Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school…

This article examines students' ability to use the balance model to solve for unknowns. A teaching experiment was conducted in four Year 3 classrooms. This experiment focused on exploring the application of the balance model as an analogue for representing equations and solving for unknowns. The teaching experiment promoted a shift by students…

Explores teachers' practices and relates them to their goals. Indicates that syllabus documents have influenced teachers' choices of teaching strategies and that most teachers had calculation-based goals for less able students and conceptual goals for more able students. Identifies teaching strategies and discusses the relationships between…