Tuesday, 30 July 2013

Column addition and subtraction

I have just spotted an extraordinary assertion in the (non-statutory) notes and guidance in the proposals for mathematics in the new primary school curriculum. This relates to the programmes of study for Year 2 – that's children aged 6–7 years by the way. Alongside the requirement that children should add and subtract numbers using concrete objects, pictorial representations and mentally, we get this: 'Recording addition and subtraction in columns supports place value ...' They are talking here about additions and subtractions such as 27 + 4, 37 – 20, 24 + 25, 3 + 5 + 9.  So, apparently, children should do these calculations by informal methods, but then record them in column form, because this recording supports place value! No, it does not! There's no evidence at all to support this assertion. I can only assume that it reveals the unjustified preconceptions about the proper ways of doing arithmetic that are held by whichever individuals are driving this curriculum.

I refer the reader to the research of Ian Thompson (Educational Review, 52(3), 2000). Few children up to the age of 9 have a good understanding of the sophisticated concepts of place value. The kind of calculations they are doing in Year 2 require only a grasp of quantity value – which is that, say, 27 is made up of 20 and 7 – and where 27 comes in the sequence of counting numbers. Column recording encourages children to think of, say, 27, as being made up of a 2 and a 7, not a 20 and a 7, so it actually undermines their development in the early stages of understanding place value.

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