MK and Tom: Blindfolded Experts?

MK and Tom came to FM class, to tackle a graduate-level problem with the students, from the excellent Creative Mathematics.


Studying Maths and eating cake, 4 years ago in Cambridge
Leave them for two minutes and they get immersed in a problem
A cake with finite volume but infinite surface-area. You can cook it with finite ingredients, but you cannot frost it! Thanks VSAUCE

Tom spoke about finally finishing his PHD – the long journey, 8-months struggle.



From Denise
Proud Mathematician. Embedded contact knot homology and a surgery formula
What a lovely note from Tom!! Tom has been in SIX times now – what a contribution. 

MK spoke about the nervousness of waiting a week to see if her computer programe would come back and tell her good news. It did! The spine of her research complete! Let’s turn it into a poster and flog it in Marseilles!

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New Knowledge!

Let’s get problem-solving. In the introduction, Alan Beardon says:

Perhaps the main difference between  these two views is that in research obtaining a prescribed answer is not the primary aim; the aim is to reach some conclusion and, if necessary, we should be prepared to change the problem in order to reach a conclusion.

Great. Each Mathematician worked with a group of 3 students. Nobody had seen the problem before. I had noticed that the FM students, when working collaboratively with their non-FM peers, often took the lead. Tom, MK and I therefore tried to model how to nudge without dominating. MK, when she spotted incorrect conjectures, would subtly think of examples to explore that would highlight misconceptions (rather than a blunt “I think that’s wrong”).

Gateway to gradate-level research!
Ifte expanded to 2d grid – Tom started thinking about tiling
MK loves a good tree.
I love a matrix, and my group love proof by contradiction. We also used our hands to represent switches – concrete is useful. 

How could an expert work meaningfully alongside learners? Shirley grabbed the pen out of Tom’s hand in excitement to make a point and illustrate it – great that she felt comfortable enough to challenge the expert. The students all felt, when reflecting, that we were learning with, rather than leading, which is great. But how could we formalise this?

  • Expert is blindfolded for the whole problem? This would ensure no pen-domination, and, excellent communication from the team. It would also be a genuine challenge for the expert (since we often rely heavily on diagrams)
  • Expert has hands tied behind back? This would just ensure no pen-domination
  • Expert wears a gag?
  • Expert has talk-cards, and spends a card every time they say something?

Obviously these are all very crude, but sometimes that is okay?



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