## Making Your Own Sense

Reflections on maths, learning, and the Maths Learning Centre.

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## Complex lines with i-arrows again

Once upon a time (in 2016), I created a way to visualise where the complex points are in relation to the real plane, and then more recently (in 2022), I modified it to become the concept of *i-arrows*. I reread those blog posts recently while updating the blog to the new website, and I got all interested in them again. Here is what I’ve been working on over the last few weeks.

## 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 *not *work 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.

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[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.