Maths - How do I know that?
Put yourself into your pupils' shoes to make sure they keep up
I was marking the other day and came across this in a rather disorganised script by a pupil called Jack:
I stopped, puzzled. Had Jack needed a diversion midway through his tough trigonometry assignment and turned to draft a love letter to his inamorata? But then I worked out what was happening. Jack's intention was to write this:
Jack was writing the letter "x" and the times "x" in the same way. I thought back and dimly recalled a time when I had done the same, maybe 40 years ago. Who was it who had passed on the wisdom that the letter x was better written as two semicircles? I can't remember, but I thank ubiquitous teacher Anon.
So what else was comparable in my mathematical make-up? I thought of the numeral 7 - I always put a line through it to differentiate it from the digit 1, and likewise with my letter z (to distinguish it from 2). But these foibles seemed to me more optional than writing an x with two half-circles. I drew up the following Venn diagram:
I found myself positioned squarely in region 8, but where would my pupils be? Studying Jack's homework placed him in region 1 and next time I would gently suggest that he migrated into the "x as two half-circles" bubble at least.
The next time I had the group, I did a survey. We had lots of "x as two half-circles" ("We were taught that at primary school"), a smattering of "seven with a line" people, and I was almost on my own with my "z with a dash" option.
What is second nature is hard to question. I am not sure that in 20 years I had ever stopped to consider that how to write the letter x deserved at least 10 seconds of the A-level course. It made me wonder - what other symbols do I use without stopping to bring everyone on board? When asked, my pupils were keen to help. It transpired that I abbreviate "positive" to "+ve" and "negative" to "-ve". For the majority, my shorthand was crystal clear, but those who skipped it, thinking "Mr Griffiths will explain that in a minute", would have been disappointed.
The moral of this tale is not complicated: if we don't put ourselves into our pupils' shoes, it is unlikely that anyone else will. And may we all be grateful to those teachers who improved our maths in ways that stay with us, but who are long forgotten.
Jonny Griffiths teaches at Paston College in Norfolk
For a colourful and fun way to introduce maths concepts, try languageisheartosay's collection.
Get pupils used to letters in maths with davecavell's "What's in my bag?" quiz. Solve equations and unscramble codes to discover the mystery objects.
If letters have a clear meaning, can algebra be easier? Beachman0274's starter task suggests it can.
Make algebra a game with kez84's top trumps animal cards.
In the forums
On the TES maths forum, teachers are chatting about common misconceptions with place values/rounding.
There is a lively discussion on the new International Baccalaureate maths syllabus.
Find all links and resources at www.tes.co.uk/resources019.