One of my best maths lessons was given by the pupils, and was more like 60 lessons.
It was a trigonometry class for 15 to 16-year-olds studying the sine and cosine rules and area of a triangle for their Standard grade exams (the Scottish equivalent of GCSEs).
There were 30 pupils and I was experimenting with some co-operative learning strategies. We had already gone through the work quickly and this lesson was to consolidate the learning.
I asked pupils to draw a numbered clock face. They were given five minutes to circulate and "arrange a date". So if Jeannie meets Johnny, and they both have 1 o'clock free, they write each other's name on the piece of paper.
Continue until the clock face is full. Pupils cannot make two dates with the same pupils. This idea, which can be noisy but good fun, forces pupils to work in different pairs so they co-operate. So for the rest of the lesson they might work with their 3, 5, 6 or 9 o'clock "dates".
To break the ice, I split the pupils into pairs and, just to get them in the mood, I got them to talk about something daft, for example, their best Christmas present.
They had a minute to speak to their partner, and then reflect back. This allowed me to discuss the importance of listening skills.
Pupils were then asked to find, say, their 9 o'clock partner. They are given a minute to teach their partner about the sine rule, and this allows the whole class preparation time. Then I tell them who goes first. The partner has to reflect back once the minute is over.
They are sent on to two more dates, in a similar fashion, to teach each other the cosine rule and the formula to calculate the area of a triangle.
The good thing about this lesson is that there's nowhere to hide. I let pupils know that anybody in the class might be asked to stand and deliver a mini-lesson to the group.
If they didn't know the content before, they had an incentive to listen to their peers during the mini-lessons. Using the teacher's sixth sense I knew which pupils I needed to "randomly" choose to deliver to the whole class.
Fifteen minutes in, 60 mini-lessons had already taken place. The pupils were ready to solve some further problems.
The atmosphere in the class told me that the pupils were glad to be there, and were enjoying the lesson. It also ticked some theory boxes:
- There is activity as pupils walk around the room and have stand-up discussion.
- The pupils are talking about maths: it is satisfying overhearing the "lessons" as I circulate the room.
- The pupils are teaching each other (and retaining 90 per cent of the content).
We got though this topic in a week, confident of retention, compared with two weeks in previous years, not confident of retention.
Having taught for 10 years to neat rows of desks, it is refreshing to take some risks and hear the buzz of activity.
And the results? We must have done something right. It was the best set of exam results I've had.
Alastair Mills is principal teacher of mathematics at Brechin High in Angus, Scotland.