Home > Maths, Teaching > All parabolas are symmetrical, right?

All parabolas are symmetrical, right?

Today I was teaching one of my classes about drawing graphs. It was going well, we’d moved from linear to quadratic and discussed the shape. After a few minutes of plotting quadratic graphs from equations one of the students asked, “Sir, these parabolas are all symmetrical, right?” we discussed it briefly and he decided that yes they were. Then he carried on working. I was circulating the class and I noticed he was flying through the work so I asked him to explain why he was going so much faster. He said, “I’ve found a short cut sir, cos they’re symmetrical you once you see when they start repeating you can easily just work out the points from the ones you know.” I was impressed by his mathematical thinking, although I wasn’t as impressed with his explanation, although he did manage to refine it and explained it much better to one of his class mates who had overheard our discussion and wanted further explanation.

The student had seemed surprised when I approved of his method. I think he thought I’d chastise him for not working all the points had. But a massive part of mathematics is pattern spotting and he’d spotted a pattern within the shape of a quadratic graph and used it to streamline his working and get to the correct answer. By spotting this he was working at a level that is streets ahead of the actual work set and I think this needs to be encouraged. It’s made me think about things I teach, and if I’m building in enough opportunities to think like this. I know I do build them in, and encourage the thinking through questioning, but I’d never considered asking about this so I figured I’d try to think where else I could find ideas like this.

Categories: Maths, Teaching Tags: , ,
  1. February 25, 2015 at 8:04 pm

    Nice observation by the student … Could segue into a discussion on the various kinds of symmetry.

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