### Geogebra and Circle Theorems

Some work-in-progress resources for teaching the circle theorems. I've been working on two of them, there are others done by the rest of my group for some of the other theorems and we're planning to link them all together via the blog.

The resources were made in Geogebra. Not a word I was familiar with until a week ago but I'm already very fond of it. My aim before starting the course was to get very good with ICT. I'm currently hopeless. I didn't use Microsoft Office through the entirely of my degree and my school was incredibly poor with ICT. I didn't use ICT much at school, I have vague memories of one non-lesson with LOGO, but the teacher got confused and we didn't get anything done. There were some rushed attempts at using ICT with the class for when Ofsted visited but were never very useful. (I took great delight in reading the Ofsted reports - these consistently stated ICT as a very weak point for the school.)

My opinions of ICT have softened in the years that have passed, my experience at first was that computers were rubbish and every attempt at using them in lessons wasted loads of time to set up and I never learnt anything from the activities anyway. I really want to be good with it, firstly because other people (Ofsted, the people who I want a job from) will probably like it, but secondly because I've seen real value in it. We get so conditioned into how shapes usually look (eg trapezium with the longer side on the bottom, right angled triangle with right angle in the bottom left corner) and rarely deal with crazy objects, like a really long and thin kite. I've really learnt from playing with Geogebra, just the simple task of creating valid shapes lead to discussion of things I've never thought about. If we drag the crossbar of a kite up to the very top we get a triangle. Are those triangles valid as kites? What if you pull the top point of the kite down below the crossbar to get an arrow sort of shape. Is that a kite? Discovering and posing these questions gives them far greater value to me than if I'd been given them on a plate.

There's one other piece of software we've been introduced too, called GridAlgebra. We've had two demonstrations of it and I warmed to it considerably during the second time. So far we've seen algebra as a "journey", it's a grid where moving down is multiplying and moving right is adding (divide and subtract are the expected inverses). It doesn't appeal much to me as a learner, when we were set questions in it I could only do them by looking away and doing the sum. I simply couldn't do it by visualising it as a journey. And therein lies it's value. It will be dead easy to write activities to appeal to pupils who think like me. Therefore, I need to put effort into finding things for pupils who don't think like me.

A wide variety of approaches is key to getting maximum understanding over the class as a whole. I discovered this by chance while tutoring over the summer. The girl wanted help preparing for a retake she needed a C in. I'd explain stuff, we'd do some practice, she'd be able to do it. I'd come back the week after and some stuff would have gotten lost whereas some would be done perfectly (and perfectly every time). I tried a different approach every time and after 2 or 3 attempts she'd have something down. Except finding the coordinates of the midpoint of a line. It came up in every single past exam. It gave two co-ordinates in the first quadrant and asked for the midpoint of the line segment joining them. After the 5th week of her not retaining a method from the previous lesson, I turned to my boyfriend for ideas. This girl is very good at the handling data and we hit upon the idea of relating it to the mean. The mean finds the average of the values it's given. If we give it only two values, it will find the midpoint. So we just need to find the mean of the x values and the mean of the y values. 3 weeks later, because the family went on holiday, and of course she didn't do any practice in that time, she could do it instantly. Hallelujah. :D

I've got familiar with Geogebra far quicker than I expected. The resources I've made could be (and hopefully, when I've learnt a bit more, will be) much better. There are limitations of the software that I've hit a brick wall trying to go around, I know exactly what I want to do but I can't find a way to do it! There is another session on it soon so I'm hoping to pick up a few more tricks.

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