ABSTRACT

Reform of the mathematics curriculum has led to a shift in teaching arithmetic from the repetition and rehearsal of standard written procedures to a focus on developing children’s own approaches. Children today are expected to observe patterns and relationships so that they understand connections among the different numbers and operations, and develop a ‘feel’ for numbers often referred to as ‘number sense’. The term ‘number sense’ is widely used across the world in reform documents (NCTM, 1989; AEC, 1991) and refers to ‘flexibility’ and ‘inventiveness’ in strategies for calculating as a reaction to overemphasis on the computational procedures that have been taught in the past that were devoid of thinking. Pupils today are expected to understand the calculation methods that they use in a way that contrasts starkly with past expectations. For pupils with special educational needs this can be both an opportunity, as their thinking about problems is respected, but also an added pressure as it can be difficult to understand the compact standard methods. In the past, understanding was not required. This is made clear in the following quote from a section entitled ‘Over-explanation of processes to duller pupils’:

… what they need to know is how to get the sum right, and when they have learned the method so thoroughly that the possibilities of getting the particular type of sum wrong are only the ordinary ones due to chance, then explanations might be attempted … Why should we burden children with unnecessary explanations in arithmetic?

(Schonell, 1937, p. 73) Reflecting current expectations, the UK Framework for Teaching Mathematics from Reception to Year 6 uses the term ‘numeracy’ to identify ‘the proficiency in number that involves a confidence and competence with numbers requiring an understanding of the number system, a repertoire of computational skills and an inclination and ability to solve number problems in a variety of contexts’ (DfEE, 1998). The National Curriculum reinforces the importance of flexibility in approaches to calculations requiring ‘efficient written methods’ rather than standard written methods and notes that ‘pupils are expected to use mental methods if the calculations are suitable’ (DfEE, 1999, p. 23).