How to Build Powerful Learning Trajectories for Relational Thinking in the Primary School Years

There are now strong arguments for building closer links between children’s understanding of numbers and number operations and the beginning of algebraic (relational) thinking in the primary school years. Rarely, however, do Australian mathematics textbooks give enough guidance for teachers to use good activities in the classroom to promote algebraic thinking. By contrast, Japanese mathematics textbooks introduce students to relational thinking about number sentences, starting from the first grade. The idea of a learning trajectory – or trajectories – seems a fruitful way of looking at how this is achieved and what it might mean for the teaching of Number and algebra in the primary years. In its scoping paper, Shape of the Australian Curriculum: Mathematics, the Australian Curriculum and Reporting Authority (ACARA, 2009) undertook to strengthen the links between the teaching of Number and algebra. Referring especially to the middle and later primary years, the paper argued that “An algebraic perspective can enrich the teaching of number …. ” (ACARA, 2009, p. 6). Likewise, in its report, Algebra: Gateway to a Technological Future, The Mathematical Association of America (2007) argued that “We need a much fuller picture of the essential early algebra ideas, how these ideas ar