This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

That the quality of teachers' knowledge has direct impact on students' engagement and learning outcomes in mathematics is now well established. But questions about the nature of this knowledge and how to characterise that knowledge are important for mathematics educators. In the present study, we examine a strand of "Specialised Content…