Colin Foster's Mathematics Education Blog

Not all commonly-used representations of number are necessarily equally helpful. We shouldn't just assume that anything 'visual'...

How accurately do things need to be  drawn  to evidence conceptual understanding? When are accurate drawings helpful and when are they unnec...

Can a factor be a fraction? People sometimes agonise over whether a fraction such as $\frac{2}{3}$ can be called ‘a factor’ of another numbe...

I have a tendency to assume that concepts get more difficult as the number of dimensions increases. Length is pretty straightforward, surely...

Sometimes a superficially small tweak to a task - changing just one little thing - can dramatically alter it, and mean that a lot more think...

People often say or imply that when teaching mathematics 'open questions' are simply better than 'closed questions'. Instead...

Do you have tasks that you use in lessons that "can't fail"? Favourite tasks that you've used many times and that always s...

Einstein is supposed to have said that “Everything should be made as simple as possible, but no simpler”. Mathematics questions often say ...

How do you introduce a new mathematical topic or concept? Do you give students a task to do, or do you start by explaining everything? I thi...

I have been very inspired by Leslie Dietiker's way of thinking about mathematics lessons as 'stories' (see Dietiker, 2015). In t...