So much of the secondary and A-level mathematics curricula can be approached as if procedures are the way into mathematics, and all that is required to do well is to learn the procedures and spot where and when to apply them. By contrast, people who use mathematics work the opposite way round – curiosity about […]

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The fast-approaching Christmas break is often a period of revision for students – some may be preparing for mock exams and others taking time to recap topics covered in their first term. At this point, I find myself asking what it is all for, and how revision might be transformed into learning for the longer […]

Read moreEven now I remember how odd it felt when, at A-level, we had to find partial fractions. Instead of solving for x, we had to solve for the numerators of the partial fractions. I don’t remember it ever being explained that we were finding coefficients, the parameters of an equivalent way to write the given […]

Read moreIsn’t it amazing how quickly and easily adolescents can learn the words of a song, and yet they struggle to remember mathematical formulae? Memory in mathematics is quite peculiar. In common with learning the words of a song, once you get started, it can be surprising how much comes back, but, as with songs, it […]

Read moreEveryone is immersed in algebra because algebra is the expression and manipulation of generality. Whenever a generality is present, algebra is present too; wherever a generality is manipulated or varied, algebra is taking place. Whenever you purchase something, you are immersed in algebra. As a customer, you are interested in the final price, whereas the […]

Read moreIn my last blog I set a task, which was to find out and explain what happens in this situation: Given a set of consecutive natural numbers from 1 to 2n, choose any n of them. Arrange these n numbers in ascending order. Next to them, in one-to-one correspondence, arrange the remaining numbers in descending […]

Read moreOn 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: […]

Read moreEuclid 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 […]

Read moreNationally, 70% of Yr 7s achieved the ‘expected standard’ in KS2 Maths SATs tests. This ‘expected standard’ was decided by a panel of teachers looking at the scores from completed test papers and comparing them to the national curriculum, as well as by the testing agency. Perhaps eventually there will be more detailed information about […]

Read moreI presented some visual approaches in an earlier blog called ‘Finding Nemo’ and I am now going to elaborate one of the ideas to show the value of looking at a mathematical structure in different ways. Each of these needs learners to ‘see’ the diagram or expression in one way, and then in another way. […]

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