Young children’s spontaneous representations of multiplicative semantic structures before formal introduction

We present an exploratory study on young children’s spontaneous representations of multiplicative problems. In contrast to prior research on this topic we investigate children’s responses to using different means of representation (manipulatives and drawings) and different multiplicative semantic structures including equal groups, allocation, comparison, and rectangular array. Nineteen task-based interviews involving Australian and Italian children were analysed. Results suggest that children aged 5 to 6 years old can represent different multiplicative semantic structures, but some structures appear to be more difficult than others. We found that drawing provided an alternative tool to manipulatives when representing the problem, and sometimes drawing was easier for children than representing with manipulatives. Some of the difficulties experienced by children seem to be related to their familiarity with the mathematical language. This observation opens possible paths for future research.