What’s 38.5% of 120kg?
Does that sound tricky?
One of the wonderful benefits of being an educational consultant is the opportunity to work alongside and learn from hundreds of outstanding educators from around the world.
Recently, I spent some time with one such teacher in Sydney Australia by the name of Rojier Eliah, who attended my ‘Thinking for Learning’ workshop. As a Maths and Music teacher, Rojier is fascinated by the pedagogy and practice associated with building a culture of thinking, perhaps in part because it connects so seamlessly with his own pedagogical identity.
When it got to lunchtime, Rojier and I enjoyed a sandwich together, and amongst many other points of discussion, we got to talking about what a culture of thinking looks like in the Maths classroom.
And here’s the thing. In great Maths classrooms, it is not just through the use of specific thinking routines that powerful cultures of thinking are created.
Don’t get me wrong – great Maths teachers absolutely do use teaching routines. Some years ago, I witnessed an outstanding Year 12 Maths lesson where the teacher employed the thinking routine ‘See Think Wonder’ to amazing effect. Prior to her students’ arrival, this teacher had filled the whiteboard with a lengthy and complex mathematical proof that wouldn’t have seemed out place in the movie ‘Good Will Hunting’.
When the students filed in, the only instruction they received was that they were to See, Think and Wonder. What did they notice in the proof? What did they think about what they noticed? And what did it make them wonder? There followed one of the richest hours of mathematical discussion I have ever witnessed, as students looked closely, theorised, made connections, speculated, raised questions and wondered, first on their own, and then in the company of their teacher, who probed, pressed and complexified as discussions went on.
So . . . yes, thinking routines absolutely do support the development of a rich culture of thinking in the Maths classroom.
But, coming back to Rojier, the lesson he taught didn’t involve any particular thinking routine at all, but was undoubtedly informed by many different routines of thinking. One routine of thinking that clearly underpins everything that happens in Rojier’s classes is this: 'how do we use what we know to figure out what we don’t know?'
Take a look at this . . .
It’s an example of what happens in Rojier’s classroom when he teaches the skill of working out percentages without the use of a calculator. Take a close look.
Here’s another example. Can you work out what’s happening here?
You see, Rojier knows that for many students calculating 38.5% of 120kg seems, at least initially, a near-impossible task.
But once they approach this challenge with ‘How do we use what we know to figure out what we don’t know?’ in mind, Rojier’s students are empowered to work it out for themselves. And here’s the most powerful thing. It is his students who are doing the thinking, not him.
So . . . if 120kg is 100%, then we can work out 50% by halving, and 25% by halving again. And then . . . some students remember that we can calculate 10% by moving the decimal point one number to the left . . . and then 1% by doing the same thing again. And once we know 10% and 1% we can work out 5% and 0.5%, and from there, well . . . we can pretty much work out anything, including 38.5% of 120kg . . . And not only that, we see that there are many different ways to work that out . . . one by finding 30% and working our way up, and another by finding 40% and working our way down.
And through it all, Rojier is there alongside his students to press, push, probe and challenge, but never to do the thinking for them.
You see, in classrooms like Rojier’s, a culture of thinking is not something we do, but something we are. It’s never the case that “Today we’re doing a culture of thinking, but tomorrow we’ll be getting on with something else.” That’s the danger if we associate ‘being’ a culture of thinking just with the ‘doing’ of thinking routines.
Rojier’s classroom is a culture of thinking, both when he uses specific routines, and when he doesn’t, because for Rojier’s students, it is the thinking itself which has become routine.