The use of additive composition in arithmetic: the case of children classified as low attainers

Abstract

This study investigated the conceptual understanding that low-attaining children have and are able to use in arithmetic. Fifteen 6–7 year old children solved pairs of conceptually-related addition problems. Conceptual relations between equal problems were constructed to reflect aspects of the principle of additive composition. Children's conceptual understanding was explored by examining their capability to use concept-based approaches in related problems, and ability to recognise and explain additive composition relationships. The findings indicate that, when prompted, children who employ only basic calculation procedures have the capability to recognise and use additive composition relations in problem solving. Almost all children showed increased sensitivity to additive composition relations when asked to explain the equality between related problems. Our findings highlight the need to develop pedagogical approaches that instigate low-attaining children's conceptual capabilities and support the operationalisation of these in the kinds of concept-based strategies that are most typically ascribed to high-attaining children.

Keywords:

• arithmetic
• concepts
• addition

Acknowledgements

We are grateful to the children, teachers and head teachers of the schools that participated in this research. The project was supported by the University of Southampton ‘Adventure in Research’ Award (A20051).