Which Mental Strategies in the Early Number Curriculum? A Comparison of British Ideas and Dutch Views

Abstract

AbstractMental arithmetic has recently gained a higher profile in primary mathematics. The question then arises whether mental strategies should be left to spontaneous development or should be taught in some didactic order? In reaction to a School Curriculum and Assessment Authority (SCAA) discussion paper and other publications a comparison is made between British ideas and Dutch views. In the Netherlands the Realistic Mathematics Education theory has, since the 1980s, inspired textbook design and teaching practice, but also discussions on mental mathematics. Better balancing between ‘mental recall and mental strategies’ led to an improved National Programme (1990) and a second generation of revised textbooks. A great difference is the radical choice for postponing (formal) place value and written algorithms and building first on pupils’ (informal) mental strategies. This principle of ‘progressive mathematisation’ is developed further with the empty number line as a new model for mental strategies up to 100. Some British experts have called for a similar curriculum change. Although current suggestions for everyday mental activities and for mental methods in relation to written procedures mark a beginning, they are analysed as not going far enough. The assumption is made that British pupils also develop informal mental strategies, which deserve more substantial attention.