In this paper, motivated by the desire to understand which forms of parent-initiated activity are productively implicated in young children's mathematics learning, we present a methodological critique of recent research. Many such studies, based on assumptions that parent-initiated activities can be categorised as formal or informal, direct or…

A clinical task-based interview can be seen as a situation where the interviewer-interviewee interaction on a task is regulated by a system of explicit and implicit norms, values, and rules. This paper describes how documenting and mapping triadic interaction among the interviewer, the interviewee, and the knowledge negotiated can be used to…

The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)

Students were asked to make up a mathematics problem that would be difficult for a friend to solve: a subsample of 11- to 13-year-olds was interviewed as they solved the problems. Made-up problems were found to be a useful tool for studying mathematically talented children. (MNS)

This comment attempts to identify different "semiotic perspectives" proposed by the authors of this special issue according to the problems they discuss. These problems can be distinguished as problems concerning the representation of mathematical knowledge, the definition and objectivity of meaning, epistemological questions of learning and…