Argues that inventions are of the utmost importance in knowledge development, and that conventions play an important role in inventions by providing support for their development. This position borrows from Piaget's perspective regarding figurative and operative aspects of thought. Contains 22 references. (DDR)

This paper examines students' mathematics learning in a social context as two versions of an instructional sequence designed to facilitate students' development of a conceptual foundation for place-value numeration are enacted in two third grade classrooms. The same instructional sequence is used in each classroom with the regular classroom…