# Category: Thoughts about maths thinking

Anything about the thinking processes required to learn and do maths, especially those about problem-solving and communicating.

#### 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.
Some reasons why students find mathematical induction difficult.
These come from a […]

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#### The complex points on a line using i-arrows

Introduction
The Cartesian plane is pretty cool. You think up an equation like y=x²+1 and find all the points (x,y) whose coordinates satisfy it, and you get a shape (in this case a parabola). Different kinds of shapes have different kinds of equations, and finding the places where shapes meet becomes solving equations simultaneously. Geometry becomes […]

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#### Where the complex points are: i-arrows

Problems with i-planes
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 […]

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#### 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. The most current version of it in handout form is this:

I’ve been meaning to blog about it for some time, but […]

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#### 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.
The idea begins with the fundamental idea in arithmetic, that maths working proceeds by replacing something with something […]

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#### 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 […]

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#### 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. […]

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#### 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.)
NUMBER NEIGHBOURHOODS: A game of analytic deduction
Players:

This game is for two players, or two teams.

Setting up:

Each player/team choose six different numbers between 0 and 10 (not including 0 […]

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#### 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 […]

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#### 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 […]

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