that question of the class and did get some response (eg. they find ratio harder than fractions) but the response wasn't sufficient to reach the point where my students felt they could design their own fraction question. My students had no intention of approaching this analytically like a teacher might, eg. go through the fractions test, find out which questions the other students got wrong, make generalisations about what they knew and didn't know and devise an intervention to bridge that knowledge gap, etc. No way!
I should explain. I have a relatively small class of year 8 "specials", a mixture of some students with learning disabilities (various), some with behaviour issues and others who are "normal" (whatever that means).
Fortunately, I had thought about this potential road block beforehand and had another question ready to facilitate my goal:
Can anyone see any fractions in the room?A few students could immediately see other fractions in the room and I wrote their responses on the white board. This included what fraction of the class were boys, what fraction were girls. Then one girl came out the front and demanded the white board marker and she wrote on the board, "1/12 is the old guy" (!!!) Of course, the class loved it and this became the exemplar I could use to illustrate how they could write their own fraction problem. We did this collectively on the white board.
The idea of fractions in real life became for me the way out of the dry pages of the maths textbook into something richer and more meaningful.
Next lesson I offered the class a deal. We would go outside for a walk provided that each one student agreed beforehand to find a fraction outside and come and tell me about it. This worked a treat and developed into questions like this:
- What is the ratio between the seats and the bin?
- What is the fraction of red cars?
- What is the ratio between the goalie and the players?
- What fraction of boys is shorter than xxx?
- What fraction of the class is wearing glasses?
- What fraction of the class took off their jackets?, etc.
I have slowed down the amount of content being covered. This is a central point. To go deeper (meta cognition) you have to find a way to go slower.