This article explores the educational and philosophical contributions of Nikolai V. Bugaev, a prominent 19th-century Russian mathematician and founder of the Moscow philosophical-mathematical school. The study specifically focuses on Bugaev's textbook, "Arithmetic of Whole Numbers," analyzing Bugaev's pedagogical approaches within the…

The development of proportional reasoning has long been recognised as a central but problematic aspect of mathematics learning. In a Year 6 teaching intervention the part/whole notion of fractions was distinguished from the part: part notion of ratio, and the "between" and "within" relationships in ratio were emphasised.…

It is argued that Australian elementary mathematics curricula have been influenced by earlier British and United States educational movements and theories and are out of touch with current research emphasizing a constructivist approach. A new model of young children's numerical development is offered, and recommendations for improving mathematical…

Presents a developmental framework for the study of culture and cognition in which cultural practice is a key organizing construct. Argues that systematic analysis of either cultural change or cognitive development requires that they be understood relative to one another in a single integrative treatment. (Author/SD)