The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

How children regulate their own collaborative learning

In this article we analyze the dialogic learning of one pair of students in order to investigate how these students cope with a collaborative learning situation in the classroom. Our aim is to substantiate the claims that not only are young students (8 year olds) capable of solving mathematical problems collaboratively, but that they also take an active role in regulating their collaborative learning activities. More specifically, our claim is that children appear to apply constructs of "mathematical level raising", "social interaction" and "division of time" to steer their own collaborative learning and that they are rather successful in balancing these three aspects. The analysis is exploratory, but this new perspective on collaborative learning is relevant theoretically and consequential for classroom practice