Researchers and governments in the UK, across Europe and in the USA and Canada have raised concern about the low average levels of educational achievement reached by children in public care, including in their home language, in reading and in mathematics. In every country, this group of children form a tiny minority of the school population: for example, approximately 0.6% in the UK (Cairns and Stanway, 2013); this means that some teachers will never work with a child in the care system. However, the experience of children in care can also illuminate the difficulties that many other vulnerable children may encounter, and examining the relationship between foster family and school provides ideas about how home-school links can be strengthened for all families. 

This paper draws on a multiple case study conducted over a year with five children in care (for my successful PhD thesis at the University of Cambridge, 2014). I examined two research questions, with a focus on mathematics teaching and learning at school and at home:

• What are the difficulties faced by children in care aged 7 to 11 whose attainment in mathematics is low, specifically in number?

• What strategies are likely to improve their understanding and progress in number?

The paper will put forward a model that considers previous and current elements of a child's mathematical learning, considering their learning at home and in school, alongside their attainment in mathematics and elements of affect and engagement in learning: their 'productive disposition' (Kilpatrick, Swafford and Findell, 2001). The paper notes that many children in difficulties will develop ways of 'coping' in the classroom that prevent them from learning effectively.

I will concentrate on describing and analysing the experience of one of the five case study children: Skye, aged 8. Skye's case shows the importance of good assessment of a child's needs, of close liaison between school and home, of listening carefully to the child's view, and of professional support for teaching staff and foster carers.

I will outline the likely experience of children before they come into public care and the effect this may have had on their educational achievement.  Skye came into care at age 7, effecting a major change in her circumstances once she was placed with a long-term foster family and moved to a new school, one identified by government inspectors as much more effective than her previous school. However, Skye's time across two academic years in her new school was with two different teachers, one who was very skilled in working with vulnerable children, the other much less so. The classroom experience provided for Skye by each teacher was very different, and affected Skye's disposition to learn and her chance of making progress. This will be examined using Skye's explanations of how she coped in lessons and her view of the relationships she had with the adults teaching her.

Liaison between the school and the foster carers was minimal from both teachers in the new school - although from very different expressed motives. I will discuss the barriers that existed from the point of view of the foster carers as well as the teachers' views.

The paper will also consider one particular method that proved useful in engaging Skye with endeavouring to understand the arithmetic problems she was faced with in class: showing her video clips of herself tackling problems, and discussing this with her. This use of visually stimulated recall seems also to have great potential for professional development work with teachers and parents or carers. 

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