This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

This article is based on a study that documented the daily work practice of an eighth-grade mathematics teacher and her colleagues at a secondary school in Shanghai when they taught the unit on geometric proofs. Four interrelated work activities were identified to highlight a pedagogy around homework errors. They form an activity system…