### Constructivist Intervention

For a long time, Constructivism seemed to me to be a theory of learning that didn't have any direct implications for the way that I taught.

Then I read "Evidence Based Learning" by Geoff Petty and the penny dropped.

Constructivism is now the lens through which I view everything that happens in the maths classrooms in my department (on good days!).  Our rooms are full of young people constructing their own versions of maths.  They do this with the support of the environments, inputs and activities which we offer them.  They do it together with those around them, and they do it, in large part, by attempting to connect new learning to their pre-existing model of maths.

I get a kick from seeing this happening. My S4 class today was looking at extending sine and cosine beyond 90º.  It involved playing with a Geogebra applet that showed how the sine and cosine of an angle can be represented by the y and x coordinates of a point moving round a unit circle.

I used show-me boards as we discussed what we were seeing, and the whole class seemed to have picked up the concept, apart from one girl.  I brought her up to my desk, and our conversation went something like this:

"So, you're not quite understanding this yet?"
"No - it's when they go negative, that confuses me."
I brought up another Geogebra page with a simple coordinate grid.  I moved the point around, and reminded her about the fact that the x and y coordinates are sometimes negative.  Then went back to the original.
"Here [with angle 120º] the sine is positive, but the base of the triangle is going in the negative direction, so cosine is negative, just like the x coordinate."
"Oh okay that makes sense now!"
"You understand better now?"
"Yes it was when you showed me the coordinates.  That helped."