What should be the focus of emotion regulation in children? A nonlinear dynamic mathematical model of children's peer interaction in groups.

This paper questions the assumption that children's social and emotional competence be placed within the developing child, rather than in the interaction of the child with the range of peer social ecologies in which the children might function. This paper presents a new nonstatistical mathematical approach to modeling children's peer social interaction in small groups using nonlinear difference equations in which both an uninfluenced and an influenced regulatory set point of positive minus negative interaction can be separately estimated. Using this model and the estimation procedure, it is possible to estimate what a focal child and the group initially brings to the group interaction and also how these regulatory set points are influenced by the interaction to determine two influenced regulatory set points. Six-person mainstreamed and specialized groups were established involving three types of unacquainted preschool boys: children with and without developmental delays and a language disordered but intellectually normally functioning group, using a methodology that ensured appropriate matching of child and family characteristics. For each 2-week play group, the social interactions of each child were observed during a designated free play period. Handicapped children were observed in either a specialized or mainstreamed setting. The application made of this modeling process in this paper is generating theory to attempt to understand influence processes. Parameters are introduced that reflect uninfluenced target child and group set points, emotional inertia, and influence functions.