Wrestling with Infinity, in Newham

I spent an enjoyable if busy week thinking with a bunch of prospective A level students about Infinity. We chose the topic of the endless because it is not explicitly A level content, but is beautiful, important, broad and relatively accessible.


Key reflections

  • The problems we gave the students were challenging, probably slightly too much so. At the beginning of the week they were struggling to cope, but by the end we had noticed a significant improvement in problem-solving skills. Students were able to stick with a problem for more time (2.5 hrs on the second day, on one problem, was maybe too much of an ask), and were more comfortable collaborating with each other.
  • I noticed (as did other teachers) a shift in my teacher personna. No longer requiring to behaviour-manage (or maybe that is wishful thinking – a few were misusing their phones for example), I was able to focus more on the mathematical concepts.
  • There are two types of problem-solving. The sniffing dog follows his nose, working forwards (sometimes haphazardly), doing what he can do, until a pattern forms. The wise elephant thinks carefully about what she wants to achieve, and then works backwards from this. The students picked up this language from the week, and agreed that excellent problem-solvers were able to use a synthesis of the two approachesjzMNRoVrqUq7gSJsRVv-wam4Qm7bS56dzbSF8-3q3vxMVbYKrNnIl2m7ZWhUaL37nbX2xFYOtuP42T4DJDVBGlsteEN3doEoaiM0hn8YdZN2Zg4cm9TExA42vka_Hh1_PnvlG2Wg
  • All maths teachers descended into an afternoon session for the Festival of Problems. We used some outstanding questions (from Westminster School, curated by Kings Maths School), and had a grand time. If the questions are good enough, then minimal structures are needed.

Feedback from students:

  • Long open problem-solving sessions were amazing (contrary to my perception that the students were burnt out by the end of it, most of them said they loved being able to spend so much time on one thing).
  • Don’t ask us to read chapters on things we haven’t learnt about yet (almost all said this)
  • Introduce more practical hands-on sessions


A few pics of the week:

We had an entire floor to work with, which was amazing.

The lecture theatre
The Problem-solving Lab
KS talking about types of numbers
Organic flurry to a whiteboard when Ashwin discovers a pattern


Understanding why infinity squared is still infinity…
Getting to know each other…
Independent study: harnessing the power of Youtube.




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