A Reference Framework for Teaching the Standard Algorithms of the Four Basic Arithmetic Operations: from Theoretical Analysis to Task Design

The study presented in this paper offers a reference framework for characterizing primary school teachers’ mathematical knowledge of the standard algorithms of the four basic arithmetic operations. The framework was first devised theoretically, from mathematical analysis of the algorithms and from past research on knowledge for teaching arithmetic operations with rational numbers. It was then applied to designing tasks for charactering and deepening the teachers' conceptual understanding of the algorithms. The paper contains examples of tasks related to the knowledge of mathematical principles underlying the algorithms, which were tested with a group of 46 primary school mathematics teachers.