I’m blogging Maths at 1.30am. My mind is blown. I have spent the last hour in a Twitter conversation about the answer to the calculation -3^2. I need your help.
Now if you ask me the question I will confidently tell you the answer is -9. That’s obvious to me. That the fundamentals of Maths. It’s convention. It’s. BIDMAS/ BODMAS/ PIDMAS/ PODMAS wherever you are whatever mnemonic you prefer. Right? Well seemingly there are Mathematicians out there who disagree. Mathematicians whom I respect I would like to point out. No marks for guessing that they think the answer to the question is 9.
I feel I need to blog to get my head straight but more because I’m interested in what camp you fall into. If you never comment on a blog post of mine again please comment on this.
So here are my key points.
Order of Operations
In the calculation -3^2. BIDMAS tells us indices first then the multiplication (by -1) this we get the answer -9
There are no brackets in the calculation so we acts as if they aren’t there?
I then got into a separate (brief) conversation about the calculation 9 – 2 + 3 with a different user. The answer to this is 10 not 4 in my opinion. This is a fundamental problem with the mnemonic and perhaps the way we expose pupils to it. The hierarchy in my mind is:
3) Division and Multiplication
4) Addition and Subtraction
The mnemonic would suggest that eg division comes before multiplication but in fact these have equal hierarchy and hence we calculate left to right. Am I right and do I/ we make this clear to pupils if so?
One of the main arguments for the 9 camp was that the notation was ambiguous. I see no ambiguity. To be directing a number negatively is the same as multiplication by negative 1 and so the first operation is square then direct. The 9 camp view was different.
I just cannot see this argument. Directing a number/ changing the direction of a number is multiplication by minus 1. This is why a negative multiplied by a negative is a positive? Hence it isn’t done first as indices are further up the hierarchy?
I’m not sure this post is completely coherent. It’s late. I’m tired. Above all I’m confused. In my head we have conventions such as order of operations to standardise our subject and to avoid ambiguity. To me the 9 camp are misapplying the rules but a little bit of doubt in my mind has me worried the very foundations of my Mathematical world are wrong.
Please, please comment. I’m going to try to get some sleep!
Note For those of you who know Colin I’m quite aware that he’s happy to play Devil’s advocate to get a debate going but he has messaged me to say he thinks that the notation is ambiguous. It’s this ambiguity I just can’t see.