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I was sharing the joy of maths...

...and then I made a mistake.

It was all going swimmingly - the talk for parents and children had touched on puzzles and mathematical magic tricks and we'd finished with a tense game of Pointless, with four young teams challenging themselves with mental arithmetic questions.

I totted up the scores.  The Bromley team had won by a point, with a score of 58 against the Croydon team's 59.  What an exciting finish!

As the audience got up to leave, three children walked up to me.  Were they about to tell me how much they'd enjoyed it?  No.  "For the winning team you added 22 + 26 to give 58.  It should be 48."

I look at the scoreboard.  They were right.  It was a glitch, a brain fade, like the other day when I wrongly put an apostrophe in "it's" after a lifetime of spotting when other people had made the same mistake. It hadn't affected the result, but it had certainly detracted from it.

A dad still seated in the audience gleefully called out "How can we trust anything you say in your books now?"

Yes I know we all make mistakes in maths (and especially arithmetic). I even support the popular mantra that if you don't make mistakes in maths it means you probably aren't learning anything.  

Still, I wonder what that audience will remember from that talk last week.  I'd love to think it was "Wasn't that an interesting way to do multiplication?" or "Should we try out that magic trick on grandma?" 

But I have a horrible feeling that the standout message for some of them was: "There was a guy who was supposed to be good at maths, but he couldn't even add 22+26."



So when is it OK to make mistakes in maths?  Dan Pearcy made an interesting distinction in one of his blogs:

"[Some people say that in maths] it is okay to make mistakes. I think this is dangerous if we aren’t clear on the types of mistakes being made. I’ve found it helpful with my classes to refer to sloppy mistakes and stretch mistakes. Sloppy mistakes aren’t great. They tend to refer to things like numerical errors, not reading the question properly or issues with algebraic manipulation. Stretch mistakes are great. They can happen when someone tries a new strategy or provides a strategy for the class to analyse. Mathematics is both creative and rigorous after-all!"

In my case, 22+26 was definitely a sloppy mistake. Had the mistake been spotted at the time, some good could have come out of it - I'd have acknowledged the error, corrected it, and the audience would have got some comfort from knowing that 'good' mathematicians sometimes make mistakes. Alas, nobody pointed it out.  In future, I'm going to try to prime audiences early in a talk to check my workings and to call out if they think they've seen an error ("I sometimes make mistakes too!"). In fact...that's a habit I should have adopted in the past.  So maybe my arithmetical error has been a good thing after all.