If we watch this teacher at work we see that: . . . * he sets the situation, giving essential information, but beyond that tells the children nothing. * he obtains as much feedback from the children as possible, by observing, asking questions, and asking for particular actions. * he works with this feedback immediately. * except on rare occasions he does not indicate whether a response is right or not though he often asks children which it is. Triangles can be approached algebraically (although this is complex!) in a similar way to rectangles - e.g. look at right angled triangles, fix the width and call the height n. Equating area and perimeter will lead to some complex algebra - but accessible and useful practice for Higher Tier GCSE students, e.g. after going through one example with a class they could try and repeat for different fixed values.
© ATM 2009 • No reproduction (including Internet) except for legitimate academic purposes • email@example.com for permissions. WATCHING THE TEACHER AT WORK Laurinda Brown and Alf Coles share with us their working relationship. If we watch this teacher at work we see that: ... The lesson write-up below is written in a style to • he sets the situation, giving essential informa- disseminate the findings. tion, but beyond that tells the children nothing. In the first issue of MTi (July, 2009) there will • he obtains as much feedback from the children be a video of Alf teaching and a lesson write-up of as possible, by observing, asking questions, and the rich task within which the sequence took place. asking for particular actions. We wonder whether people who have read our • he works with this feedback immediately. writing in MT will see what they imagined from • except on rare occasions he does not indicate this classroom, and we are hoping some of you will whether a response is right or not though he write in reflections after seeing this video, on the often asks children which it is. interconnections between text and image. (Wheeler, 1970, p.27) When we met in 1995, Alf was starting his teaching Equable shapes career and Laurinda was a teacher educator researching the professional development of Starting point teachers. Our work together has recently been Draw these two rectangles on the board. marked by the publication of a book, Hearing Question: What is the same or different about Silence. When we thought about the invitation to these 2 shapes? outline what we did together, it has felt like a journey punctuated by ‘watching the teacher at work’. In 1995, Alf ’s ideal was to emulate the teacher in the article by David Wheeler quoted above, but he had no image of how that looked in practice. Alf also talked about reading MT articles and ‘all the things that these people had just got their classes doing anyway, things like discuss in pairs and bring it back to the class and I’m thinking, how on earth Someone will comment on the rectangles being different do you do that?’ sizes. They may mention area and perimeter. If not, Early in our work Laurinda taught one of Alf ’s introduce these terms as ways that mathematicians classes, with a focus on using strategies for ‘sharing determine the sizes of shapes. responses’. Later in various projects we co-observed videotapes of lessons, with different groups of Add underneath each rectangle, A=
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