Magazine article Mathematics Teaching

The Draft National Curriculum for Primary Mathematics

Magazine article Mathematics Teaching

The Draft National Curriculum for Primary Mathematics

Article excerpt

Ian Thompson looks at the detail in the documentation

After many months of deliberation by the Expert Panel for the National Curriculum review and by the official Advisory Committee (in addition to a rumoured 'unofficial' one [see Pollard, Observer website 17 June 2012]), a range of documents appeared on the Department for Education's (DfE) website. These documents comprise mainly studies of highachieving jurisdictions, but also include the longawaited National Curriculum for mathematics Key Stages 1 and 2- Draft (DfE 2012).

Since the publication of these curriculum documents all three members of the Expert Panel - Professors Andrew Pollard, Mary James and Dylan Wiliam - have complained that their expert advice appears to have been ignored. According to the Guardian website (12 June 2012) Tim Oates, chair of the Expert Panel and member of the Advisory Committee responded to these defections by saying that "The draft programmes of study are drawn from a rigorous research base both domestically and internationally". This research appears to focus solely on the curricula of the world's highest performing jurisdictions and of 'outstanding' schools in England, with a view to selecting the best bits and cobbling them together to create our own English National Curriculum. There appears to be no reference to the wealth of extant research on the actual teaching and learning of mathematics.

The supporting documents do show awareness of some of the potential problems with adopting curricular elements that work in other countries, but nevertheless they still make recommendations. Perhaps the government needs reminding that this type of cherry-picking was attempted on at least three occasions in primary mathematics in the late 1990s, with differing - and some might say, hardly memorable - levels of success:

* the Barking and Dagenham Project based its approach on Swiss materials and methods, with textbooks, teachers' manuals and scripted lesson plans translated into English;

* the Panorama programme on maths teaching in Taiwan, based on David Reynolds' Worlds Apart? report (Ofsted 1996), supplied Her Majesty's Chief Inspector, Chris Woodhead, with ammunition to fuel his argument for much more whole-class teaching. In the form of 'interactive whole-class teaching' this became one of the original three key principles of the National Numeracy Strategy (NNS);

* the NNS also attempted to adopt the Dutch 'Empty Number Line' approach to the teaching of mental calculation (another key principle). However, one reason why this was only partially successful was that we did not fully acquaint ourselves with the details of the underlying pedagogy.

This cherry-picking is no more apparent than in statement 56 in the document: Year 3 when they are taught column addition with carrying and subtraction with borrowing. It is difficult to imagine that even Mr Gove wishes us to return to a method of subtraction not (officially!) taught in school since the mid-1960s (see Figure 1). This is the 'borrowing and paying back' method that those of us educated in the 1940s and 1950s were taught, and probably never really understood, particularly as the method had nothing whatsoever to do with 'borrowing and paying back' but with the more sophisticated concept of 'equal additions' to the minuend and the subtrahend.

Figure 1 illustrates what 'borrowing' in subtraction means in the UK, whereas what it means in the USA is the algorithm we call 'decomposition' (see Figure 2). Now since the maths curriculum of the jurisdiction of Massachusetts was investigated as one of several that performed better than England in the PISA tests, i.e. the international tests for secondary-age children, it is hard not to conclude that 'borrowing' was simply lifted from their curriculum and imported into ours, with no awareness of the different meanings. Of course, I may be completely wrong, and perhaps 'equal additions' is making a comeback after 50 years on the sidelines! …

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