# Procedural and conceptual changes in young children’s problem solving

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## Abstract

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach, clinical interviews were conducted with ten 5–6-year-old children. The aim was to document how children combine knowledge of addition facts, calculation procedures and arithmetic concepts when solving a multiple-step task and how children’s application of different types of knowledge and overall solving approach changes and develops when children engage with solving the task in a series of problem solving sessions. The study documents children’s pathways towards developing a more effective and systematic approach to multiple-step tasks through different phases of their problem solving behaviour. The analysis of changes in children’s overt behaviour reveals a dynamic interplay between children’s developing representation of the task, their improved procedures and gradually their more explicit grasp of the conceptual aspects of their strategy. The findings provide new evidence that supports aspects of the “iterative model” hypothesis of the interaction between procedural and conceptual knowledge and highlight the need for educational approaches and tasks that encourage and trigger the interplay of different types of knowledge in young children’s arithmetic problem solving.

## Keywords

Arithmetic Addition Problem solving Procedural knowledge Conceptual knowledge Iterative model## Notes

### Acknowledgements

This study was supported by a grant from the Economic and Social Research Council (PTA-026-27-0697). I am very grateful to the children who participated in this project. I would also like to thank my colleagues Keith Jones and Lianghuo Fan as well as the three anonymous reviewers for their very constructive comments on this article.

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