Plato's Circles and School

Draw a circle on a piece of paper. Zoom in and you'll find uneven lines and flat spots yet you still know that it is a circle. 2000 years ago, Plato used this observation to ask the question: where does our idea of a perfect circle come from and further our idea of a perfect form?

No circle that you can create or see will ever be a real perfectly smooth circle. But intuitively we all understand what a perfect circle is and as a species we have even defined it: all points are exactly the same distance from the centre. This is an example of a Form, an unchanging idea that the physical world can only imitate.

This is seen in our maths too. When we use the formula pi*r^2 to find the area of a circle, we are working with the perfect worm. Our geometry deals in ideals: shapes, lines with no thickness, points with no size. This contributes to why maths can feel certain in a way that a real object may not.

Beyond the theoretical and school problems we can learn study tips from this. Think of textbook questions, past paper problems and worked examples as our imperfect physical representation of the ideas we learn. Each one is a slightly different version of the idea, which is the Form.

Students who only memorise examples or specific questions are learnign imperfect ideas, copies, so when a question comes up with different wording or numbers they can find themselves stuck. Students who understand and work out the ideas behind the examples can tackle any copy that comes their way because their understanding goes beyond the question on the paper in front of them.

So, after finishing a question, stop and ask what idea is it really testing. A dozen different graphing questions might look nothing alike but the form and idea behind them is all the same. If you can explainan idea in one sentence, youll recognise it on exam day even when its dressed up as something new.