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By Pavlov N. D.

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I hated maths. I still hate maths’. There is no need for us to lose so many children at the first hurdle. The relationship between numerical representations and operational calculation is subtle, and crucial to the way both teachers and children operate in classrooms. It is very far from being of solely theoretical importance. It deserves very close attention whenever the Framework becomes due for revision. References Anghileri, J. ) (2001) Principles and Practice in Arithmetic Teaching. Buckingham: Open University Press.

So the answer is 27’. As you would probably agree, this is not too easy to follow! The point being made is that there is not a particularly smooth transition from the language and reasoning associated with chunking to the language of the standard algorithm. 4 Calculating 972 ÷ 36 by standard algorithm Deconstructing NNS ‘calculation’ 25 levels of sophistication in children’s confidence and understanding, in that the less confident can remove small chunks; the more confident can take away larger chunks; and the most confident can subtract the maximum-sized chunks.

It is here that a substantial shift in philosophy can be observed. ’ The NNS would appear to be providing conflicting messages about mathematics. We appear to be saying to children, ‘When calculating mentally you can use whatever method you like, but when doing written calculations you should use just one method, which I will teach you’. This is likely to result in children having difficulty in deciding when it is acceptable to use one’s own methods. In Years 4, 5, and 6 (DfEE 2001: 76) the advice for progression towards a compact written method is: • • • • • establish mental methods, based on a good understanding of place value; present calculations in horizontal format; show children how to set out calculations vertically, initially using expanded layouts that record their mental methods; as children become more confident, refine the written record into a more compact method; extend to larger numbers and to decimals.