The importance of compression when learning maths

I've been reading Jo Boaler's book Mathematical Mindsets and have become really interested in the idea of compression.  This is not a brain process I've heard much about before, but it's described in the following way:

When you learn a new area of mathematics that you know nothing about, it takes up a large space in your brain, as you need to think hard about how it works and how the ideas relate to other ideas. But the mathematics you have learned before and know well, such as addition, takes up a small, compact space in our brain.  You can use it easily without thinking about it.  The process of compression happens because the brain is a highly complex organ with many things to control, and it can focus on only a few uncompressed ideas at one time.  Ideas that are known well are compressed and filed away.

What this means is that when necessary you can recall the maths quickly, to use as a step in another mental process.  However many students see maths as a bit of a slog because they are not engaging in compression - and the reason for this is because maths is often taught as rules and methods, and not as concepts.  The brain can only compress concepts and not rules - hence students who learn the rules have to struggle to hold onto them - they are unable to be compressed, organized and filed away for later use.

This is why it's important to help students approach mathematics conceptually at all times - and the conceptual understanding of maths is what Jo Boaler refers to as a mathematical mindset. This also explains why in Making the PYP Happen it states: "In the PYP, the mathematics component of the curriculum should be driven by concepts and skills rather than by content."

Jo Boaler is a British mathematics educator and is currently Professor of Mathematics Education at the Stanford Graduate School of Education.  Her website is Youcubed.

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