Even harder sums...

La Rentrée, as the French call it, is fast approaching. I'd better get on with my list of good ways to get to the challenging stuff. These are of course obvious to many of us teachers, but then again, they are not at all as universal as they could and should be, so they're worth reiterating.

Last time I gave my three ways of making maths harder - without the useless drudgery:

1. Pick subjects that give power. 
2. Find the subjects where kids can be creative
3. Go into history and biography.

So, three more:

4.  Enthusiasm

5.  Discussion 

6.  Presentation

alder trees in the New Forest

4. Enthusiasm - the teacher's, that is. This can be squeezed out by an over-structured curriculum, and pressure to get numerical results. But when it's there it can make school something more than just school. Take this case: Roger Deakin in his brilliant book Wildwood describing what his biology teacher set up:

…Barry infected us all with his wild enthusiasm. 

Although he would modestly deny it, Barry Goater was the instigator of an extraordinary educational experiment. In a quiet corner of the New Forest he established a camp for the detailed study and mapping of the natural history of a stretch of the wild forest woodland, bog and heath surrounding Beaulieu Road by his Biology sixth form. The camp became something of an institution at our school in the relatively treeless Cricklewood. It was traditional for each generation of us sixth form naturalists to return there again and again and taste the intoxicating pleasure of exploration and discovery in the wild for ourselves. Each of us had a particular project, literally a field of inquiry, and the work we were doing was genuinely original. We learnt the scientific disciplines of botany, zoology and ecology, and we kept our eyes open as all-round naturalists. What we discovered was particular to the place, and, best of all, it belonged to us. 

Beaulieu Road was our America, we were pioneers, and the map we jointly drew and refined through gradual accretions of personal observation represented not only the complex natural ecology of the place, but also an ambitious and entirely novel cooperation between several generations of the sixth form botanists and zoologists of our school. Through our cumulative endeavours we were charting the relationships between the plants and animals of the place. But the records we kept were also a testament to our own human relationships as naturalists, biologists and zoologists. We were learning at first hand how exploration and scholarship can evolve and progress in time through cooperation and the free exchange of ideas. Small wonder that the experience influenced so many of our lives so profoundly.

There's so much in this description. But isn't it interesting how a teacher's enthusiasm can lead to "the intoxicating pleasure of exploration and discovery in the wild"for themselves, to  a world that the students discover that belongs to them?!

4. Discussion: Roger Deakin talks about cooperation and the free exchange of ideas. Ideally, it comes naturally when there's some big project that the class or group is working on. Sometimes it needs to be structured. Lots of teachers naturally use a variant of the think-pair-share strategy: students think about a question on their own a little, then they talk about their ideas with someone else, then they might share what they've arrived at with the bigger group. It gets away from the teacher questions-pupil answers routine (which is useful some of the time) where only at most one student is getting to put their ideas into words at any one time. This is important, because to know something really well, it's best if you can explain it too, and hear other people's explanations of it. And even better if you can modify your understanding as you discuss, refining what you first thought.

5. Presentation - the students that is. As I say, it's important to be able to explain something, and you get to know it more deeply in doing so. When we made factor trees last year we explained our factor forest display to the other classes who would see it.  When four girls created a beautiful mathematical square, they explained it the other classes. 

To be continued.