Microgenetic analysis of young children's shifts of attention in arithmetic tasks: underlying dynamics of change in phases of seemingly stable task performance.

A key aim of mathematics teaching is for children to develop appropriate and efficient strategies for solving tasks. The analysis presented in this paper moves beyond the exploration of changes in the strategies that children employ to solve tasks and extends to observation and exploration of changes that occur when their overall solving approach remains seemingly stable. We present an analysis of data from two qualitative studies, each of which combined a microgenetic design with task-based interviews, to examine changes that occur in 5–6-year-old children's verbal reports when solving an additive task, and in 9–10-year-old children's verbal reports when solving fraction word problems. Children's verbal reports were analysed through the lens of the theory of shifts of attention. We found that phases of stability are underlain by dynamic changes in how the same strategy is communicated and conceptualised over a number of sessions and these changes appear to be accounted for by changes related to shifts in the object and structure of children's attention, i.e. what children attend to and how, when reporting on their solving approach. The paper extends the theory by revealing and studying microqualities that underlie different learners' structure of attention during phases of stability in arithmetic tasks. The findings provide new, significant insights for understanding qualitative dynamics of change in learning. Sensitivity to differences and changes in learners' shifts of attention is essential for teachers to make sense of what learners experience and identify opportunities conducive to further learning. [ABSTRACT FROM AUTHOR]