Becoming fluent in Maths

In How I Rewired My Brain to Become Fluent in Math Barbara Oakley writes that developing an understanding on a topic isn't enough. You also need memorisation and repetition to retain that understanding and develop fluency. In other words for understanding to turn from ephemeral to permanent students need to practice.

Oakley explains how chunking is vital in developing skills (in language and maths):
This approach—which focused on fluency instead of simple understanding—put me at the top of the class. And I didn’t realize it then, but this approach to learning language had given me an intuitive understanding of a fundamental core of learning and the development of expertise—chunking.

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Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.