Surprise, we are told, is Ingredient X, the pedagogical Viagra that we can all add to our lessons to enthral our students and revolutionise learning. It is hard to challenge this received wisdom. Yet can surprise become so pervasive a strategy that it becomes mundane?
The Man Who Knew Infinity by Robert Kanigel tells the story of brilliant Indian mathematician Srinivasa Ramanujan. The following describes his attempts at being a tutor: "Ramanujan couldn't stick to the course material. He'd teach the standard method today, and then if his student forgot it, would improvise a wholly new one tomorrow."
The chance to hear Ramanujan improvising on mathematics is an experience many of us would die for, but for his tutees, grappling with the material for the first time, there seemed to be no solid ground, no familiar signposts that were invariant from lesson to lesson. Some students (the more gifted ones) were inspired by Ramanujan; others grew irritated by his improvisatory approach and sacked him.
I wonder if the problem can be "too much surprise". Some of my students find A-level maths hard. Camilla experiences wave after wave of surprise each lesson, as the number of ways in which she can fail to understand seems to grow exponentially. She sits next to students who do understand, who greet yesterday's formula as an old friend. Camilla struggles to construct questions that will not betray her complete at-sea-ness in too embarrassing a way. While she is battling to do this, she is missing the point of the next piece of maths.
I do believe in surprise, but my responsibility as a teacher is to manage it a little. The aim is to create a gentle shock, where the surprise of seeing one's mathematics exposed or confirmed is neither "failure" nor "success", but a way to grow.
Jonny Griffiths teaches maths in a sixth-form college.
Get to the root of pupils' problems with fractions using itjohn1's PowerPoint.
Help pupils conquer multiplication and division with the Gattegno chart and louordman's handy guide.
In the forums
Join a discussion in the TES maths forum about whether it is valid to use sudoku, origami, abacuses and tangrams as extension work.