In 2006 Borthwick and Harcourt-Heath decided to explore the mathematical methods used by children who had been educated after the introduction of the national numeracy strategy (NNS). They looked at how much teaching had progressed since then and also whether children were using a range of strategies and examined what they were. They analyzed the answers of 995 Year 5 children from 22 schools across Norfolk to four questions, each covering addition, subtraction, multiplication and division. Furthermore, because there was no "bridging" involved, they did not feel able to draw conclusions about the effectiveness of the standard algorithm compared to other methods. With subtraction they found a higher percentage of correct than incorrect answers using the number line (13% versus 2%) compared to using the standard algorithm (10% versus 9%). With multiplication, the vast majority of children chose to use the grid method, which has been shown to provide the highest percentage of correct answers. They felt that an even distribution of methods across all categories should be used to answer the question of division. The authors were very impressed by the high number of incorrect answers for all operations except addition. They concluded that “when children use a strategy, based on mental methods, they usually reach the correct solution” (Borthwick & Harcourt-Heath, 2007). They also noted that in the survey there were a number of children who appeared unable to draw on any strategies, and it was therefore evident to them that mental methods had not been taught. When the NNS Framework was published in 1999, one of the characteristics mentioned was “the ability to calculate accurately and efficiently, both mentally and with pencil and paper, drawing on a range of calculations… half the paper… methods of calculus written dents after five years of implementing the national calculus strategy in England”. Oxford Review of Education, 32, 3, 363-380Beishuizen, M. & Anghileri, J.:1998, 'What mental strategies in the early years curriculum? A comparison of British ideas and Dutch opinions'. British Educational Research Journal, 24, 5.DfEE: 1999, Framework for Teaching Mathematics from Reception to Year 6, London: DfEEPlunkett, S.:1979, 'Decomposition and all that rot'. Mathematics at school, 8, 3, 2-7Russell, R.:2013.'Let's take away the confusion!'. Mathematics Teaching, 234, 47-49 Skemp, R.: 1976, 'Relational understanding and instrumental understanding'. Mathematics Teaching, 77, 20-26Thompson, I:1993. "Thirteen Ways to Solve a Problem." Mathematics Teaching, 144, 27-30Thompson, I.:2012. "To Chunk or not to Chunk?". Mathematics teaching, 227, 45-48
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