MENTAL STRATEGIES AND MATERIALS OR MODELS FOR ADDITION AND SUBTRACTION UP TO 100 IN DUTCH 2ND GRADES

Dutch mathematics programs emphasize mental addition and subtraction in the lower grades. For two-digit numbers up to 100, instruction focuses on ''counting by tens from any number'' (N10), a strategy that is difficult to learn. Therefore, many children prefer as an easier alternative ''decomposition'' in tens (1010) and units. Instead of the use of arithmetic blocks (BL), the hundredsquare (HU) was introduced in the 1980s because of a (supposed) better modeling function for teaching N10. In a field study with several schools, (a) we compared the strategies N10 and 1010 on procedural effectiveness and error types, and (b) we assessed the influence of the support conditions BL versus HU on the acquisition of mental strategies (we had also a control condition NO with no extra materials or models). Results confirmed the greater effectiveness of N10 but also the preference of many weaker children for 1010. Support for BL or HU had differential effects on mental strategies. Differences are discussed in terms of cognitive psychology: the role of declarative knowledge and the relation between conceptual and procedural knowledge. New Dutch proposals for the 1990s emphasize teaching both strategies N10 and 1010 to enhance the flexibility of students' mental arithmetic.