The “Four Fours” is a very well-known little problem that encourages some creative thinking and use of the order of operations. It goes like this:

Using exactly four of the number 4, any of the operations +, -, *, / and as many brackets as you like, see if you can produce all the natural numbers […]

When doing algebra and solving equations, there is this move we often make which is usually called “doing the same thing to both sides”. For many people it is their fundamental rule of algebra. (It’s not mine, but that’s a discussion for another day.) You use it when solving an equation like this:

4x-3=13

4x-3 + 3 […]

Upon Amie and Cathy‘s request, I am writing a blog post about a problem we worked on at One Hundred Factorial recently. In fact, in order to do so I am creating a whole new category for the blog called One Hundred Factorial, so I can talk about the things that happen there. (Just so […]

If you google “fundamental trig identity” you will get many many images and handouts which all list the fundamental trig identity as:

sin2 t + cos2 t = 1

This is, of course in the wrong orderĀ and it should really have cos firstĀ then sin, like this:

(cos t)2 + (sin t)2 = 1

“But David,” you say, “it’s addition, […]

Posted in How people learn (or don't), Thoughts about maths thinking
Tagged memory, trigonometry

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In the Drop-In Centre, the majority of students visit to ask for help learning in a very small number of courses, mostly the first-year ones with “mathematics” in the title. Of course, any student from anywhere in the uni can visit to ask about maths relating to any course, and we do see them from […]

After writing the previous blog post (Finding errors by asking how your answer is wrong) and rereading one I wrote three years ago (Who tells you if you’re correct?), I got to thinking about how students are supposed to learn how to check if they are right.

It occurred to me that, at least at university, […]

Posted in Being a good teacher, How people learn (or don't)
Tagged errors, lecturing

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One of the most common situations we face in the MLC is when a student says, “I’m wrong, but I don’t know why”. They’ve done a fairly long calculation and put their answer into MapleTA, only to get the dreaded red cross, and they have no idea why it’s wrong and how to fix it. […]

Yesterday the Maths 1M students handed in an assignment question that asked them to prove a property of triangles using a vector-based argument. It’s not my job to help students do their assignment questions per se, but it is my job to help them learn skills to solve any future problem. This kind of problem, […]

Did you know that cats have scent glands just inside their bottoms that are constantly being filled with liquid and are squeezed as their poos come out, and if their poos are too skinny the glands are not squeezed enough and get over-full making them very painful and inflamed? Neither did I, until my cat […]