# 300 minutes of Tom

Tom, study-partner-in-crime, kindly came in for a day to work with the sixth form students, 300 intense minutes of A level maths. This is the FIFTH time he has worked in schools with me – such kindness (including last summer in Cambridge and last term in London).

Some thoughts:

• When Tom is graph-sketching, he draws in multiple possible versions of what the line could be. Thinks a while (often fairly loosely – “it becomes very very very big” rather than bothering to use any actual numbers), decides on the correct version, and discards the others. Excellent drafting process.
• When talking about problem-solving, L said “when you started with us in Yr10 I thought it was trash. Now it’s amazing”.  I wonder what changed? Is this an inevitable slow conversion to a new way of thinking about Maths? Something to explore more.
• I briefly mentioned how you could use the power series expansion of e to define how to do “e to the power of a matrix”.  W exploded – “Here is circle of nonsense that I accept” she shouts as she draws a small circle on the table. “Square root of minus 1, that’s in here. Infinite series, that’s in here. But a number to the power of a box?! That is way over here! You need to get your ideas and drag them into my circle!”. Hilarious, and so fascinating that she now is completely used to such ridiculous things as complex numbers. The ideas don’t change – it is her circle that simply expands as nonsense slowly becomes nonsense that she accepts.
• In the afternoon we explored Kepler’s model of the solar system – spheres within polyhedra within spheres within polyhedra… The kids loved struggling through the three-dimensional thinking. Found the problem in an excellent collection of problems from Stanford University.

15 minutes after the end of the day, the students still refused to leave. A good sign?