Apparently ‘what we do is more important than what we say’. Perhaps. But what we say (and how we say it) is pretty damn important. David Butler blogged recently about how one word — Let’s — can empower students. I want to talk instead about a word that I try to avoid.
In the world of Harry Potter, a curse is the worst kind of Dark spell — words that consistently affect someone in a negative manner, usually associated with varying levels of discomfort. Curses are the most wicked, strongest, longest-lasting, and their effects are hard to reverse1.
Many words are unspeakable curses in teaching. The one I am currently focusing on eliminating in my classrooms is not the worst, but it is insidious and disempowers students. The word is trick.
‘There’s a trick to use here.’
The whole point of a magician’s trick is that the audience isn’t privy to the inner workings. The audience isn’t meant to understand how the trick is done. If students see a mathematical process as a trick, then, almost by definition, they don’t understand the concept. This problem is hiding in other vocabulary too. A recent tweet by Annie Fetter made me realise that ‘formula’ can masquerade as a trick, too.
Coincidentally, at the same time that I was working on this post, Dan Anderson, Christopher Danielson, Justin Lanier, Michael Pershan and Avery Pickford were digging deep into this on Twitter. I haven’t processed their thoughts yet but I’ve storify-ed three of the threads for later contemplation: Thread 1, Thread 2, Thread 3.
One fix: Stop teaching tricks like BODMAS, cross-multiply2 and FOIL. Aim for understanding. Nix the Tricks is a free compendium of fixes by Tina Cardone and the #MTBoS community. Warning: your eyes might start to bleed after seeing some of the tricks, like peanuts and butterflies:
‘This one’s a bit trick-y.’
This use of the word ‘tricky’ seems harmless enough. It’s often said to be helpful; to warn students that difficulties lie ahead. But what I hear, and more importantly perhaps what students hear, is ‘I’ve already made a judgement that this is too hard for you. Be warned.’
One fix: Stop signalling to your students that you think a problem is too hard or too easy for them to tackle. Rather, let them use their own strategies and support them along the way. What they can do when given a chance will likely surprise you.
‘That’s a trick question!’
Search the web for ‘trick questions’ and you find ones like these:
There were 10 birds in a tree. The hunter shot one. How many were left?’3
I’d rather call these ‘brain teasers’ or ‘riddles’. You might think that’s just tomayto, tomahto but I want to dissociate them from mathematics questions that deliberately mislead.
I delight in counter-intuitive maths problems. They often reveal hidden mathematical beauty. But, for students whose relationship with mathematics is not so strong, these types of problems leave them skeptical and distrustful. It’s like trying to ride a bike that, for no reason, occasionally and randomly throws you off — even though you are riding it exactly the way you did yesterday4. You can’t predict it, you don’t really understand why it happens, it bloody hurts, and you probably don’t want to ride anymore.
Two fixes: 1. Pose these problems as opportunities to ‘wonder’ rather than to ‘mislead’. (Thanks for the prompt, David!) 2. Build a bridge between intuitive and analytic modes of thinking. I plan to write a lot more about the role of intuition in mathematics. If you can’t wait, go take a look at Ejersbo and Leron’s article5, and we can discuss it together.
A final thought
If I’ve left you with the impression that I never say ‘trick’, well, I said it at least three times in today’s class. But, I’m trying.
What is your unspeakable curse? What words do you try to avoid saying, and why?
 Source: Harry Potter Wiki
 Fuck cross-multiply. If you teach students to cross-multiply, just stop. Stop now. It is one of the most destructive tricks.
 Answer: ‘None. The rest were startled and flew away.’
 Okay, not convinced about this metaphor but it’s getting late, and #mtbos30.
 Ejersbo, L.R., Leon, U., 2013, ‘Revisiting the Medical Diagnosis Problem: Reconciling Intuitive and Analytical Thinking’, in ‘Probabilistic Thinking: Presenting Plural Perspectives’, Chernoff, E.J. And Sriraman, B. (Eds), Springer. You can find a free pre-print on the web.
It’s funny how we can find ourselves saying these kind of words without even realising it! I have been talking more and more with my students about their thought processes when looking at (or for) a problem. Also, I have been working with some PS teachers who find themselves battling with some of these weird ways of finding answers without understanding… Interesting and insightful post!
For the PS teachers I recommend checking out Nix The Tricks — it has the fix as well as the trick!
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I love this post so much!