Saturday, 12 April 2014

Context-free calculations

So we now know that the national tests for children at the end of Key Stage 2 from 2016 onwards will include one paper (of the three) that will consist of context-free calculations.

That seems a strange idea to me. Mathematics – as far as I understand it as a humble mathematician –
does not generate calculations without a context. Calculations only ever occur in a context. Normally this would be a practical context in which mathematics is being applied, and where the numbers are likely to be attached to sets of items or units of measurement of some kind. Even in pure mathematics, on the rare occasions you might want to do a calculation it would be to investigate the relationships between two numbers that have some property – like finding the ratio of successive terms of the Fibonacci  sequence (1, 1, 2, 3, 5, 8, 13, 21, ...) – so there is a context which provides the need to do the calculation.

Yet our children will be given a test paper consisting entirely of context-free calculations, to be done by prescribed formal written methods, the argument being that these calculations are 'the fundamental processes' of mathematics.


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