A problem with the metaphor of 'progress' in learning is that the 'journey' becomes roughly linear:
If that's extended to an individual lesson, students will be making 'progress' through the lesson. They won't all make as much 'progress' as each other.
Some of them have shot forwards, others are tarrying back nearer where they started.
And what to do with them then, in the next lesson? Put those three shoot-aheaders in a separate group? Ask them to hang around for a bit? Teach them and hope the tarriers will keep up?
Solve an unusual problem.
Because maths isn't just forwards, it's sideways too. Maybe it's like this:
Or perhaps it's like this:
But whatever it's like, it's not in a straight line. So when the students go sideways,
make sure to show the ones on the left what the ones on the right did. And the ones on the right should see what the ones on the left did too.
For me the images show the situation from the teacher's point of view. For each student their learning follows a line -tho not often a straight line.
ReplyDeleteWhen students wanted to explore a sideline I'd let them do so if it seemed to me to be productive for them at the stage they were at. If I felt they didn't have the prerequisite mental tools, I'd put make the gesture of putting the problem in the cupboard and say "For later".
It's very delicate to decide what's for "now" and what's for "later" and I don't pretend I always made the right decision. I was very aware that the course was very short (about 50h) and I had to be sure the students spent their time as efficiently as possible.
You have a whole year with the same students - what bliss!