First, a bit of theory about learning. In 1980, Shlomo Vinner, an Israeli mathematics educator, coined the terms ‘concept image’ and ‘concept definition’ to highlight the difference between what students actually know about a concept and the formal meaning of the concept. David Tall, an English mathematician and educator, is credited with promulgating the term […]

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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 […]

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 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 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 moreWhen I meet people for the first time and they discover that I am a maths teacher/author I usually receive one of two reactions: ‘I hated maths at school and was never any good at it!’ or ‘I loved maths’. It is rare to find anyone in between these two extremes. Of those that hated […]

Read moreIn 2016, children will sit the new national tests for the first time. We’ve taken a look at the sample tests and frameworks to see what’s in store for them (and for you). Arithmetic Paper The introduction of the arithmetic paper is a key change for the Key Stage 2 National Tests (the mental maths test is no […]

Read moreLast time we were talking about subtraction, among other things. Let’s continue with this, and then discuss addition and multiplication. We’ll save division for another day – young people, unless they’re very well trained, find sharing difficult! I’ve suggested that subtraction may well involve partitioning the number which is being subtracted. That’s OK, but I’m not sure […]

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