Knowing and Building on What Students Know: The Case of Multiplicative Thinking

Identifying and building on what students know in relation to important mathematics is widely regarded as essential to success in school mathematics. However, determining what is important and identifying what students actually understand in relation to what is deemed to be important are by no means uncontested or straightforward endeavours. In recent years attention has turned to the development of evidenced-based learning trajectories (or progressions) as a means of identifying what mathematics is important and how it is understood over time. But for this information to be useful to practitioners, it needs to be accompanied by accurate forms of assessment that locate where learners are in their learning journey and evidenced-based advice about where to go to next. This chapter traces the origins of the Scaffolding Numeracy in the Middle Years (SNMY) research project that used rich assessment tasks and Rasch analysis techniques to develop an evidence-based framework to support the teaching and learning of multiplicative thinking in Years (Grades) 4 to 9.