I used to do an act when teaching air resistance. I would write ‘A’ on one piece of A4 paper and ‘B’ on another. I’d then say that I was going to drop them from the same height and ask the class to vote for which one they thought would hit the floor first. Whichever one they chose, I’d say I was backing the other. Then I’d screw that one up into a ball and let them both go. I always won.
I’ve never considered if this was motivating. It was intended as a bit of fun. I would only do it with a class I knew well because, otherwise, it’s a risk. You risk implying that you think the students are stupid and some may take offence.
I thought about this when reading Dan Meyer’s latest post. He’s been touring maths conferences, asking maths teachers to take a bet: he thinks of a number between 1 and 100 and they get ten guesses. Each time they get it wrong he tells them if the real answer is higher or lower. The catch is that it’s not a whole number and so Meyer always wins.
I’d groan if someone played this trick on me. But there are many other ways it could go down if a teacher did it in class. Students might conclude that their maths teacher is an otherworldly geek; a definitional pedant. They may be annoyed by the trick because, again, it potentially implies that they are stupid.
According to Meyer, it is intended to build motivation by giving a reason to students for why we might have different categories of number such as natural numbers and rational numbers. This fits with Meyer’s pet theory about maths motivation which is the idea that maths is an aspirin and students need to experience the headache to appreciate it.
If we think about the specifics, what are we trying to motivate these kids to do here? Do we want them to learn the names of different classes of numbers? If so, that’s pretty low level and at best incidental to the maths I’m keen for students to learn. It’s also not hard to convince kids of the need for labels because categorising things is human. And for interest I tend to go with a schtick about infinities of different sizes; the infinity of natural numbers is smaller than the infinity of real numbers and so on.
Do we perhaps think that the trick will motivate students about maths more generally? If so, they’re going to be disappointed when they get to quadratic functions.
Ironically, Meyer’s game seems like a solution in search of a problem.
This is a reflection of a much bigger issue in maths education. Some folks are holding on to motivation for dear life. If you believe in constructivist maths teaching, for instance, then that can be hard to maintain when the evidence stacks up against its effectiveness. So you can rationalise your position by claiming it’s motivating.
But the theories of motivation that these claims rest upon tend to be homespun. They fail to distinguish between a passing or ‘situational’ interest in a specific activity and a long term or ‘personal’ interest in mathematics. You also have to swallow that solving problems is inherently more fun than listening to people explain things. But problems can be frustrating and explanations can be interesting.
To really sort this out we would need to run robust trials. That’s a problem because the literature is full of research where students are asked if they found the new thing interesting. And that’s not robust.
So anyone can grow their own unproven theory of motivation. For what it’s worth, I’m not convinced that you can ensure students develop a personal interest in any subject. That’s because we are humans with independent tastes and desires. However, I believe that the greatest threat to developing a personal interest is a lack of success. I reckon that constantly being hit with the fact that you can’t do something would bum you out. In that case, we need to avoid gratuitous struggle and instead teach maths really well so that our students experience success. That, if anywhere, is the place instructional theories and motivational theories intersect.