News: Being a good teacher
Actually, I am a maths person
I am a mathematician and a maths teacher. Therefore it is an occupational hazard that any random person who finds out what my job is will respond with "I'm not a maths person." The most frustrating people are my own students who I am trying to tell that my actual job is to help them learn maths. I used to tell them that there was no such thing as a "maths person", but I have recently come to the conclusion that this is a lie. There is definitely such a thing as a maths person because I am a maths person.
Problem strings and using the chain rule with functions defined as integrals
In Maths 1A here at the ×îÐÂÌÇÐÄVlog of Adelaide, they learn that says that, given a function of x defined as the integral of an original function from a constant to x, when you differentiate it you get the original function back again. In short, differentiation undoes integration. And then they get questions on their assignments and they don't know what to do. They always say something like "I would know what to do if that was an x, but it's not just an x, so I don't know what to do".
[Read more about Problem strings and using the chain rule with functions defined as integrals]
SQWIGLES: a guide for action and reflection in one-on-one teaching
It's university holidays again (aka "non-lecture time"), which means I'm back on the blog trying to process everything that's happened this term. Mostly this has been me spending time with students in the Drop-In Centre, since I made a commitment to do more of what I love, which is spending time with students in the Drop-In Centre. When trying to decide what to write about first, I realised that a lot of what I wanted to say wouldn't make much sense without talking about SQWIGLES first. So that's what this post is about.
[Read more about SQWIGLES: a guide for action and reflection in one-on-one teaching]
One reason I'll still use pi
Every so often, someone brings up the thing with tau (Ï„) versus pi (Ï€) as the fundamental circle constant. In general I find the discussion wearisome because it usually focuses on telling people they are stupid or wrong for choosing to use one constant or the other. There are more productive uses of your time, I think.
All dogs have tails
In maths, or at least university maths, there are a lot of statements that go like this: "If ...., then ..." or "Every ..., has ...." or "Every ..., is ...". For example, "Every rectangle has opposite sides parallel", "If two numbers are even, then their sum is even", "Every subspace contains the zero vector", "If a matrix has all distinct eigenvalues, then it is diagonalisable". Many students when faced with statements like these automatically and unconsciously assume that it works both ways, especially when the subject matter is new to them. This post is about a way of helping students see the problem.
TMC16 reflections from someone who wasn't there
This post is about my response to TMC16. For the uninitiated, TMC is short for Twitter Math Camp. This is a conference designed by teachers for teachers with teacher speakers, organised through the collective efforts of the Math Twitter Blog-o-Sphere (MTBoS) – a group of people who blog and tweet about their experiences teaching math(s). That description is not the best description of the MTBoS, but I'll get to that later.
[Read more about TMC16 reflections from someone who wasn't there]
A Day of Maths
Last Monday, I was invited into my daughter's Year 7 classroom to do a full day of maths with the students. It was the Best Day Ever. I had so much fun giving the students things to think about, and watching and helping the students think and talk about them.
Things not sides
When doing algebra and solving equations, there is this move we often make which is usually called "doing the same thing to both sides". Quite recently this phrase of "both sides" has begun to bother me.
Do you get tired of the same topics?
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 everywhere, but the courses called Maths 1X have between them a couple of thousand students per semester and that's a lot of people who might need help to learn how to learn.
Showing how to be wrong
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.
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