An Australian longitudinal study of 319 Kindergartners developed, implemented and evaluated an intervention, the Pattern and Structure Mathematics Awareness Program (PASMAP). It comprised of repetitions and growing patterns, structured counting and grouping, grids and shapes, partitioning, additive and multiplicative structures, measurement and…

We report on 25 Year 5-6 students' written responses to two items taken from an assessment of mental computation fluency with multiplication, alongside their reasoning of the strategy they had employed, which may or may not have made use of the associative property. Coding of this interview data revealed four distinct levels of conceptual…

This is a position paper in which we argue for "Teaching for Mathematising" as a pedagogy that supports teaching mathematics for understanding in primary school. Mathematics education in Australia currently emphasises teaching for mathematical understanding, a shift that redirects children's learning from merely memorising computation…

Evidence suggests that some students have learned procedures with little or no underpinning understanding while others have a much more connected and conceptual levels of understanding. In this article, the work of four primary students is discussed in terms of their contextual understanding of multiplicative concepts. The difference between…

Multiplicative thinking is a critical stage of mathematical understanding upon which many mathematical ideas are built. The myriad aspects of multiplicative thinking and the connections between them need to be explicitly developed. One such connection is the relationship between place value partitioning and the distributive property of…

Multiplicative thinking is accepted as a "big idea" of mathematics that underpins important mathematical concepts such as fraction understanding, proportional reasoning, and algebraic thinking. It is characterised by understandings such as the multiplicative relationship between places in the number system, basic and extended number…

Multiplicative thinking has been widely accepted as a critically important "big idea" of mathematics and one which underpins much mathematical understanding beyond the primary years of schooling. It is therefore of importance to consider the capacity of children to think multiplicatively but also to consider the capacity of their…

Lorraine Day and Derek Hurrell provide a convincing argument for using arrays to promote students' understandings of mental computation strategies for multiplication. They also provide a range of different examples that illustrate the benefits of arrays in the primary classroom.

Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This article reports on a recent study that utilised an interview tool and a written quiz to gather data about children's multiplicative thinking. Our research has so far revealed that many primary…