I have a deep and abiding love of maths. Largely I think this is due to how I was taught.
I was lucky to have three amazing maths teachers; my mum, Peter Watts and then Dennis Archer.
The fundamental approach all these teacher took was that they understood that maths was simply an abstract language (just like writing) and that it was useful because you can use it to solve interesting real world problems.
I could talk about the maths exercises that excited me the most for hours. Really! They were that memorable and enjoyable. But it may not be particularly interesting to read about! So instead here is a 16 TED lecture on exactly the type of maths education I had.
This video entertainingly demonstrates that formulating the problem one-self helps with understanding the answer and the implication is that this results in lifelong rather than short term learning.
To a large extent this is counterintuitive. Why should maths problems be harder to understand when all the parts are broken down and all the right information is given? There must be a reason, yet psychological research does not yet have an answer to this fascinating question, which probably lies at the heart of intelligence.
I have my suspicions about why formulating the questions aids comprehension. My speculation is that it relates to how the frontal lobe responds when it creates a simulation of the situation and what related knowledge and tools come to bear when this happens. In this view I’m aligning myself with Piaget in his belief that concrete experience is crucial in order to understand the world and with the very recent work of Lakoff and Johnson (1999) who conclude that conceptual knowledge is grounded in experience and concrete sensori-motor information and that abstract knowledge is grounded in metaphor.