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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