What do students know about functions?

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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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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Equation building

When 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 […]

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Mental Mathematics – Part 2

Last 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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