An empirically based practical learning progression for generalisation, an essential element of algebraic reasoning

Abstract

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is then elaborated and validated by reference to a large range of assessment tasks acquired from a previous project Reframing Mathematical Futures II (RMFII). In the RMFII project, Rasch modelling of the responses of over 5000 high school students (Years 7–10) to algebra tasks led to the development of a Learning Progression for Algebraic Reasoning (LPA..