Having a vision of mathematics, of what is possible in the way of appreciating and comprehending mathematics (distinct from simply gaining facility with arithmetic), is surely an important part of teaching people to think mathematically. One important aspect of mathematical vision is being aware of ubiquitous themes, and one theme that has been impressing itself […]

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In a previous blog post I outlined a very basic memory technique which works by creating a story out of to-be-remembered information. This makes the information more memorable than recalling a list of unrelated words and the technique itself requires no real groundwork, after all, you are just making up a story. Whilst impressive results […]

Read moreConsider x + y = 5 How do you know what this will look like plotted on equal aspect axes? How do your students know? Some possible ways include: using a graphical calculator display rearranging the equation and plotting three points (including one to ‘make sure’) using one intercept and the gradient of –1 recognising […]

Read moreI am able to commit a huge amount of information to memory in a very short space of time. I can memorise the order of a shuffled deck of playing cards in less than 2 minutes, a list of 240 random words within a 15-minute time limit and, given an hour, I can memorise the […]

Read moreOne of my favourite lessons on graphs is when I use the floor of my classroom as the x–y plane. I fix an origin in the middle of the floor (in order to make sure negative coordinates are included). I use masking tape to represent the axes along the floor, with masking tape dashes marked […]

Read moreSuppose you want students to gain facility in factorising the difference of two squares, and make use of this when expanding a product of the sum and difference of two quantities. A direct approach might be to invite learners to expand products of sums and differences of quantities, varying the complexity and format of those […]

Read moreSo 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 […]

Read moreThe 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 […]

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