After observing five lessons that involved some element of peer assessment focussed on mathematical problem solving in Tokyo what have I learned?
First I should clarify that the lessons all involved students in developing a mathematical model of some reality – or situation that is easily realisable to teenage students. By this I mean, in the sense of the Freudenthal group in Utrecht, that it is some form of reality that is more or less real and meaningful to students. In one particular lesson this reality was concerned with a virtual reality character, or avatar, so perhaps both real and virtual at the same time!
The lessons with respect to peer assessment were very similar to what we might expect in such lessons in England – I feel secure in this judgement given that one of the lessons was taught by an accompanying teacher from England (and the others taught by Japanese teachers were similar in form and structure).
It was very much noticeable that peer assessment is time consuming. Perhaps this isn’t surprising as we are asking students to make sense of someone else’s mathematical thinking and decide what they were doing – and how, make a judgement about how well this matches against the learning objective in relation to the design of the lesson, then give feedback about what to do next. This would be difficult enough if it were entirely in relation to understanding a mathematical concept but given that we have been exploring problem solving process skills we are definitely in uncharted waters. So it all takes some considerable time and requires a great deal of support. More than we saw in any of the lessons in Tokyo.
Indeed, given that the amount of time and support students will need with such peer assessment we need to be very convinced of the long term value of investing so much effort on the need to involve our students in this. Our ultimate aim in working on peer assessment in this way is that it will help students understand how best to monitor their own work and reflect on how to improve it. This seems a very useful, if not essential, skill in problem solving and therefore it does seem worthwhile to invest the time and energy in lessons that develop peer assessment in this way.and if this is the case we have to provide time and space in lessons to work on this – and to have a conversation with the whole class about how to support each other in making progress.
During the post-lesson discussion if one if the lessons I was reminded of this YouTube clip about Austin’s Butterfly. In this Austin makes huge progress as he drafts and redrafts his drawing of a butterfly to get closer to reality. We are a long way from being able to assist a problem solving Austin in becoming more proficient with his problem solving but that’s what we – and Japanese colleagues are aiming to do.
For more information about our current work see here.
A little more detail about lesson study by our colleagues in Japan can be found here.