Investigating division concepts at entry to school

It is often assumed that young children have no concepts of division before they are formally introduced to division at school. Our earlier research showed that many children achieve early multiplicative reasoning before it is formally taught (Cheeseman et al., 2020). The research question we sought to answer here was: What concepts of division do young children develop prior to school instruction? We conducted a teaching experiment study (Steffe & Thompson, 2000) with 21 children of 56 years of age who were 5 months into their first year of school in Australia. A dancing game elicited thinking about equal-grouping (composite) thinking that is at the core of multiplicative thinking. When the music stopped, a number would be called and everyone would get into a group of that number. In addition to classroom-based observation/video data, we analysed student’s drawn responses to a pencil-and-paper assessment protocol (Streit-Lehmann, 2019). The assessment consisted of six worded problems, three quotition division situations where children had to arrange objects into equal groups and count the groups; three partition division situations where children had to share all objects equally. Results indicate that many children (83%) could divide objects into equal groups and some could visualise division situations involving groups of a given size. Further, based on a detailed analysis of the responses of six children, results show that children could interpret stylised diagrammatic partitive (75% correct) and quotitive (100% correct) division contexts and add to diagrams to represent their solutions to worded problems. Our research shows that some young children develop concepts of division prior to school instruction in meaningful contexts. Furthermore, many young children can interpret, and successfully complete, iconographic representations of partition and quotition worded problems. These findings make a new contribution to the field and warrant further study of young children’s division concepts.