When and where is algebra?

Everyone 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 […]

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The problems of problem-solving

In 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 […]

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Euclid knew about diagrams

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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Now you see it; now you don’t

I 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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Exercise is good for you

‘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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Unconventional units of measure

Units of measure

Some people are fantastic at estimating measures, well certain measures. I could estimate someone’s height in metres and centimetres and I would be equally happy to use feet and inches.  I suspect the generation above me would prefer to use imperial units on the whole, and the generation below me seem able to do a […]

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Eliminate the Negative

I have been thinking about negative integers and wondering how anyone I taught ever managed to understand them. Many did, but when I am asked, by KS2 and KS3 teachers, ‘Is there a good task for discovering the rules of negative numbers?’, I find it impossible to answer. There seem to be a few popular […]

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