# Arithmetical Strategies

In 2001, Swan and Sparrow argued that learning arithmetical strategies is best done through rich, dialogic talk and participation in rich, worthwhile tasks. Rather than an ‘ad hoc, laissez-faire approach’ (Swan and Sparrow, 2001), quality teaching of strategies involved the careful consideration of the questions to be asked, stimulus and tools to be used, the observations to be made and the strategies and talk to be highlighted. They synthesised research and listed what, at the time, we knew about computation:

- ‘Children invent their own strategies for calculating mentally (Kamii, 1994; Kamii, Lewis & Livingston, 1993);
- Children often adopt one method in school and another out of school (Carraher, Carraher & Schliemann, 1985);
- Methods vary from child to child and even the same child may choose to use different methods to solve similar problems at different times (Hope & Sherrill, 1987);
- Mental strategies differ from written methods: for example, many mental strategies for addition, subtraction and multiplication start from the right, Mathematics: Shaping Australia 237 whereas most mental methods start from the left (Askew, 1997; Hope & Sherrill, 1987); the teaching of written methods, particularly at an early age can stifle the development of mental strategies (Carraher & Schliemann, 1985; Kamii & Dominick, 1989);
- Some mental strategies are more efficient than others: for example, counting on in ones from a smaller number rather than the larger of two numbers if adding (Hope & Sherrill, 1987); and
- Strategies have been identified and coded, although strategies are often referred to by different names and codes in the literature (McIntosh, deNardi & Swan, 1996).’ (Swan and Sparrow, 2001, pp. 236-237)