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.
I won’t give the solution away, try it for yourself. But also give thought to what we, as maths teachers, mean when we ask “is this reasonable”. A solution with four-fifths of a chicken, for example, wouldn’t be. But would the actual solution, or even aspects of the question like the relative prices, seem reasonable to a student from an agrarian society where buying and selling animals at market is part of everyday life? How much of what we call “reasonable” is actually real-life reasonable, and how much is maths-classroom cultural construct?
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.