Despite the important role that metacognition plays in school mathematics, attention has only recently turned to primary grades. The aim of this exploratory qualitative study was to find out to what extent 6 second graders engage in metacognitive behaviors during mathematics problem-solving. The analysis was based on the adaptation of the…

Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and…

One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous…

Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic…

Six experiments with 42 kindergartners, 190 first graders, and 15 second graders in Germany investigated why arithmetic word problems with an unknown reference set are more difficult for children than are problems with an unknown compare set. Lack of access to flexible language use makes these problems so difficult. (SLD)