4. Methods
4.1. Participants
The overall sample for the study consisted of 10 children (5 boys and 5 girls) aged 5–6, selected from an infant school in southern England (i.e. the sample was taken from a UK Year 1 class). The school was attended by children of mixed socio-economic background. The researcher spent two weeks in the classroom observing and working with the children during their daily arithmetic lessons. This classroom observation and the teacher's previous assessment of individual children's progress informed the selection of the sample. Children who were using addition strategies with confidence were selected to participate in the study. It was considered that by working with children who were applying calculation procedures confidently (i.e. with limited errors) there would be time to focus on the post-success changes that occur in children's problem solving behavior within a suitable number of sessions. A small-scale pilot study conducted before the main data collection with 5–6-year-old participants at a different school had indicated that five sessions provided reasonable time for changes to be introduced and newly generated strategies to be evolved and consolidated while maintaining children's interest in the task.
It is not feasible to present qualitative data from the work of all 10 children in one paper. For this reason, an analysis of the work of four children is presented here in order to illustrate different itineraries of post-success qualitative changes in children's strategies.