When I first started the geometry block with my son Tristan, I was surprised how quickly I fell back to my own education and methods of being taught. Spewing out technical terms and hard to grasp explanations it didn’t take long for me to realise what I was doing wrong. Despite Tristan’s ability to learn quickly, I could see the puzzled expression on his face. Cutting the lesson short, I took the rest of the afternoon to do research and reflect. Geometry is a hands on subject, but it doesn’t end with the use of a standard protractor and compass set. In fact, geometry is so vast that one can take examples from anywhere in nature, whether we use examples from our homes or the infinite possibilities in the great outdoors.
I found the book ‘String, Straight Edge, & Shadow the story of Geometry’ by `Julia E. Diggins to be an extremely useful resource. Not only can you learn the history and evolution of geometry, you can imitate and recreate the experiments and examples used by the fore fathers who helped shape the subject to what it is today.
Being smack dab in the middle of winter, I figured we could use the fresh white snow as a giant black board for our drawings and experiments, but due to an unusually warm winter the ground was sparse. Instead, I brought the boys to a lakeside park where we would be able to draw in the sand and play in the warm sun.
The first part of our lesson consisted of finding sticks in the forest that we could cut down into equal sized stakes. Then, once cut we took two of the sticks and tied a long piece of string from one to the other. The idea was to make a giant compass, staking one end into the ground and using the other to draw with. Tristan set to drawing intricate designs in the sand using different sized circles, while and extending the string, allowing it to revolve around the point in the center. I left him to experiment on his own, only offering suggestions from time to time. It was easy to slip in the various terms such as the diameter, radius and circumference with such a huge drawing at our feet. We avoided measurements and calculations and focussed on the meaning and method above all else.
I then designed a sundial with Tristan and reviewed the positioning of the clock hands with the shadow of the stake in the center of the sundial. I had Tristan draw in the numbers and we decided to leave it until the end of our play to check and see if the time on our watches would correspond with the diagram in the sand.
This was also a good opportunity to reintroduce the various triangles and angles I had bombarded him with the day before. Taking the extra string we had brought along with the additional stakes, we were able to make a multitude of different triangle and shapes. We even made a square and bisected the angle to make different kinds of triangle shapes. Tristan quickly saw the shapes within shapes and how together they could form others. For example, he saw how two right angle triangles could be placed together to make a square or rectangle. It even offered a chance to touch upon the various odd shapes like the Polygon or Trapezoid.
Thanks to the time taken the afternoon prior to get reacquainted with geometry myself, I was able to cover a lot of ground in a short time. Tristan no longer felt overwhelmed and instead grasped the basic principals and much more by creating these designs on such a large scale. We really enjoyed our selves and spent the rest of that afternoon playing in the park and enjoying the crisp air and bright sunshine.