"That's the nice thing about maths," said someone who shall remain nameless. "There's always one right answer!"
I coughed. I may have said 'bullshit' under my breath, a little bit. It's my second-least-favourite thing to hear anyone say1 .
The idea of maths problems always having one right answer is not only wrong, but dangerously, restrictively, soul-crushingly wrong.
This is the kind of thinking that leads to people thinking there's no creativity in maths.
This is the kind of thinking that leads to people saying "I don't like the 'explain' ones!"
This is the kind of thinking that - most damaging of all - says 'we haven't been taught that.'
It's the most dangerous kind of bullshit, the kind of bullshit that's a limitation disguised as a compliment.
There are trivial counter-examples: the answer to any problem in mechanics or statistics depends critically on the assumptions you make (and many of the assumptions you make in M1 and S1 are ludicrously simple; as you go further in maths you start to develop more and more sophisticated models). If you look at a core mark scheme, you frequently see several possible ways of expressing an answer, and often six or seven different ways of solving a question.
Read an exam paper carefully, sometime. The examiners go to great lengths to phrase the questions extremely carefully so that there ought to be only one possible answer: if a single answer was a given, they could express themselves much more clearly and succinctly.
I spent a summer coding in Perl - a horrible, horrible language that some people claim is useful. I don't remember much about it, other than the constant headaches; the one thing I do remember is the motto of the Perl community: there's more than one way to do it.
There's always more than one way to do it. When Andrew Wiles proved Fermat's Last Theorem - you know it, the one Fermat claimed to have a marvellous proof of but too narrow margins - his proof involved all manner of fantastic modern maths that simply wasn't available in Fermat's time. Wiles's proof was certainly not the same as Fermat's (assuming Fermat did, indeed, prove it).
The most dangerous thing about the idea that there's always One Right Answer is the way it makes you approach a question: once you have the One Right Answer, that's is, end of question, bring on the next one.
That's insanely harmful.
It doesn't leave any room for 'what else can I do with this answer?' or 'how can I improve the model?' or 'what analogies can I draw?' It doesn't leave any room for discussion, or extension, or reinforcement.
It turns maths into a pub quiz, where your thinking begins and ends in a question-shaped box.
And it makes it very easy to think: "I didn't get the One Right Answer so I must be rubbish at maths".
I don't know how we escape from the question-shaped box. But I know there's more than one way to do it.
* Edited 15/12/2013 for formatting.