Leren vermenigvuldigen met meercijferige getallen

The reason for this study lies in the fact that efforts to create a learning trajectory for the domain of multidigit multiplication based on the realistic approach of mathematics education and building on children’s own informal strategies with the aim of transforming these strategies into efficient notation-supported calculation strategies, have not been quite successful. That this is the case, can not only be concluded from an analysis of common learning trajectories in recent Dutch mathematics textbooks, but also from a number of personal experiences of the researcher with the development of one of these textbooks. Moreover recent research in the field of multidigit multiplication in The Netherlands, shows that the success rates being obtained by 11-12 year old Dutch students with solving problems in this field such as the one below, have dropped over the last ten years substantially from about .75 to .60. Research also shows that the number of students that use mental strategies without supporting those strategies with appropriate auxiliary notations, is increasing considerably. With these facts in mind a research was conducted that addresses the following questions: (1) How can a learning trajectory for multidigit multiplication be shaped that builds on students’ own, informal strategies and that helps them to develop theses strategies into efficient, notation-supported calculation strategies in the domain of stylized mental computation? (2) How do the solutions and the notations of the students develop under influence of such a learning trajectory? And to what extent does this learning trajectory provide also weaker students with sufficient support to develop the intended strategies? (3) What are the key elements of a local instruction theory that constitutes the rationale for such a learning trajectory? The research fits in with the tradition of developmental research that has been established in The Netherlands as a type of research in which, on the basis of an overarching domain specific theory (known ...