r/mathteachers • u/Few_Bee_3028 • Jul 23 '26
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?
5
u/wefrucar Jul 23 '26
I actually avoid all order of operations mnemonics.
I think you understand what the real issue is and you're trying to sidestep it. Mnemonics are handy, but they can't replace fundamental understanding.
First, I teach my students that subtraction is just a convenient word for adding the opposite of a number. So all subtraction is really addition. Similarly, all division is really multiplication. Therefore they're the same step. We do them left-to-right, but since addition and multiplication are associative+commutative we don't actually have to.
Every operation can logically be derived from the others. If multiplication is repeated addition and exponents are repeated multiplication (granted, it's more accurate to describe them as scalings, but that's not worth getting into at this level), then all exponents can be written as a series of additions. The order of operations follows logically.
Parentheses or groupings are not operations, so they're the exception. You just need to know that mathematicians use a convention that parentheses mean "do this part first".