What can we learn from the 2019 GCSE Mathematics papers? By Jemma Sherwood We have now seen the third year of the new GCSE in Mathematics and we are starting to get a feel for the question types, the mix of procedure and application, and the complexity of the problems. It is clearly a different […]
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I was surprised to hear that in the pre-2013 Key Stage 3 national curriculum there was only one statement about ratio, whereas in the current version there are ten statements. I was surprised because I did not remember, from my work on the development of the current curriculum, that there were so many, so I […]
Read moreLesson 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 […]
Read moreConsistent 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 morePreparing students for the new A-level exams The first cohorts for the new linear Maths A-Level exams are well over halfway through, so our attention is now turning to how best to prepare for the upcoming exams. I’d like to reflect on some of the changes in A-level Maths that I think we should all […]
Read moreFrom last year’s headline figures and the increasing grade boundaries it seems that most pupils are being prepared well for the new(ish) 9–1 Maths GCSE. A benefit of the course is that it provides welcome additional challenge for the most able pupils, preparing them better for future study. However, some teachers are concerned about how […]
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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When Euclid wrote about ratios of lengths and areas and similarity, without algebra, theorems were dependent on spatial representations. Five diagrams, all related to each other, appear in his text in various places, so I designed a ‘Match the theorem’ task in the manner of Malcolm Swan’s tasks. There isn’t a one-to-one correspondence and you […]
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Exponentiation I was prompted by a recent tweet to think more about exponentiation. The problem being posed was how to convince students that the laws of indices apply even when the exponent is not a whole positive number. There is a deep issue lurking here, which is that the more abstract the mathematics, the less […]
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