We've just finished our first week of the new year, me and my class of fiveyear olds.
I've been thinking about Graeme Anshaw's blog post where he asks, What type of maths inquiry do we employ the most and the least in our classrooms?
He outlines these different forms of inquiry:
Demonstrated Inquiry

Structured Inquiry

Guided Inquiry

Open Inquiry
 
Posing the question

Teacher

Teacher

Teacher

Student

Planning the procedure

Teacher

Teacher

Student

Student

Drawing conclusions

Teacher

Student

Student

Student

How do we find a place for open inquiry, where the students are asking the questions? More specifically, how do I do it, with my class, especially as most of the students don't have English as a first language?
For young children like mine, how they ask questions is often through their play. If I pile these up here, what would it look like? How could I arrange them more satisfyingly?
Here's a couple of students arranging wooden blocks in a line, then arranging frisbees and bats on top.
You need lots of components to get good patterns going  we need more bats and frisbees! We've just got more magnetic Polydron and the building is impressive. Here's T asking how he can transform shapes, and what happens if he uses triangles to add starpoints to other shapes?
Others were enjoying our new straws and connectors, starting with squares, building cubes, and then puting them together to produce a tall tower:
Arranging squares:
Cutting holes in folded paper:
Making balls and worms of play dough:
Creating train track networks:
and playing with Cuisenaire staircases:
EL made this last series of staircases. Actually she had to make it three times. The first time someone slid some rods into it, and it was too late to repair, the second time it was standing up and got knocked over during lunch time. I made sure there was time when she could get it finished and photographed.
I think it's important that everyone recognises that there is maths implicit in all these things. Many people still think of maths as needing to be about counting or numbers or sums, and feel anxious that these should happen. But these things are there in the physical things that the students are doing already! And also:
 Spatial and geometrical awareness
 Categorising and sorting
 Creating patterns
 Investigating the results of processes
There are also the social skills being exercised in much of the group and paired work. All of the IB PYP social skills are needed at various points:
 Accepting responsibility
 Respecting others
 Cooperating
 Resolving conflict
 Group decisionmaking
 Adopting a variety of group roles
Of course, it's great to connect all this making to language, to talking about what we've done and reflecting on it, and ultimately to symbols too. And to start to abstract from the particular. But I don't want to be hasty with this. A lot of the student's creations are so pregnant with mathematical possibilities that I want to (as Helen says) repropose them to the class, perhaps along with what they said to me at the time. I'm also this year, annotating photographs of the students' creations with them.
And there will be time to start making connections to some of the big concepts in maths. Like the way Graeme starts with the big central idea, "Our base 10 number system evolved for a variety of reasons and led to place values that extend infinitely in both directions." What these big ideas are varies from list to list. I see Jo Boaler and her team have just developed some:
Others have come up with big overarching ideas that stretch right over the years. Like Mike Askew's:
In addition to considering this, in the IB PYP we work with transdisciplinary themes, that bring out the connections between traditional subject areas. Including maths of course.
So, I'm hoping, for instance, to connect, for our current unit of inquiry on transport systems, the train track building that's going on with some discrete maths. How places are linked, how are nodes linked by edges. Moving from very concrete things like trains and cars, onto networks, reasons for networks, connections. I tried this last week, asking students to make roads between every pair of two houses, and after a few asking them to guess how many roads there will be:
What happens if the roads are not allowed to cross?— Justin Lanier (@j_lanier) September 8, 2017
What I really want to keep though in all this, while trying to develop the big ideas, is the wonderful, individual, confident play and creativity.
Thankyou so much for this, Simon. Such a lot to think about, and your accounts always make me wish I was in the classroom alongside your's.
ReplyDeleteA couple of thoughts, I think Graeme Anshaw's table of inquiry oversimplifies the relationship between teacher and learner; for e.g.; open inquiry isn't just decisions made by learners, the teacher has significant input. Thus I think these stark divisions can be unhelpful, as it may make people think open inquiry is rather laissez faire, when in reality it probably  as you demonstrate in this post  is the most complex to plan effectively and remain responsive to the learners.
Second  I wondered if you had seen Sue Gifford's Big Ideas? or those on the Erikson website http://earlymath.erikson.edu/bigideas/ ? I happen to think Sue's are really strong  not sure how to attach a document to this? any idea and I'll send them to you.
Keep posting! I must start....
Yes, I agree entirely about the inquiry, and I think Graeme would too. Ideally teaching is a dialogue where we bounce ideas off each other. In the PYP learner profile though, being an inquirer is something we want for our students, and I want to give a place for the child as initiator, with the noticing and encouragement and guidance of the teacher, of further inquiry in the classroom. I see play as one source of starting points that the teacher can pick up on, 'reproposing' as you say sometimes, presenting to the class, augmenting perhaps. Also short routines where the children contribute ideas and questions in response to some kind of starting point that the teacher introduces.
DeleteI see Sue's big ideas mentioned here:
https://nrich.maths.org/11441
"Big ideas would include number values to 10 and 20, comparing numbers and numbers within numbers: contexts would include outdoor and indoor activities and games, like scoring goals or cooking, routines like snack time and rhymes and stories, including opportunities for discussing puzzles and problems."
These lists (and I've seen a few more in some Mathematics Teaching articles) are getting me thinking, what are mine...
A great share with so much to think about, Simon. The pictures really capture the mood that hits me when I wander in  enthusiastic, purposeful, engaged and creative (and this is just the first week!). The activity of making play dough shapes and sorting them into the tray with compartments caught my eye. I've got a tray like that  must dig it out of the cupboard. In my class there's been lots of spontaneous play with the shop  it's become a dinosaur shop. There has been shopping for big and small dinosaurs, counting out dinosaurs and working with money ( Friday's shop keepers loved giving great quantities of change). Pop by and purchase a dinosaur or two if you get chance tomorrow :)
ReplyDeleteI was thinking I needed a dinosaur.
DeleteDid you see that thing where you put a balloon over a dinosaur and then begin to fill it with water until it's round, and then freeze it to make a dinosaur egg?
And there's more of those trays. I think they might be in the maths cupboard in the rangement.
Delete