Of late, I have been having some very productive conversations with Jen Brewin, the author of the last post on my blog. She recently mentioned a nice analogy that I have decided is worth sharing, especially because it goes some way to explaining my scheme of work, and some of Jen’s blog post comments.
We both taught at Highgate School and although we only overlapped by one year, we both experienced the same ethos. In Jen’s words:
…as a teacher in this department, I was being given a great responsibility: to join in the telling of a story. This story was one that all of us were in the process of revealing to our pupils, and it was one that was revealed to them over the course of their five (or seven) years at the school.
Everyone who has taught maths at Highgate (or Westminster, where it arguably began… that’s for another time) knows the story to some extent. The extent is limited because it took many years to learn the story, and not everyone stayed for long enough to pick up the whole tale. This is partly because of the way in which it was passed on: meetings between new and experienced members of the department.
There is a written scheme, but it sadly doesn’t reflect the true brilliance of some of the ideas and leaves a lot to the imagination. So I was talking – complaining – to Jen about how it will take me so long to write up the details in order to fully explain the current spreadsheet list of topics with brief descriptions. Jen said that she feels similarly, and introduced an analogy which I rather enjoyed: a long time ago there were oral tales of a great story, but they weren’t written down until years later by the disciples. As a devout Atheist, I’m not sure why this appeals to me: perhaps because it rather aggrandises the impact of my life’s work! Anyway, as I am aptly named Luke, here is a sneak preview of a small part of my gospel:
This particular section of the scheme of work exemplifies really well another point from Jen’s blog:
The discovery that a highly selective private school would pay so much close attention to the sequencing of teaching was something of a surprise to me.
You may have been surprised that calculators were not introduced in either of the first two occasions on which we teach trigonometry. Perhaps you found it unusual to only introduce tangent first time around; what about sine and cos?
Why these unusual features? This scheme carefully takes into account the limits of children’s working memory and doesn’t try to introduce too many new ideas at once. The gaps between these topics allow time for consolidation and retrieval practice of each new element, before the next one is introduced.
Jen and I discussed how the really funny thing is that it is Highgate and Westminster that are breaking down the content into these small chunks. These are two of the most academically selective, high-achieving schools in the country. If anywhere could get away with introducing many new ideas at once, these schools could. And yet they do not.
Secondly, there is also probably a lot more detail than you’re accustomed to in schemes: for example, the unusual approach of writing the trigonometric functions as scale factors rather than ratios. This fits in beautifully with other parts of the scheme of work: percentages, proportion, similar triangles to form a thread which link different parts of the story together.
When teachers first join the department they often find the specificity of such approaches disconcerting, especially when they are quite different from what they may have done before. But with time, they usually come to realise the beauty of the links, and appreciate the luxury of teaching pupils who have been introduced to mathematics in a familiar manner. If they still don’t like it, they can argue that the department should change: indeed, many department meetings were dedicated to discussing threads from the scheme of work. There are definitely similarities between this approach and that of the departments of Danni Quinn and Greg Ashman.
So, I’ll be writing down the rest of my gospel over the next year or so, as I build my own department around it in Geneva, whilst Jen gradually introduces her version of its ideas to her school in York and there are others out there who know it too. But one big question remains: If Jen and I are some of the disciples, who is Jesus?