Aaargh Ruddy BIDMAS
The order of operations is commonly taught using one of the following mnemonics: BIDMAS, BODMAS, BOMDAS, BIMDAS, PEMDAS, PEDMAS or, if you’re Colin Beveridge (@icecolbeveridge) Boodles! (I’m not going to discuss that here, so if you’re interested, do follow the link)
For the first six the letters stand for the following: B: Brackets, P: Parentheses (essentially the same thing) I: Indices, E: Exponents, O: Orders (Again, the same in essence), D: Division, M: Multiplication (Inverse operations) A: Addition, S:Subtraction (Again inverses).
There is a massive problem with these mnemonics, and their use in teaching. I do, however, think it’s down to the teaching rather than the mnemonics themselves, and possibly down to a lack of understanding from some who teach it.
And example of the problem I’m hinting at occurred on Friday with my top set year 8 class. As part of a ten quick questions core skills starter I included the question: 3 – 1 + 2 = . A problem free, easy, question for a class working at level 6-8 one would think, but the uproar when going through the answer was unbelievable. I asked one lad what he had written, he told me zero, I asked if anyone could tell me what he’d done wrong and was met first with blank stares, then with “Sir, it is zero. Have you forgotten about BIDMAS”. The scale of the misconception was enormous. After the first person said it the entire class were up in agreement. I settled them down, jettisoned that days lesson plan and retaught them the order of operations, but properly.
The misconception is heavily tied to the mnemonic. A comes before S in BIDMAS, so Addition comes before Subtraction. But this isn’t the order of operations. When I teach it I make a point of telling them all six mnemonics mentioned above and specifically drawing their attention to the way the D and the M are interchangeable. Discussing that because Division is the inverse of Multiplication they are, in essence, the same operation, certainly “of the same order”, and as such take equal precedence in the order of operations so you read from left to right. I then ensure they know this is true for Addition and Subtraction. If I ever write one of these mnemonics I always write it:
With the R standing for roots, as this shows the inverse relation for that level too.
The year 8 class now understand the order of operations, despite protests that “(insert name of former colleague here) told us addition ALWAYS comes before Subtraction!” as they all thought this, it is possible. I’ve seen it taught wrong in more that 1 school. I had a real row with another trainee on my PCGE course in a microteaching session when she taught it wrong and tried to say I was wrong. Every year the pupils from one of the feeder primaries get it wrong, so I think their yr6 teacher must teach it wrong. I’ve also been brought in to settle arguments on social media networks that have erupted over those stupid viral questions based around this. All this shows that there is a perpetuation of this misconception in this country, and we need to stamp it out.