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You might be interested in reading this Collaborative Teaching Project led by Barbara Nicolson Martin in 2012.The improvement agent and the maths subject leaders from 5 primary schools within the Braunton Learning Community plus the feeder secondary school researched the current methods of calculation used within their own schools, made comparisons and shared best practice. Together they formulated a joint approach to calculations and mathematical proficiency. They used current research including international comparisons and improved subject knowledge within their schools and encouraged mathematical flexibility across these phases of education leading to improved outcomes for children in: EYFS, KS1, KS2 and year 6 to year 7 transition.
In this article Ian Thompson discusses the difference between mental arithmetic and mental calculation and shares examples of how young children work out simple calculations. He draws conclusions on the most effective mental calculation strategies that our young children need to develop.