These sessions absorbed a lot of my thinking time. It took me a long time!  I too, am a slow reader.  I am not particularly quick as a mathematical problem solver either.  But I enjoy them both equally.

Sessions 3 and 4 raise important questions for me concerning attitudes to mathematics amongst students and teachers.  I meet many teachers and parents who admit to a residual anxiety about maths, mostly born out of their school experience.  The testing culture discussed in this session is an obvious contender for the source of this maths anxiety.  Similarly, the association of speed with recall tests or other mathematical tasks is another cause of stress in the learner. The session highlights the negative effects of a testing culture, in particular, the learner's association of mathematics with testing. To the learner, mathematics and testing have become synonymous.  In test-driven environments, students become preoccupied with test scores/grades and the net result of this is often raised anxiety.  

In our school we are not constrained by such a testing culture and have worked hard to develop positive attitudes to mathematics with our students, however, negativity concerning errors still persists amongst some children and finding ways of changing this is important.  The references to the brain research were very thought-provoking; the realisation that your brain is actually growing when confused! (I need to read more about this).  An environment with a growth mindset accepts that mistakes are inevitable, especially when confronting difficult problems, and they can pave the way to conceptual leaps.

  We need to move away from maths problems that are always resolved in one lesson, or a set time, and lead students towards greater complexity and challenge.  Persistence was a theme here.  I was reminded of 'Thinking things through', by Leone Burton, written in 1984 and still a very relevant book on, in my view, dismantling the didactic contract.  The problem solving work of mathematicians working in Silicon Valley referenced in the session had to deal with 'messiness' and complexity, persist and be resilient ...  We need to continue to engage students in rich problem solving that resonates with the real world.