Young children's knowledge of fair sharing as an informal basis for understanding division: A latent profile analysis

This study examined patterns of individual differences in young children's early understanding of division. Two hundred and thirty-seven 5- and 6-year-old children completed division tasks that assessed their understanding of the direct and inverse relations in division in two different situations – partitive and quotitive. Two main results emerged from our latent profile analyses. First, all children who had good performance in the inverse-relation problems also performed well in the direct-relation problems, but the converse was not true. Second, all children who performed well in the inverse-relation problems in quotitive situations also performed well in the inverse-relation problems in partitive situations, but not vice versa. The findings highlight the importance of situations in determining children's success in recognizing the inverse relation in division. Several theoretical implications for the development of children's division concepts and educational implications for assessment and teaching are discussed.