Lesson Study in Japan is a model of teacher-led research in which a group of teachers collaborate to target a particular area for development in their students’ learning. Based on their prior teaching, the group of teachers work together to research, plan, teach and observe a series of lessons, using ongoing discussion, reflection and expert […]
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Consistent use of images supports the understanding of mathematical structures. The outstanding examples of this in mathematics have become ‘canonical’, that is part of the mathematical canon. At school level these canonical images are: number line; function graphs (thankyou Descartes); 2-dimensional combination grids (thankyou Omar Khayyam and Cayley); Venn diagrams (thankyou Cantor and Charles Dodgson). […]
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I have been floating the idea of treating key mathematics ideas as handrails for teachers and students. Recently several positive comments about this perspective have floated back to me, so I am sharing the idea with you. In mathematics, teaching key ideas could be handrails. Handrails can be held, used as guides or supports, or […]
Read moreCongratulations on surviving your first term in teaching! Now that you’re into Term 2, and are getting used to proceedings, here are three suggestions that have always served me well in my teaching: Don’t plan lessons That was a little misleading, of course you need to plan lessons. But, as you may already be realising, […]
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On meeting someone new and them discovering that my work revolves around a love of maths, here is an example of a common conversation that will then ensue: Person: I never did understand any maths at school. Me: Do you know the answer to 25 + 20? Person: Yes, of course, that is 45. Me: […]
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Euclid knew that using similar diagrams over and over again, each time looking at them in a different way, was a powerful way to see mathematics as a connected whole. Euclid used similar diagrams several times throughout his Book 2 and Book 13 to provide visual reasoning contexts for relationships between segment lengths on straight […]
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‘Practice makes perfect’ is a commonplace phrase, but like most commonplace phrases, it is an over simplification. Certainly an expert has to put in lots and lots of practice, but the psychology of successful exercising involves a particular flow of energy. The mathematics has, in some way, to inspire the learner to want to practice. […]
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