Here’s how I see it, it’s easier to learn from the maths mistakes of others than from your own. Probably because there’s an emotional association with making a mistake, I find pupils jump at the chance to dissect and discuss the root of misconceptions of others, and by others I mean the Simpsons, rather than their own.
In a class discussion, if you single out any of the pupils for making mistakes, you run the risk of embarrassing them and awakening the “I-was-never-any-good-at-maths” spectres that you’ve probably worked so hard to banish.
But when Bart makes a mistake or Lisa can’t figure something out or Homer makes a booboo, then pupils are all over it.
“Bart never remembers to include 1 and the number itself in the list of factors!” “Lisa seems to forget at least one factor – she’s probably not checking for pairs.”
Every year I teach pupils how to find all the factors of a number and it always surprises me how I find a new way to make a meal of it. I would never seem to give the same definition of factors or use the same method twice – not because I didn’t want to or couldn’t remember but because the ones I was trying were not getting through to pupils. They just kept making the same mistakes no matter how I explained it. [Please share your winning ways for teaching factors in the comments!]
So I made a list one day of the ways in which my pupils were struggling with factors and it occurred to me that there were enough to make it worthwhile spending a whole lesson just dealing with the common misconceptions (“classic mistakes” I like to call them); and so it turned out to be.
Not wanting to make pupils feel like I was pointing a finger at them, I brought in the Simpsons. Here’s a format I’ve tried a couple of times and it seems to work.
- What mistakes did they make? – Four Simpsons characters are displayed on the screen and in pupil workpacks, each of them making a mistake to do with listing or understanding factors. Pupils ‘think, pair, share’ the classic mistakes the characters are making and then write them down in their own words on the sheet.
- Card sort – Pairs of pupils sort cards according to which mistake is evident on the card. Some of the cards are correct (i.e. no mistake has been made). Then they share their results with the other pair on their table. A class discussion wraps this up.
- Make some classic mistakes for your friends to find! – Pupils must answer questions to do with finding factors and deliberately make classic mistakes on some of them. Their partner then has to check how they did.
The experience I had with this last year is that even after this lesson, pupils continued to make mistakes of the same kind as the Simpsons. However, what was different was that each of their errors now had a Simpsons character associated with it. As a result, we could talk about the misconceptions without the faintest hint of embarrassment and sooner than before, my pupils were correcting themselves… “Ah look – I’ve made Lisa’s classic mistake” or “I did what Milhouse does and got factors and multiples the wrong way round” or “I’ve just done a Jimbo Jones!”
There’s a complete set of posters to download below. They contain images of the Simpsons making classic mistakes relating to finding factors, finding multiples and working with powers.
Oh, one last thing…I don’t teach factors and multiples at the same time anymore. The words are too inter-related and trying to learn both at the same time means that they’re liable to get used incorrectly. I usually give a couple of weeks between them.
Here are a couple of related products that I like to use to generate discussion around misconceptions: