Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric…

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

This paper is a translation of a report on two Swedish investigations concerning children's lack of understanding of the quantitative value of numbers (specifically, decimals and fractions). (MN)

Students recognized as less successful individuals in mathematics are tested for their understanding of fractions. The data reveals that most were only able to apply remembered rules to problems without actually knowing if the rule worked for the given situation. (MP)

Presents two case studies of learners attempting to understand the concept of normal distribution, specifically why physical phenomena such as height fall into normal distributions. Draws conclusions about a Connected Mathematics learning environment that enables confrontation with epistemological anxiety and the features of modeling languages…