Posts Tagged ‘Parabola’

A conic extention

January 17, 2016 4 comments

This week has been a strange one, I’ve been trying to shake an illness but it keeps on getting worse,  and my lessons have been disrupted a little bit by mock examinations. This, however, has given me a chance to work.woth small groups in some classes and to see how some classes are getting on with their courses.

In one of further maths lessons a student who takes maths but not further maths asked if he could.sit in the classroom and revise for his maths, asking if he needed help, I said it was fine and started the lesson,which was a review of the conic sections topic and an assessment sheet to identify any areas of weakness that may be apparent. I gave the none further maths student a spare copy of the assessment sheet, told him it was basically C1 skills but applied in a much more algebra heavy context, and asked him to have a crack.

Not only did he have a good crack at it, he answered it near perfectly. I was extremely pleased with his resilience in working through a question that has way more algebra than anything he’s looked at before and was glad he could make the links to the C1. His thoughts on the question were interesting, and I think they allowed the rest of the class to see more clearly how the conic section of FP1 fits with, and build on, the coordinate geometry sections in C1 and 2.

I think that in future I will use these parabola and hyperbola questions with all my high attaining AS maths students.

This was cross-posted to the “One Good Thing” blog here.

All parabolas are symmetrical, right?

February 24, 2015 1 comment

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: , ,
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