A Developmental Multimodal Model for Multiplication and Division

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 equalgrouping 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.