Week 6: Teaching and learning about geometry
Our brains have been constructed in such a way that they are extremely concerned with vision. Vision, I understand from friends who work in neurophysiology, uses up something like 80 or 90 percent of the cortex of the brain... Understanding, and making sense of, the world that we see is a very important part of our evolution. Therefore, spatial intuition or spatial perception is an enormously powerful tool and that is why geometry is actually such a powerful part of mathematics – not only for things that are obviously geometrical, but even for things that are not. We try to put them into geometrical form because that enables us to use our intuition. Our intuition is our most powerful tool... I think it is very fundamental that the human mind has evolved with this enormous capacity to absorb a vast amount of information, by instantaneous visual action, and mathematics takes that and perfects it.
In his article, Atiyah (2001) makes the point that geometry is a valuable part of mathematics because it allows us to use our spatial intelligence, gleaned from our visual experience of the world, to make connections with mathematical concepts.
Geometry gives learners the opportunity to form reasoned arguments based on geometrical figures that they can see (and perhaps touch, in the case of 3D figures) to convince themselves and others. This can eventually lead to the more sophisticated skills of conjecture and deductive reasoning.