How big an issue is literacy for mathematics teachers? After all, if students are literate in the precise and symbolic language that is mathematics, surely that is enough. But that is a narrow view. It takes a good command of English to understand the difference between "differentiate" as used in everyday life and the same word as used in A-level maths. And when our students stretch for a word that is just outside their vocabulary, what happens? We may well have a howler.
When it comes to these, I seem to have an angel on one shoulder and a devil on the other. The angel looks solemn and says, "Isn't there something rather tyrannical about your desire to smile at your students' errors? We all make mistakes, and we don't like to have our own ridiculed.
"If you are trying to promote a culture in your classroom where questions, any questions, are welcome, then to lampoon howlers publicly at the time or privately later is, to say the least, contradictory. If you enjoy it when your students are idiots, then might they not become idiots just to please you?"
I nod sheepishly, and feel guilty. But then the devil on the other shoulder has a word: "My comrade's speech contains some truth but isn't it a little severe? Teaching, as you know, can sometimes feel like the perpetual triumph of hope over experience. It can be disheartening to find that lessons that are beautiful in your own eyes have not created understanding of comparable beauty within your students.
"Sometimes the gap between what you hope your students have learned and what their answers show they have learned is so great that you must either laugh or cry. If their answers do contain a grain of humour then accept that gratefully as a way of lessening the pain."
The best howlers are those that create appealing alternative vistas in your mind; fresh perspectives it would be hard to arrive at any other way. My three favourite howlers all do this.
I remember marking some numerical methods coursework and reading: "This method defiantly misses the root." I smiled to picture Messrs Newton and Raphson shaking their fists at this elusive solution while shouting, "We'll get you next time".
And I guess we have all seen the next one - "The distribution peeks at 7" - which summons up the vision of a party where Miss Seven, attractive and flirtatious, is being coyly admired by Mr Normal, a shy man with an overly symmetrical head.
My final favourite, from a statistics lesson, came after I asked: "A 'parameter of a distribution'. If I used that phrase, what might I be thinking of?" I was hoping to hear, "the mean" or "How about the variance?", but instead I was asked, "Would you be thinking of the distance round the outside?".
Jonny Griffiths teaches maths at a sixth-form college.
Try SRWhitehouse's worksheets to revise numerical methods.
Make sure pupils really understand what differentiation is with phildb's worksheet introducing the essentials.