Making Your Own Sense
Reflections on maths, learning, and the Maths Learning Centre.
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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.
Running out of puzzles
Because people know I run the One Hundred Factorial puzzle sessions, they often ask me if I have a repository of puzzles they can use for their classroom, enrichment program, maths club, or their own enjoyment.
My first Maths Teacher Circle
Last week I participated in my first Maths Teacher Circle. I just want to do a quick blog post here to record for posterity that I did it and it was excellent. I choose to take the practical approach of just relating what happened.
The Solving Problems Poster
This blog post is about the Solving Problems poster that has been on the MLC wall for more than ten years in one form or another.
Quarter the Cross: Connect the Dots
This blog post is about a new variation on the classic Some resources linked from this post: problem, which I call Quarter the Cross: Connect the Dots.
Sticky operations
This blog post is about a metaphor I use when I think about the order of operations: the idea that the various operations are stickier than the others, holding the numbers around them together more or less strongly.
Replacing
I have had many people say to me over the years, "But algebra is easy: just tell them to do the same thing to both sides!" This is wrong in several ways, not least of which is the word "easy". The particular way it's wrong that I want to talk about today is the idea that doing the same thing to both sides is somehow the only move in algebra, because it's not even the most important or the most common move.
Questions with a morally wrong answer
I think asking students questions is an important part of my job of helping students succeed. Good questions can help me see where they are in their journey so I can choose how to guide them to the next step, or can help to make clear the skills they already have that will help them figure things out for themselves. But there is a class of questions that shuts all of this down immediately. Here are some examples:
Changing the goal of the Numbers game
I conscripted the game Numbers and Letters seven years ago to help promote the Maths Learning Centre and the Writing Centre at university events like O'Week and Open Day. Ever since then, it has always bothered me how free and easy participation in the Letters game is, while the Numbers game is much less so. This Open Day I had a remarkable idea: instead of stating in the rules that the goal is to achieve the target, and trying to encourage people to take a different approach, what if I just changed the stated goal! I don't know why I didn't think of it before, to be honest!
Number Neighbourhoods
This blog post is about a game I invented in February 2020, the third in a suite of Battleships-style games. (The previous two are Which Number Where and Digit Disguises.)
