Flexibility and Adaptivity in Arithmetic Strategy Use: What Children Know and What They Show

Abstract

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from the Netherlands completed a comprehensive assessment of adaptive expertise in the domain of multidigit subtraction, designed to measure, first, the strategies students know and use to solve subtraction problems (potential and practical flexibility). Second, it measured to what extent students know which strategy is optimal and to what extent they use the optimal strategy (potential and practical adaptivity). Findings for flexibility showed that most students consistently used the same strategy across all problems: practical flexibility was low. When prompted, students knew more strategies than they used spontaneously, suggesting hidden potential in flexibility. Findings for adaptivity showed that students hardly ever spontaneously used the task-specific strategy that is efficient for specific problems since it has the fewest and easiest steps. However, almost half of the students could select this strategy from a set of given strategies at least once. Furthermore, an innovative, personalized version of the choice/no-choice method showed that the task-specific strategy was usually not the optimal strategy (fastest strategy leading to a correct answer) for individual students. Finally, students used the strategy with which they performed best more often than the other strategies, but there is hidden potential for the adaptive use of task-specific strategies.

Keywords

• mathematics
• subtraction
• strategies
• flexibility
• adaptivity
• adaptive expertise
• primary school