Abstract
This paper presents an analysis of young students’ development of multiplication and division concepts based on a multimodal SOLO model. The analysis is drawn from two sources of data: a two-year longitudinal study of 70 Grade 2 to 3 students’ solutions to 24 multiplicative word problems, and examples from a problem-centred teaching project with Grade 3 students. An increasingly complex range of counting, additive, and multiplicative strategies based on an equal-grouping structure demonstrated conceptual growth through ikonic and concrete symbolic modes. The solutions employed by students to solve any particular problem reflected the mathematical structure they imposed on it. A SOLO developmental model for multiplication and division is described in terms of developing structure and associated counting and calculation strategies.
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