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Using animations and films
There is a tradition in the use of mathematical films, animations and images as a stimulus for classroom discussion that can be traced through the work of Mary Boole, Nicolet, Caleb Gattegno, Dick Tahta, Laurinda Brown and others.

Rather than try to summarise such a rich corpus of work I will try to offer below something of how I work with mathematical films.

I am aware of wanting to create a sense of drama and performance before showing a film. I make myself as still as I can and offer a minimum of context save that the task, having watched the film, will be to try and re-create together what we saw. However, students should not worry about trying to remember it, but just be present in what they see.

As the film finishes I am again aware of wanting to make myself as still as possible, pausing for as long as possible and speaking as slowly as I can. 'We are now going to try and re-construct what we saw. We will all have lots of images in our heads and images will be sparked off by what others say. Before we start sharing these images, there is one rule. When someone is talking your task is to try and see what they say and, as much as you can, to let go of your own images in order to do that ... Okay, could someone offer us an image from the very beginning of the film. What did you see?'

One rule I give myself is not to speak second. With many groups the second speaker will not make a comment related to the first. If this happens I will remind the group of the rule and invite a comment about what the first speaker said.

I am not sure it is possible to say much more about working with film (and I have possibly said too much already) except to try it out!

I offer below some questions and comments specific to each animation that may be useful either as a way of focusing discussion or to work on with a class before viewing.

trigonometry - a key element to discussion of this animation is deciding an unambiguous way of refering to where the point is on the circumference. If this is established it is possible to ask: when is the red/sine line a half?

polyominoes - how many shapes can you make with 5/6 squares? (The idea for the sequencing of pentominoes and hexominoes offered in these animations was inspired by a poster by Laurinda Brown, which in turn was inspired by a conversation between Alastair McCleod, Chris Smy, Fiona Clemes, Alf Coles, Laurinda Brown and Jan Winter.)

mystic roses - how many lines are needed to complete any mystic rose?

van shooten's theorem - inscribe an equilateral triangle in a circle. Draw a point on the circumference and join it to all three vertices. How are these three lengths related?

parallel lines - what do you see? How many angles are there?

tessellation - find me a quadrilateral that will not tessellate