The ideas of Kuhn and Lakatos are used to study four issues in mathematics education related to values, units of analysis, theory of mind, and nature of mathematical entities. The goal is to determine whether differences between the assumptions are best understood in Kuhnian or Lakatosian terms. (MNS)

One cannot begin considering the topic of this colloquium without asking, why twenty years? Why not two hundred? Two hundred years ago, Silvestre Franois Lacroix was about to be named chief officer of the Commission Executive de L'Instruction Publique. Out of that experience, together with his long career in instruction, especially as professor of…

Advanced is the hypothesis that students organize their beliefs about mathematics to resolve problems that are primarily social rather than mathematical in origin. The contextuality of cognition, meaning-making, and learning in interactive situations are each discussed. (MNS)