by Ruth Colenso (May 2020)
I was fortunate (and I think brave) enough to attend the London maths event on problem solving. It was run on Zoom with the added twist that you could choose to have a blind date. I was paired with a lovely Scottish chap and we choose to use facetime to talk, and the collaborative whiteboard website bitpaper to share our work.
The free version of bitpaper gives you one whiteboard with lots of pages but you cannot talk. The paid version allows talking. I have teacher friends who use it as a tutoring platform.
Problem solving is something you can develop and this session taught me new skills. Catriona Shearer (@Cshearer41 on Twitter) makes amazing puzzles and many of them involve variables. One skill I learnt is that you can consider special cases of this variable that make the problem easier to solve. I also used accurate drawing to get a better feel for the question or check an answer. Other people at the meeting created dynamic images on GeoGebra or Desmos.
Below are mine and Tom’s parallel methods for finding the area of the pink rectangle given the hexagon has an area of 30. As we were talking through and adapting our workings these images ended up being messy – but we could start a new image or rub it out and start again.
The lockdown has many negatives but I found this session liberating – I could start the puzzle on my own with no-one looking and without the pressure of others doing it faster than me. I could then ask help from my blind-date (using audio not video) and we were not disrupted by others. We then came back as a group and shared our solutions and then looked at other peoples’ solutions that had been shared on Twitter. It was amazing to learn other techniques – for example shearing. Different solutions can be seen here, including a dynamic image of the rectangle shearing into parallelograms with the same area.
Catriona then suggested other similar puzzles [here and here] we could look at that had a similar structure.
Dedicating time to problem solving was very good for me and I must ensure I do this more often.
Now I want to consider how I can transfer this into my teaching either during lockdown or in the future. Can I persuade my students to post their solutions in a communal space? Can I set homeworks which involve paired collaboration?
Do I include puzzles more with a theme that can develop skills, maybe with hidden circles or triangles? And the most important thing: How do I stimulate a love of puzzles?
I really enjoyed this session and I wonder whether the concept of an online training session with breakouts may become the new norm.
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