“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:
Making meaning without understanding a word
At the MAV Convention on Thursday, the team from Sunshine College, Thao Huynh and Alex Mills, gave an excellent presentation on how they use reciprocal teaching to scaffold their students into worded problems. To get us into thinking about the language demands of a maths problem for their EAL students, they gave us this problem to solve:
Without being able to speak the language, but assisted by their tool, all of us were able to make a start on understanding the question, and some of us were able to solve it.
But what got me rethinking about it this morning was reflecting on exactly what other resources we were able to bring to the problem. Without being to recognise any of the words in the question except Markt, Frau and Schweine, what enabled me to decipher the meaning?
- A familiarity with the pattern of mathematics worded problems (a genre in their own right)
- Multiple previous encounters with questions of this type
- That the punctuation is close to English, so that I can tell what is a piece of information and what is the question
- Some educated guesses about those small words like und
- And, of course, the ability to read those numbers and recognise what is a count and what is a price.
What else have I missed?
Could I have solved the problem if it had been in Persian or Chinese?
Could I have solved it if there had been a superfluous piece of information in there? I very much doubt it, and yet we wonder why students struggle with questions where there is more data than they need and want to use every number in sight.
It’s interesting to notice not only what I can manage without, but also how much else I need to use to replace it. We bring so many skills to bear to make meaning from a text, unaware that we are doing so. And then we don’t understand why our students, who don’t yet have those resources, are having difficulty.