The Pedagogical System for Mathematics

Teaching ways of communicating mathematically demands skilful work on the teacher‘s part (Walshaw & Anthony, 2008). Students need to be taught how to articulate sound mathematical explanations and how to justify their solutions. If students are to make sense of mathematical ideas they need an understanding of the mathematical language used in the classroom.

In whole-class discussion, teachers are the primary resource for nurturing patterns of mathematical reasoning. Teachers manage, facilitate, and monitor student participation and they record students’ solutions, emphasizing efficient ways of doing this.

Posing tasks of an appropriate level of mathematical challenge fosters students‘ development and use of an increasingly sophisticated range of mathematical thinking and reasoning.

Open-ended tasks are ideal for fostering the creative thinking and experimentation that characterize mathematical “play”. For example, if asked to explore different ways of showing 2/3, students must engage in such fundamental mathematical practices as investigating, creating, reasoning, and communicating.

Teachers have a critical role to play in ensuring that tools are used effectively to support students to organize their mathematical reasoning and support their sense-making.

Effective teachers draw on a range of representations and tools to support their students’ mathematical development. These include the number system itself, algebraic symbolism, graphs, diagrams, models, equations, notations, images, analogies, metaphors, stories, textbooks, and technology. Such tools provide vehicles for representation, communication, reflection, and argumentation.

If tools are to offer students “thinking spaces”, helping them to organize their mathematical reasoning and support their sense- making, teachers must ensure that the tools they select are used effectively.