Taking a horse to water….
After last week’s billing I was expecting Khan to be pulled apart but it seems to me that Michael Pershan’s critique is more about the US (and general Western?) teaching approach than Khan per se. It left me wondering why Khan was particularly in the firing line for his critique.
As to what I thought about his, and Andrew Blair’s, actual argument about efficacy in maths teaching. I liked the idea of problem solving approach. In my limited experience I have seen a mix of problem solving and the more here’s an example and lets now do some practice. I think learners I have seen would be up for this type of approach but would need to understand that doing an inquiry (or taking on a problem without the rules being given) they have the permission to be creative, to be different and to be solution focused.
And I think that this is where I see one of the rubs. I have been taught some very solution focused ways of getting to a answer which are (rightly) now considered inappropriate methods as they are very rules based and do not help the learner form solid foundations for other more complex work. So maybe there needs to be freedom on the other side too. And instead of being worried about how a student arrives at a solution the teacher is free to ignore the method used. But given all the concern about how maths is explained and taught are we comfortable that an any which way but win approach is adopted?
I suspect not. So here is a compromisy sort of comment (sorry). Lets by all means become more liberal about letting learners own the problems and the solutions but lets not move to a situation whereby all common method is lost as it seems to me from last week’s article that learning works best when the brain can move some things from the new to established thinking (through practice I recall) and surely some of that must depend on being taught some of the hows rather that ‘just’ learning them from individual problems or inquiries.
My almost final thought relates to the Blair’s argument that the idea that learning maths can be done in a correct sequence is not right. I can see where this argument comes from. The idea that the ‘right’ path can be imposed when learning is such a messy process must surely hold some truth. And yet I loved the knowledge tree that the Khan Academy uses as I see that as empowering as it sets out a shared path for teacher and learner. So if I had to choose where which side would I come down on? The knowledge tree. I don’t want to deny that any individual’s learning doesn’t follow a unique path but surely even if all I did was pose problems and set inquiries then surely I am imposing a structure but one that isn’t open to all.
PS I loved that geometry game.