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Teaching in Singapore and Shanghai is often (wrongly) identified as just rote learning of facts. It is true that learning facts to automaticity is an important part of the mastery approach, as this frees up the learners mind to think about concepts and solve problems. But the one of the main goals of the National Curriculum and a big idea for teaching for mastery is fluency. Fluency is about being efficient, accurate and flexible with calculations.

‘… fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. The computational methods that a student uses should be based on mathematical ideas that the student understands well, including the structure of the base-ten number system, properties of multiplication and division, and number relationships.’ – Principles and Standards for School Mathematics (p. 152)



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