Tuesday, 12 November 2013

The heart of mathematics:

In an interview about the new primary mathematics curriculum, Debbie Morgan, Director of Primary at the National Centre for Excellence in Teaching Mathematics, has stressed that mathematical reasoning and problem-solving are to be at the heart of children's experience of mathematics.

She argues for the prominence of the three aims given at the start of the mathematics section of the document in determining what children learn and how they learn it. These three aims are, in summary, (1) fluency based on conceptual understanding; (2) reasoning mathematically; and (3) problem-solving.

All this would be great, if it were not for the fact that the detail in the subsequent pages and pages of statutory requirements focusses almost entirely on the first of these and contain very little to indicate how precisely the other two are to be developed.

Two factors that will be crucial in this are the end-of-key-stage 2 national tests (the so-called SATs) and Ofsted's approach to inspection.

Over the years those responsible for the national tests have at least identified aspects of 'using and applying mathematics' as defined in the current curriculum that can be assessed in the context of written tests. This has been possible because, for all its deficiencies, the current curriculum does actually  contain specific statutory requirements for children's learning in this respect. I fear that the likelihood is that there will be political pressure on test developers for the 2016 tests onwards – when Gove's new curriculum will start to be assessed – to emphasise disproportionately the assessment of written, formal arithmetic skills and to assess only the detailed statements in the programmes of study. Is there any hope that aims 2 and 3 will be not be overlooked entirely in the national tests? If they are then teachers will overlook them in their classrooms as well. And Debbie Morgan's laudable aspirations will prove to be a fantasy.

And is there any hope at all that Ofsted will give the highest endorsements to those schools who seek to embrace all three of the aims in the experience they provide for children? Will they be checking that children are engaged in genuine mathematical reasoning, following a line of enquiry, conjecturing relationships and generalisations, developing arguments, applying their mathematics to non-routine problems? Or will they just be checking that Year 4 children can multiply a 3-digit number by a single-digit number using the formal layout, that Year 5 children can multiply a mixed number by a whole number and that Year 6 children can divide a fraction by a whole number?

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