How Do Preschoolers Estimate Proportions?

Although formal proportional reasoning abilities have been thought to develop around eleven years of age (Inhelder & Piaget, 1958; Piaget & Inhelder, 1975), recent work suggests that children may understand basic proportional relationships and scaling at an intuitive level as early as preschool age (Hurst & Cordes, 2017; Singer-Freeman & Goswami, 2001; Sophian, 2000; Sophian & Wood,1997). Nearly all previous research on intuitive proportional reasoning has used choice tasks that involve picking proportionally equivalent matches from a fixed set of options. While these tasks help determine whether young children recognize proportional relationships, they do not reveal precise information about accuracy or strategy use. With two novel proportional reasoning tasks, we explored preschoolers' ability to reproduce equivalent proportions when presented with relative quantities. Preschool children (ages 3-5 years) and adults were asked to estimate proportional matches across formats. The same proportional relationships were presented in two different formats: pairs of separate red and blue circles (Experiment 1) and single circles divided into red and blue parts (Experiment 2). Preschoolers showed a remarkable ability to replicate proportions across formats. Though many 3-year-olds did not understand the task and failed to make estimates correlated with true proportions, a small number of 3-year-olds were able to make estimates with reasonable accuracy. The large majority of 4- and 5-year-olds made accurate, correlated estimates, demonstrating that even very young children with no formal knowledge of proportions are capable of proportional estimation given simple, intuitive tasks.