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

My first post of 2018 is a record of some rambling thoughts about remainders. I may or may not come to a final moral here, so consider yourself warned.

What has prompted these ramblings today was reading this excellent post by Kristin Gray about her own thoughts on division and remainders. In that post, I saw […]

Yesterday I talked about one of the common responses to people finding out I am a mathematician/maths teacher, that of saying, “I’m not a maths person.” The other common response I get is, “I don’t have a maths brain.” (John Rowe mentioned this in his comment on the previous post.)

This is how I reacted last […]

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 […]

Posted in Being a good teacher, Thoughts about maths thinking
Tagged identity, maths, my life

15 Comments

15 Comments

Two books I’ve read recently have encouraged me to investigate my memories from childhood. In Tracy Zager’s “Becoming the Math Teacher You Wish You’d Had“, she urged me to think about my maths autobiography to see what influenced my current feelings about maths. In Stuart Brown’s “Play“, he urged me to think about my play […]

Posted in How people learn (or don't), Thoughts about maths thinking
Tagged geometry, my life, play

1 Comment

1 Comment

In the online resources for Becoming the Math Teacher You Wish You’d Had, Tracy Zager provides information about the benefits of writing a “math autobiography”. I really have tried to do this, but I am having a lot of trouble organising my thoughs and memories. However, I reckon I can track some of my memories […]

Posted in How people learn (or don't), Thoughts about maths thinking
Tagged applications, my life

4 Comments

4 Comments

There is a procedure that people use and teach students to use for finding the inverse of a function. It goes like this (this image comes from page 10 of this document from Edexcel, but this pic is from Jo Morgan’s blog where I first saw it):

My problem with this is that it doesn’t make […]

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

3 Comments

3 Comments

What trig subsitution is

Trig substitution is a fancy kind of substitution used to help find the integral of a particular family of fancy functions. These fancy functions involve things like a2 + x2 or a2 – x2 or x2 – a2 , usually under root signs or inside half-powers, and the purpose of trig substitution […]

It seems like ages ago — but it was only yesterday — that I wrote about differentiating functions with the variable in both the base and the power. Back there, I had learned that the derivative of a function like f(x)g(x) is the sum of the derivative when you pretend f(x) is constant and the […]

In Maths 1A here at the University of Adelaide, they learn the following theorem (this is taken from the lecture notes written by the School of Maths here):

It 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 […]

Last week, I helped quite a few students from International Financial Institutions and Markets with their annuity calculations, which involve quite detailed stuff like this:

There were several small issues a lot of them had, which combined to stall their calculations. One of the more important problems was about how the calculator interprets what they type […]