Making Your Own Sense
Reflections on maths, learning, and the Maths Learning Centre.
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Gerry-mean-dering
A recent video from Howie Hua showed how if you split a collection of numbers into equal-sized groups, then find the mean of each group, then find the mean of those means, it turns out this final answer is the same as the mean of the original collection. He was careful to say it usually does ²Ô´Ç³ÙÌýwork if the groups were different sizes. Which got me to wondering: just how much of an effect on the final mean-of-means can you have by splitting a collection of numbers into different-sized groups?
Making the lie true
We at my university regularly sell quite a big lie.
Introducing Digit Disguises with a small game
Because [reasons], my game Digit Disguises has been on my mind recently, and reading the original blog post from 2019, I suddenly realised I had never shared my ideas on how to introduce the game to a whole class at once.
[Read more about Introducing Digit Disguises with a small game]
Why mathematical induction is hard
Students find mathematical induction hard, and there is a complex interplay of reasons why. Some years ago I wrote an answer on the Maths Education Stack Exchange describing these and it's still something I come back to regularly. I've decided to post it here too.
Space to enter
This is a photo of the entrance to my Maths Learning Centre. What do you notice?
Book Reading: You're Not Listening
This blog post is about the book You're Not Listening by Kate Murphy, and in particular my reactions to it from a teacher's perspective.
Four levels of listening
Listening is one of the most important aspects – no, scratch that – the most important aspect of my work in the Maths Learning Centre.
Other(ing) Explanations
Most people who teach mathematics are aware that it's useful to have alternative explanations for concepts, and useful to have different ways to approach problems.
Arbitrary mnemonics
A mnemonic is a mental trick to help you remember things.
Where the complex points are: i-arrows
Once upon a time in 2016, I created the idea of iplanes, which I consider to be one of my biggest maths ideas of all time. It was a way of me visualising where the complex points are on the graph of a real function while still being able to see the original graph. But there was a problem with it: the thing I want, which is to see where the complex points are (or at least look like they are) is several steps away from locating them.
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