A look at my new teaching and learning toy
I started writing about multiplication methods yesterday (read Part 1 here), but waffled for rather longer than necessary, and as a result, didn't actually get to discuss what I originally wanted to, namely which from grid, lattice (Gelosia, Chinese, Napier's etc) or long multiplication we should be teaching as a method to pupils.
In one of those weird twists of coincidence, I went on some subject leader training today run by Sheila Eastwood, and we ended up discussing - you guessed it - exactly what I blogged about yesterday, and how this fits in with the idea of mastery in mathematics. We pretty much concluded as I did yesterday; at the moment, no-one really knows what will be allowable as a method on the new GCSE papers.
So in my follow-up post, I thought I'd look at pros and cons of all three methods on the assumption that pupils are allowed to use any in the new GCSE exams, and then consider implications for only allowing long multiplication at the end. Any claims I'm making here are backed up by absolutely no proper research and are mostly anecdotes from my classroom, but I can't seem to find much independent research on multiplication methods.
As a department, we seem to have spent the last six months debating exactly which method is OK for multiplying large numbers. Personally, I learnt column/long multiplication at school, and got pretty good at it, although to be honest, past about midway through Year 11 I can't recall a situation where I've really had to accurately multiply two large numbers without a calculator - but that's another debate. Teacher training introduced me to the grid method, and I immediately went "ooh fantastic!" and taught that for three years without any critical thought as to whether or not that's even the best method.
Then I did this activity from the NCETM and several of my Year 7s decided they really liked Gelosia multiplication. Some of them had previously been really unsuccessful with grid method - although they understood what they were doing, they invariably lost the odd zero along the way, or made a pig's ear of lining up the addition calculation at the end. I told them to go with Gelosia if they understood it.