Thinking Like a Mathematician

A two part question to determine if you "think like a mathematician," from Prof. Eugene Luks, Bucknell University, circa 1979.

Part I: You're in a room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on the floor. How do you make hot water for tea?

Answer to Part I: Put tea kettle on stove, turn on burner, heat until water boils.

Part II: Next, you're in another room that is empty except for a functioning stove and a tea kettle with tepid water in it sitting on a table. How do you make hot water for tea?

Non-mathematician's answer to Part II: Put tea kettle on stove, turn on burner, heat until water boils.
Mathematician's answer to Part II: Put the tea kettle on the floor.

Popular posts from this blog

Planning for Learning or Planning for Behaviour?

Several months ago I found myself sitting beside a quite senior staff member from one of our colleges of initial teacher education, who complained to me that her student teachers all seemed to be obsessed with behaviour management.

I was flabbergasted, but failed miserably to put together a reasonable argument for why the students were quite right.

That conversation came back to me today as I taught a maths cover class, who were learning about the graphs of linear equations.  The class had some lively characters in it, and they were clearly struggling with the central concept: that a line on a coordinate diagram represents all the points where a particular linear equation involving x and y is true.

As they explored this concept through a series of activities, many of them experienced confusion and frustration. These are normal, healthy emotions for learners. We were able to stick with these challenging experiences partly because the pupils were operating in an environment in which mis…
Read more

My Leadership Story

I have volunteered to "share my leadership journey" for ten minutes before leading a discussion with other middle leaders at a SCEL event in Edinburgh.  This blog post is a rehearsal of those ten minutes, and I would gratefully appreciate any constructive feedback.
I have a leadership story rather than a leadership journey to share. This is the story I tell myself about how I got to where I am now as a leader, and about where I might go next. It is very subjective and selective. Nonetheless I think it is worth sharing, because this is the truth I inhabit. You also have stories you tell yourself, and you inhabit your stories every day of your professional life. It is sometimes easy to recognise these stories in others - the colleague who sees themselves as the victim of unreasonable burdens regardless of changing circumstances or another who sees themselves as blessed and lucky no matter what misfortunes befall them. It is much harder to identify the stories we tell ourselves,…
Read more

And what if we don't achieve our dreams?

"If A then B" is logically equivalent to "If (Not B) then (Not A)". For example "if a shape has three sides, then it is a triangle" is logically equivalent to "if a shape is not a triangle, then it does not have three sides". The second statement in quotes is called the contrapositive of the first statement in quotes. Logically speaking, they are identical statements. If one is true, the other must be, and vice versa. In this case, they are both true statements.
A commonly touted inspirational message we deliver to young people can be distilled down to "if you do all the things right that are within your power, then your dreams will come true". Consider its contrapositive.
Read more