There are two main thoughts that I'm left with from the day.
Firstly, that beauty is important in an image. I chose to redescribe the part of the circles film that had given me an affective charge. That charge was very significant.
Secondly, that seeing changes happen provokes questions. My need to know was excited. (But the rate of change is important. Some of the circle movements were too fast for me to get any sort of handle on. One needs an entry point into the challenge.)
Piers Messum
Twenty four hours later and my thoughts are very much on the clash between my attempts to recount what it was that was in my imagination – the mental image I had evoked upon my distracted viewing of the circles film – and the image my colleagues thought they knew I was attempting to describe. Instead of an attempt at construction of the image I was proposing it felt like there was an attempt at correction to make me describe the image which was already in their own imaginations, having experienced the film in a different way – as it transpired, correctly!
Firstly, that beauty is important in an image. I chose to redescribe the part of the circles film that had given me an affective charge. That charge was very significant.
Secondly, that seeing changes happen provokes questions. My need to know was excited. (But the rate of change is important. Some of the circle movements were too fast for me to get any sort of handle on. One needs an entry point into the challenge.)
Piers Messum
At the recent working group day, it was good to work with others, many of whom I had not met before, in a very supportive exploratory environment. I was enabled to gain new insights into some mathematical situations: for example, in the morning, a film made me see circles as I had not seen them before, particularly the sequence about generating circles from a pair of tangents.
But for me I think the most interesting part of the day was the time we spent considering the Leapfrogs poster Circle Packings. I hadn’t look at this poster for 20 (or maybe 30!) years, and it had never been one of my favourites but, sitting where I was and looking at the poster on the floor, I first saw lovely lines of stars I hadn’t really seen before. Then I listened, and contributed, to the discussion about what we saw in the poster. People spoke of six-sided holes and three-sided holes. After a while, someone spoke about five sided holes, to some gentle laughter – most of us ‘knew’ there were no five-sided holes! The speaker corrected himself, saying he meant six-sided holes, of course. But then later I, and I think many others, were taken by surprise to find there were indeed five-sided holes to be found. A wonderful insight into the poster and into how limited our vision can be without others to help to change our awareness of we see.
I look forward to many more such learning experiences in future meetings of the group.
Anne Haworth
Twenty four hours later and my thoughts are very much on the clash between my attempts to recount what it was that was in my imagination – the mental image I had evoked upon my distracted viewing of the circles film – and the image my colleagues thought they knew I was attempting to describe. Instead of an attempt at construction of the image I was proposing it felt like there was an attempt at correction to make me describe the image which was already in their own imaginations, having experienced the film in a different way – as it transpired, correctly!
How does this relate to my experience in the classroom and that of my unwitting victims/students? We each experience the world in our own ways and bring with us our own memories, awarenesses and sensations - whilst sometimes shared, always unique. Are my classrooms a battle of wills where I attempt to meld an experience into the way in which I envision it or do I seek to find out how it was experienced by my students and develop from there? How can than this be developed if there are thirty two different experiences?
David Lawrence
2(a+6)
How would you write this expression?
I have been working on reading and writing expressions a lot this half-term and using Grid Algebra in particular. The other day I was writing some expressions involving brackets by hand and not in front of a class and became suddenly aware that I was beginning by writing the a first. This was striking for me because I think I have always thought of this expression as something like ‘2 ‘lots of’ a+6’ or ‘2 times a+6’. Possibly because I have been thinking about eventually wanting learners to appreciate equivalence with an expanded form and although I have often worked on building expressions up, this is the first time I have noticed myself not writing from left to right as if some shift has occurred in me where I see the expression more as ‘a add six, times two’ at the moment. I am conscious that I can slide between the two images of 2(a+6) if I attend to it and this is something I would want my pupils to be able to eventually do but I was interested by the subconscious change in my writing of it.
As I was interested by it I asked some colleagues to write the expression and we compared similarities and differences. We then considered some other expressions such as ,100-a and 2(6-a). Dave then wrote an equation and we tried to read it starting from different places. This also raised new awarenesses for me. In particular, the language of ‘however many times seven goes into 6 – t...’
Tom Francome
On returning home today from the Science of Education meeting I have been reading the recent publication from Educational Solutions “The Gattegno Effect - 100 voices on one of history’s greatest educators” and the powerful idea of the ‘subordination of teaching to learning’. This is a phrase I have lived with for many years as a guiding idea in my own teaching and I have been considering the extent to which I embodied this today. I am particularly struck with a moment when I feel I did not subordinate my ‘teaching’ to the learning of others. In one of the last activities of the day, I laid on the floor a poster (created by the ‘Leapfrogs’ group) of circle packings. There felt like a rich discussion of what participants saw – and my invitation was for us to work on ‘seeing the same’, i.e., it was each individual’s responsibility, if something was said that they could not see, to ask a question. At one point there was an offer from a member of the group to see a square formed by the centres of four circles. I was aware of an urge to pursue this idea as, in my work on the poster, I knew that there was a richness to the poster from linking it to tessellations of regular polygons (which linking can be made by ‘seeing’ the shapes formed by joining centres of circles). I hesitated, someone else offered another thought and I chose not to pull the conversation back – laissez faire. As I reflect now, I see this as an abdication of my role of “teacher” in that session. Part of subordinating my teaching to the learning of others is a commitment to act when the moment arises.
Alf Coles
No comments:
Post a Comment