As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

Describes study of elementary school children in Australia which was designed to determine their sequential knowledge of measuring length and to apply recent cognitive theories to predict the sequence of development of knowledge. Recent literature is reviewed, information processing skills are discussed, and skills required for measuring length…

Proposes that ability is a concept central to the current practices of mathematics teaching. Argues that the widespread view that mathematics learning is an ordered progression through a hierarchy of knowledge and skills subjects students to "ability stereotyping" and serves as a gross global model. (TW)