Solving multiplication and division problems: latent variable modeling of students' solution strategies and performance

National large-scale assessments have demonstrated a decrease in Dutch primary school students' performance on multidigit multiplication and division problems (e.g., 56x23 and 544:34) in the past two decades. This performance decrease appears to be related to changes in students' use of mathematical strategies: the use of relatively accurate strategies for which calculations are written down has decreased, while the use of inaccurate mental strategies has increased. To gain more insight into these developments and how to possibly turn them around, factors that affect students' mathematical strategy use and performance were investigated. New applications of latent variable models to national large-scale assessment data were used to relate teachers' reports of their mathematics teaching to students' problem solving. Follow-up experiments were conducted at primary schools for a more controlled investigation of students' strategy choices and of how to influence those choices (and thereby, performance) favorably. It was found that teachers mainly influence students' choices between strategies with written work, and that they have less influence on choices for the inaccurate mental strategies (made more frequently by boys and weaker students). Extra instruction targeted at the latter was found to increase weaker students' choices for writing down calculations, and this improved students' performance.