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Teaching can be fun!
Just had a very good lesson with C, who is one of my favourite pupils of all time. I've had him for quite some time now, and we clicked right from the beginning.
What I love about him (and this is something that I very much encourage) is that he's willing and able to look at more than one method of solving a problem. Most pupils will methodically follow the rule they've been taught, but C will often find a way to short-cut the process.
Today, we were playing with enlargements, as he'd been having problems with them at school. By the time we'd finished the lesson, he was able to do fractional reductions with a point other than the origin as the Centre of Enlargement. But what I loved was the details. He got part way through one problem, and then did a measurement that wasn't a ray trace (the 'method') - I asked him what it was. He was working out the centre point of the new shape. It was rotationally symetric, so as soon as he had the centre, drawing the rest from what he already had was a pushover.
Later, he used a pair of dividers to quickly do four times a distance along a ruler do the ray trace for an enlargement of four. He'd realised that he didn't actually need to know the numerical measurement, as long as he could multiply it by four in this manner.
The sad thing is that one of his teachers at school had told him that using dividers to measure distance was 'cheating' (though I don't think it was said in an unkind way). I told C it was a jolly good idea.
For kids who don't have C's intuitive feel for things, it probably would be a bad idea - those who can barely memorise the 'method' will get confused if they use different ways of doing things. In C's case, it shows that he really understands the method and is confident enough to start using variations.
He's come a long way from the lad I used to teach tables to. He enjoys maths. We treat it as a game and I am forever grateful that his mother has the confidence to allow me and C to wander off the syllabus occasionally and explore random corners of maths and science.
How may lads would look thrilled at seeing a new prism I bought (with him in mind, as it happens), and look forward to when we do more science so that we can play optics with it? (I didn't even tell him I'd got it, he spotted it on the table!)
He has the potential to go a long way.
What I love about him (and this is something that I very much encourage) is that he's willing and able to look at more than one method of solving a problem. Most pupils will methodically follow the rule they've been taught, but C will often find a way to short-cut the process.
Today, we were playing with enlargements, as he'd been having problems with them at school. By the time we'd finished the lesson, he was able to do fractional reductions with a point other than the origin as the Centre of Enlargement. But what I loved was the details. He got part way through one problem, and then did a measurement that wasn't a ray trace (the 'method') - I asked him what it was. He was working out the centre point of the new shape. It was rotationally symetric, so as soon as he had the centre, drawing the rest from what he already had was a pushover.
Later, he used a pair of dividers to quickly do four times a distance along a ruler do the ray trace for an enlargement of four. He'd realised that he didn't actually need to know the numerical measurement, as long as he could multiply it by four in this manner.
The sad thing is that one of his teachers at school had told him that using dividers to measure distance was 'cheating' (though I don't think it was said in an unkind way). I told C it was a jolly good idea.
For kids who don't have C's intuitive feel for things, it probably would be a bad idea - those who can barely memorise the 'method' will get confused if they use different ways of doing things. In C's case, it shows that he really understands the method and is confident enough to start using variations.
He's come a long way from the lad I used to teach tables to. He enjoys maths. We treat it as a game and I am forever grateful that his mother has the confidence to allow me and C to wander off the syllabus occasionally and explore random corners of maths and science.
How may lads would look thrilled at seeing a new prism I bought (with him in mind, as it happens), and look forward to when we do more science so that we can play optics with it? (I didn't even tell him I'd got it, he spotted it on the table!)
He has the potential to go a long way.
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Translation, rotation, reflection, enlargement...
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You've reminded me of the biology teacher I knew when I was working as a lab tech. I was setting up that osmosis experiment (I daresay you've done it) where you have three salt solutions of different strengths and you're supposed to work out which one's which by bathing strips of potato in it and seeing how much they change length.
Teacher said he would not mark down a student who identified the solutions by dipping his finger in each one and licking it.