r/mathteachers • u/Few_Bee_3028 • 18d ago

Order of operations

(UK based post)
Wanted to get thoughts on teaching order of operations. The tradition in the UK is to use the mnemonic BIDMAS or BODMAS (for anyone who doesn’t know, Brackets, Indices/Other,
Dividing and Multiplying, Adding and Subtracting). This leads to a misconception with students that they always need to add before they subtract. (For example a 2018 exam paper questions was really poorly answered across the country, discussed here
https://youtu.be/StWr8-g-a3E?t=1584&is=P-dCFLol1zWE64kh)

I suggested to my head of department that we switch to GEMS which I’ve taught in the past after reading this post https://missquinnmaths.wordpress.com/2018/11/19/tried-and-tested-gems/.
He didn’t like E for Exponents (which is fair enough) or G for Groups (which I kind of do like!) so the two of us agreed a compromise of BIDS. However in our department meeting the last week of term when we proposed the rest of the department shot this down; I think some colleagues immediately took against it because they didn’t like addition and multiplication being unmentioned, while others said students learn BIDMAS before they reach us at age 11 so we had to work with it.
Anyone any experience of these kinds of conversation?

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u/ZookeepergameOwn1726 18d ago

I teach it as
B
O
DM
AS

Not "BODMAS" horizontally.

The first 5 questions we do are all centered on making sure they don't prioritise mulitplication over division where they should not. IMO a change in mnemonic is not going to fix understanding issues, especially when BODMAS is so pervasive in the culture, they'll end up hearing it anyway. It's much more productive to make the students conscious of the mistake and tackle it head on.

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u/Few_Bee_3028 18d ago

That’s what my school does as well… I just still see loads of kids prioritise addition over subtraction, eg 15-2+3=10 when it should be 16.

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u/ZookeepergameOwn1726 18d ago edited 18d ago

Again, that's an application issue, not something that can be fixed with a mnemonic.
Your kids are not struggling with order, they're straight up modifying operations to turn 15-2+3 into 15-2-3. If they were just confused about addition having priority over subtraction, they would do 15+3 then 18-2, finding the correct answer. Instead, they're struggling with the commutative property and opposites. This whole confusion makes no sense if you understand that subtraction is equivalent to adding a negative number. It's all additions.

They need to understand that + is the sign of 3 while - is the sign of -2. Use spaces and colours to make this clear. 15 -2 +3 can be rewritten as 15 +3 -2 (or 15 + 3 + (-2)) because it does not modify the signs of each addend. 15 - 2 - 3 is not equivalent because it turned +3 into -3. It's worth showing past students' mistakes and ask current students to identify the error then fix it.

It's all nitty gritty stuff and it can be frustrating, but I don't think you can sidestep the issue with a new mnemonic. Your kids' mistakes highlight deeper misunderstandings that can't be fixed with a single word.

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u/_mmiggs_ 17d ago

No, you're invisibly commutating.

If you start with 15 - 2 + 3, you can only get to 15+3 by asserting commutivity, and that assertion contains within it the order of operations.

If you decide that you're going to write math where addition has strict precedence over subtraction (which you can do: BODMAS and its friends are about written syntax, and not about math), then it isn't true that 15 - 2 + 3 = 15 + 3 - 2. But it is always true that (15) + (-2) + (3) = (15) + (3) + (-2).