### Magic Moments 1

We set by ability in S2, and my S2 class is a small set of the least able students.

This week we were doing the old "join the dots" investigation from Standard Grade which looks at how you can generate circular patterns from simple formulas using modular arithmetic. They completed the bits I had intended them to do in a period of one hour.

The next lesson, boy A asked "can we do some of those join the dot patterns really big today - like on a poster?" My lesson plan did not involve anything to do with the investigation, but I didn't rule it out. I asked them to think individually in silence for 2 minutes about exactly how we would do what the boy had suggested, then gathered the thoughts of the class.

They identified that the two key  problems would be: drawing a really big circle on a poster and; marking 18 equidistant points on the circumference.

We had a fruitful discussion about ways of drawing a big circle, until boy B  said (obviously excited about his idea) "draw a big circle on the [interactive] whiteboard and we can hold our posters up to it and trace it." Following this, girl C  said "and we could use the protractor on the whiteboard to mark out the points around the edge."

Problem solved!  Now, this episode felt very different from usual class discussion, for at least these two reasons:

• the problem was authentic, in the sense that failure was a real possibility, and failure would mean that we would return to my original lesson plan;

• I did not have solutions to the problem up my sleeve.  I had no idea how we might proceed.

They were really fired up about making the big patterns, and a member of senior management happened to come in to the class about 20 minutes before the end of the lesson.  I made a point of telling her in earshot of the class how boy A had come up with the idea for the lesson, and how boy B and girl C had come up with the creative solutions that had allowed the activity to take place.

Boy B, who has serious emotional and behavioural problems, was obviously delighted with his achievement, and left the class with fists in the air saying "that was my best maths lesson EVER!"

A magic moment.

1. I love these sorts of lesson, where an idea comes from the moment and is allowed to develop.
A lot of preparation is involved to enable you to teach the authentic problem when you do not have a solution. The preparation is long term an non-specific.

2. I agree completely. It's like the Zen Buddhist approach to enlightenmen. You can't force it to happen - it can happen at any time, but you need to be very well prepared in order for it to happen, and very open to the moment for the opportunity not to be squandered.