There seems to be an even greater number of pupils and adults who panic at Maths – or merely arithmetic. Too often I think the non maths specialists in primary school don’t feel confident themselves and this comes through to the students.
Using the spirograph is just one way some of the power of pattern can be explored in a way that at first sight, seems to have nothing to do with maths. I think we are all familiar with the concept – a game with wheels and open circles, all toothed so one can move round inside or outside another to create magical looking patterns. When children play with these, sometimes they may get really disappointing designs looking more like an aeroplane propeller than the intricate firework explosions of the more appealing designs. With just a little prompting and consideration of the number of teeth on the pieces used, it doesn’t take too long for many to realise that numbers which are relatively prime give the more intricate patterns.
This sort of thing could be introduced at various ages. For example I could see that a good project/investigation aimed at GCSE level would be possible. Equally it could be used in primary school. At about age 8/9 it could be a gifted and talented project (and be linked with curve stitching or envelopes of curves). By age 10/11 with a little planning it could be used in mainstream, larger groups.
After my Countdown audition we dropped into an exhibition in the Wellcome building nearby. Their shop seems to be run by Blackwells and I spotted a pack that seemed to have identified the scope of these spirals and I couldn’t resist seeing what they had done. It is attractively packaged – a few spirograph pieces plus a small booklet. The booklet would possibly not appeal to many children but could help a teacher who wanted to make some activities. I think I would have liked to see some worksheets or suggested tasks and I may even try to make some myself.
Many years ago, there was a program called Spirals we used to run on BBC computers. It created the spirograph drawings on screen once the user had chosen which pieces they wanted to use and allows students to extract the patterns and underlying maths without being troubled with the mechanics of slipping pens or hands. How well we used that software and I’ve never seen similar for the PC. There are some websites with a few of the same characteristics.
An online spirograph using Java. I will try to add the code to embed it here.
Each link will give rise to sites where you might find other interesting maths games and ideas. Curve stitching is a little like a spirograph – it allows us to create curves by enclosing an area between straight lines. It is a nice way to create a cardiod – perhaps an interesting task nearing valentine’s day? I really think such investigations can awake a child’s mathematical curiosity which is perhaps almost as important as success in manipulating number if we want young mathematicians. These sorts of experiments could be managed as easily in a home educator’s environment as in a classroom or an after school maths club.
<applet codebase="http://wordsmith.org/anu/java/" archive="Spiro.jar" code="Spiro.class" width=680 height=400> <param name="R" VALUE="81"> <param name="smallr" VALUE="2"> <param name="O" VALUE="71"> <param name="movingCircleOut" VALUE="false"> <param name="redBits" VALUE="242"> <param name="greenBits" VALUE="255"> <param name="blueBits" VALUE="139"> <param name="colorMode" VALUE="multi"> </applet> <br> Created by <A HREF="http://wordsmith.org/anu/">Anu </A> <a href="http://wordsmith.org/anu/">Garg</A>. <p>