News: Thoughts about maths thinking
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.
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.
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.
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.
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.
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.)
Roosters don't lay p-values
I've just started teaching an online course, and one module is a very very introductory statistics module. There are a couple of moments when we ask the students to describe how they interpret some hypothesis tests and p-values, and a couple of the students have written very lengthy responses describing all the factors that weren't controlled in the experiments outlined in the problem, and why that means that the confidence intervals/p-values are meaningless. When all we wanted was "we are 95% confident that the mean outcome in this situation is between here and here".
Which Number Where
Last year I invented a game called Digit Disguises and it has become a regular feature at One Hundred Factorial and other events. But before Digit Disguises came along, there was another game with a similar style of interaction that we played regularly, and this blog post is about that game. The game is called "Which Number Where?"
