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 (LPAR). Our learning progression in generalisation is more specific than the LPAR, more coherent regarding algebraic generalisation, and enabling teachers to locate students’ performances within the progression and to target their teaching. In addition, a selection of appropriate teaching resources and marking rubrics used in the RMFII project is provided for each level of the learning progression.

概括是学习代数的一个关键特征，需要澳大利亚课程的所有四个熟练程度：数学 (AC:M)：理解、流利、解决问题和推理。通过对文献的回顾，我们提出了一个由五个级别组成的代数泛化学习进程。然后通过参考从先前的 Reframing Mathematical Futures II (RMFII) 项目中获得的大量评估任务来阐述和验证我们的学习进度。在 RMFII 项目中，Rasch 对 5000 多名高中生（7-10 年级）对代数任务的反应进行了建模，从而开发了代数推理学习进程 (LPAR)。我们在泛化方面的学习进展比 LPAR 更具体，在代数泛化方面更加连贯，并使教师能够在进程中定位学生的表现并针对他们的教学。此外，RMFII 项目中使用的适当教学资源和评分标准的选择适用于学习进程的每个级别。