Research in the psychology of mathematics education has been confronted with the fact that people blatantly fail to solve tasks they are supposed to be able to solve correctly given their available domain-specific knowledge and skills. Also researchers in cognitive psychology have encountered such phenomena. In this paper, theories that have been…

This paper argues that the metaphorical representation of concepts and the appropriation of language-based construals can be hypothesized as additional sources of conceptual change alongside those previously proposed. Analyses of construals implicit in the lay and scientific use of the noun "energy" from the perspective of the theory of conceptual…

The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

In order to understand the advanced, scientific concepts of the various disciplines, students cannot rely on the simple memorization of facts. They must learn how to restructure their naive, intuitive theories based on everyday experience and lay culture. In other words, they must undergo profound conceptual change. This type of conceptual change…