There is a little trick someone played on me once as a child and I have been playing on the students in the Drop-In room this week. It goes like this:
Answer the following questions:
- What would you find in a haunted house?
- What do you call a meal of meat cooked in an oven?
- What is the part of the country that is next to the sea?
- When you have more than everyone else, what would you have?
- What do you put in a toaster?
The answers to these questions are of course, a GHOST, a ROAST, the COAST, the MOST and… BREAD. You weren’t thinking TOAST were you? 😉
You may ask why I’m playing such a mean trick on my students, when normally I am adamant that we shouldn’t make our students feel stupid. Fair point, but I think it will help them feel less stupid in the end.
You see it all started when one of the students was doing “volume of revolution” problems. Every problem so far had required him to take a 2D shape and rotate it around the x-axis, thus creating a solid 3D shape. The next problem, however, required him to rotate around a different line outside the 2D shape, thus creating a 3D shape with a hole in it. It said on the page it had to be rotated around a different line, and yet he still rotated around the x-axis anyway. “Why did I do that?” he asked. And in response I played the above trick.
The point is that humans are good at following patterns, so good that we don’t even know we’re doing it. In general this is actually a good thing — it means you can set a table, sing music, do jigsaw puzzles, count, learn languages and and even learn maths. But sometimes it fails us, because things don’t always fit into a pattern. Just because the first four answers rhyme with GHOST, it doesn’t mean they all will; just because all questions so far require rotating around the x-axis, it doesn’t mean they all will.
So for students, the message is to keep your mind open. Don’t just follow the pattern, but think carefully about what the problem at hand requires you to do. For teachers, we should be careful to put in more than one type of example, so that students aren’t encouraged to form a pattern that isn’t there. In short, for all of us: BEWARE OF THE TOAST.