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. (Contains 6 figures.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]