In most epistemologies, practical actions and speech are the consequences of thought. In this study, I provide three case studies of highly educated scientists producing aspects of graphs only to erase these as soon as they have been drawn. The case studies are consistent with an alternative approach, already formulated by L. S. Vygotsky and M.…

Standard approaches to thinking in the mathematics curriculum depict it as the result of some stable constructions in the mind of the person, constructions that are the results of individual efforts in the mind of subjects or of collective efforts that are then appropriated by and into the mind of individuals. Such work does not appreciate what…

Provides an example of the integration of science and mathematics learning of one high school physics student in a constructivist classroom. Discusses the student's integration of mathematical and nonmathematical representations and of different mathematical representations in a nonuniform acceleration experiment. Describes a model for integrating…