1 Intuitive learning
Learning about circles is part of learning about geometry. Geometry is often regarded as a part of the school mathematics curriculum that is difficult to understand and, as a result, can only be learned by memorisation.
This may seem surprising because life is full of geometry and we use it all the time and by doing so, develop an intuitive understanding of geometry. Byers and Herscovics describe intuitive understanding as ‘the ability to solve a problem without prior analysis of the problem’ (1977, p. 26).
So it should be possible to experience school geometry as an interesting, understandable and relevant subject area that relates to life experiences and builds on existing and often practical knowledge. There are barriers to achieving this, however.
Pause for thought
Thinking of your own classroom, list three barriers to building on the intuitive understanding of your students to learn geometry.