Meaningful learning of formal mathematics in regular classrooms remains a problem in mathematics education. Research shows that instructional approaches in which students work collaboratively on tasks that are tailored to problem solving and reflection can improve students' learning in experimental classrooms. However, these sequences involve…

This case study discusses an activity that makes up one of five lessons in an ongoing classroom teaching experiment. The goal of the teaching experiment is (a) to gain insight into kindergartners' spatial structuring abilities, and (b) to design an educational setting that can support kindergartners in becoming aware of spatial structures and in…

This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

Shows fragility of knowledge in connection with a false application of mathematical induction, as observed in a problem-solving course for prospective teachers. The attempt to explain the observations is based upon an analysis of the logic underlying proof by mathematical induction and a concept formation theory. (MKR)