Reflections on a thought provoking and pedagogical changing day.
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Two radii make an isosceles triangle in a circleI have just taught my S4 National 5 class about Isosceles Triangles in Circles. On Saturday, John and Anne used the question ‘how do you know?’ and mentioned that they didn’t like the question ‘why?’. Right now, I can’t think of a lesson more appropriate to constantly ask ‘how do you know?’ than today’s lesson. Once the class were working, I went straight over to a pupil who normally finds becoming familiar with new concepts difficult. She said she was getting on fine today and knew what she was doing but I was interested in her thinking and the processes she was going through in her head. She said she would find the shaded angle by adding 77o and 77o and taking this away from 180o.
Me: Why are you adding another 77o? You only have one 77o. A: This other angle is 77o. Me: How do you know this? A: The triangle is isosceles. Me: How do you know this? A: Because there are two radius’ and they make an isosceles triangle. She said she was fine. She told me how she was going to find the first answer. However, did I really know she was fine until I questioned her further? I left her certain that she knew how she would start tackling similar questions. I approached a few other pupils in the class and had a similar conversation but on approaching two pupils who work well together and normally help each other. One said he didn’t really understand what was going on. He knew what he was looking for but couldn’t work out how he was meant to do that. He mentioned that he could see the triangle but didn’t know which sides were the same to make it isosceles. The pupil next to him said ‘yeah, but you just see it’. We talked through the properties of the circle again and drew more diagrams and he then saw why the triangle was isosceles which I was happy with. He then managed more of the questions comfortably, but what concerned me more was the other pupil who said she just saw it. Was she quickly becoming an expert or was she guessing? I was aware I hadn’t been around the class to see quite a number of the other pupils yet so moved but I think now I should have waited and questioned her further. Did she have a good understanding already or was it guessing? I’ll find out tomorrow as she’ll be one of the first pupils I speak to tomorrow asking ‘how do you know?’ until I am sure of her understanding. |
AuthorS McKenna Archives
March 2021
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