“How do I get students talking about numbers and ‘sums’?”
I have been asked that a number of times, and it’s a good question. Students are not going to acquire the basic language of maths unless they are using it.
Having played around with a few ideas for a while, I have come to the conclusion that one of the best ways is to spend 15 minutes of each lesson on a number talk.
The essential idea of a number talk is simple. The teacher writes a single problem on the board (28 × 12, say). Students are not allowed to write anything and are asked to silently calculate an answer in their head. The teacher collects the various answers, and then asks a student to explain how they got their answer. In the EAL classroom I insist that they do so from their seat, and that they are not allowed to write anything. I will write what (I think) they said on the whiteboard. Other students are then invited to ask questions, and other strategies collected.
Building up effective mental strategies (and representing them) builds number sense and is far more practically useful in the age of the iPhone than written algorithms, but in the EAL maths classroom we have the added bonus of rich language production, and giving students a genuine need for that language. Great maths pedagogy and EAL teaching come together.
Executing number talks is a little less straightforward than it sounds, but fortunately there are great resources out there to get you started. The best I’ve found for secondary teachers is Cathy Humphreys and Ruth Parker:
Their book gives a teachers a clear guide on how to select questions and manage the routine for best effect, as well as what mental strategies we would like students to develop and how to represent them: