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…

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

Contemporary research from a psychology of mathematics education perspective has turned increasing attention to the structural development of mathematics as an explanation for the wide differences in mathematical competence shown upon school entry and in the early school years. Patterning, multiplicative reasoning and spatial structuring are three…

Presents an analysis of young students' development of multiplication and division concepts based on a multimodal Structure of the Observed Learning Outcome (SOLO) model. Describes a SOLO developmental model for multiplication and division in terms of developing structure and associated counting and calculation strategies. Contains 48 references.…

This article explores children's responses to a task that requires them to represent square units in a grid pattern, and highlights the importance to a child's mathematical development of recognizing pattern and structure. The grid task explores children's imagery association with area measurement, and provides clear evidence of students'…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…