Better student talks

Having a mathematical idea is only one part of the equation (excuse the pun!); we also need to be able to communicate it. A good example is Fermat writing next to his conjecture that he (purportedly) had a proof that the margin was too small to contain. If Fermat really did have a proof, then he could have saved mathematicians 350... Continue Reading →

Another party puzzle

More party puzzles! This one is from a thoroughly-recommended book, Puzzle Based Learning1. Mr and Mrs Smith invited four other couples for a party. When everyone arrived, some of the people in the room shook hands with some of the others. Of course, nobody shook hands with their spouse or themselves, and nobody shook hands with... Continue Reading →

Ramsey’s party problem

I love games that require no special equipment because they can be played at a moment's notice. This is one of my favourite pen-and-paper games. It is played on the complete graph K6. In other words, a board with six dots where each dot is connected to every other dot by a line. Although the game-board can... Continue Reading →

Tracy Zager’s word clouds

Over the past year I have held this image in my head as a reminder and a motivation. It comes from Tracy Zager's 2015 NCTM ShadowCon talk 'Breaking the Cycle', which is mandatory viewing. (If you have limited time, stop reading this post and go watch Tracy's talk instead.) At the same time that Tracy was giving her talk... Continue Reading →

Friday Five: #4

Turns out that Desmos already posts a 'Friday Five'. Wonder if I subconsciously stole the name from them? I'm posting this early (although it is Friday here) because I have a hundred little things — and one big thing — to do today. Megan Schmidt (@veganmathbeagle) is wowing us on twitter with her number spiral investigations. See below. Megan's... Continue Reading →

The tea towel of multiplication

(If you want to understand the title, you can just skip straight to the end.) When I think back on the inflexible way in which I remember being taught maths, I am often surprised that I became a mathematician. I don't mean this to be unkind to my teachers — I enjoyed maths in school and I liked my teachers —... Continue Reading →

Focusing on the relationships

I'm feeling a bit punchy tonight as I write this. You might find it preachy, confronting or self indulgent. Be warned. The most eloquent and uplifting writing about good teaching that I've read is by Francis Su: 'Lesson of Grace in Teaching'. You should probably read that instead. Forget curriculum, student thinking, feedback. Next year I'm focusing on... Continue Reading →


Whenever I say this, the unfinished sentence in my head is 'Fold-and-cut, baby! Fold-and-cut.' I am totally weird. The fold-and-cut theorem states states that any shape with straight sides can be cut from a single sheet of paper by folding it flat, possibly with many folds, and making a single straight complete cut. I have been impatiently waiting to try this... Continue Reading →

My motivating images

This morning I read Sara Van Der Werf's post, 'The Story of 2 Words & One Simple Tweak to Get All Students Talking'. Her post is great, and you should definitely check it out, but what prompted me to write this post was the photo I've included below. Sara has it pinned up near her desk. If I walked in... Continue Reading →

Why students might choose the textbook

(In the same week that I wrote this, Carl Oliver posted on a similar experience. I recommend that you go and read 'CLOG: The chose the worksheet?!?!' for some interesting reflections.) I like to give my university students choice about the kinds of questions they tackle in tutorials. Usually it's as unsophisticated as grouping questions by type and giving them the choice... Continue Reading →

#QuarterTheCross and @FractionTalks

Something that has captivated me from the Maths Twitter Blog-o-Sphere (#MTBoS) in the last few months is Quarter The Cross. It is a classic low-threshold high-ceiling task. And, the more you experiment, the deeper and richer your mathematical understanding becomes. This can lead to some quite sophisticated and beautiful solutions. The solutions above are six of mine. They are rather... Continue Reading →

Friday Five: #3

On Fridays I plan to list five highlights from the #MTBoS and the internet at large. I could have discovered them in the last week, or the last year, but for some reason want to share them with you this Friday. I know it might be Thursday in your part of the world when I post this; what can... Continue Reading →

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