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I had a meeting with an international student in the MLC on Friday who has having a whole lot of language issues in her maths class.

She was from the USA.

Yes, the USA. Her problem wasn't the everyday English; it was with the different terminologies for mathematical things here compared to her experience where she comes from. Her only experience with vectors was in physics where a vector is a quantity with magnitude and direction, whereas in maths class here, a vector is usually just a list of coordinates. She knew how to find a derivative, but had never heard the word "differentiate" used for that action. She had only ever used the word "anti-derivative" for what we call an "integral" most of the time.

I was talking through the transpose of a matrix (something else new to her) and how it interacts with other operations on matrices, and how since it's normally written as a power it takes precedence over nearby multiplications like powers do. She asked me if, here in Australia, we still use the same order for what is supposed to be done before other things. I said, yes, we do, and told her that most local high-school students use the acronym BEDMAS to describe that order.

She wrote underneath the acronym familiar to her: PEMDAS. First she focussed on the fact that one had DM and the other MD, but reconciled that quickly saying, "Well I suppose they go in the order they come and so it doesn't matter which way around they are." But she had no idea what to do with the B.

I told her the B stood for brackets, and I drew what brackets look like: ( ), [ ], { }. And then she freaked out. To her, those things are called parentheses ( ), brackets [ ] and braces { }. I said, yes, those are the official titles of those things, but here in South Australia they're thought of as different kinds of brackets. If we want to distinguish between them we'll call them round brackets ( ), square brackets [ ] and curly brackets { }.

And suddenly a light came on for her and a whole lot of stuff people had said this week made sense. She also suddenly understood the very odd look her class tutor gave her when she mentioned the word parentheses. "Yes," I responded. "Most maths students and tutors here would never have heard the word parentheses."

And what happened next? Well we'll have to wait and see. I think we made some excellent progress, and we agreed to keep meeting across the semester to help deal with anything more that might come up.

For me, I'm so glad I knew a little about the differences between Australian and American mathematical-English. (Thanks MTBoS!) And perhaps if anyone is reading this, then you will know too.

These comments were left on the original blog post:

Claire 31 July 2016

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This is very interesting. I teach high school in Southern California. When I teach the Order of Operations, my students have seen it before from middle school. They were either taught PEMDAS or Please Excuse My Dear Aunt Sally to learn the order. I always use these acronyms as a way to highlight the limitations of some of the “tricks” they use to memorize math concepts.

It’s interesting that the parenthesis, brackets, and braces are all called “brackets” where you are. Having 1 word for that is super helpful. I tend to say that they are all “grouping symbols” and if it were up to me, the acronym would be GEMDAS. Because then, for example, absolute value symbols are grouping symbols.

We also discuss why MD doesn’t matter the order… That they are inverse operations and part of a mathematical family. Same with AS.

This family idea is helpful to explain where roots and logs might go in the order of operations.

This post gave me a lot to think about.

Geoff Coates 1 August 2016

I helped an African student once who learned his high school maths in French. They used commas where we use decimal points and full stops where we use commas in large numbers. He was very confused for a while …

David Butler 2 August 2016

This came up in the Chemistry labs last semester, when all the pipettes had their volume listed as “0,25mL”.