The Early Development of Proportional Reasoning: A Longitudinal Study of 5- to 8-Year-Olds

The present study longitudinally investigated proportional reasoning abilities in early elementary school before the start of its instruction. Three aims were put forward: (a) distinguishing the different developmental states in young children's understanding of missing-value proportional situations, (b) investigating how children transition through these states, and (c) exploring possible predictors that explain individual differences in young children's development of proportional reasoning abilities. We longitudinally investigated 5- to 8-year-olds' (n = 315) proportional reasoning abilities in a fair-sharing missing-value proportional reasoning task. First, results showed that the development of proportional reasoning already starts at a very early age and is still ongoing when children are in their third year of elementary school. Second, latent class analysis revealed five different early states of proportional reasoning. The understanding of one-to-many correspondence was identified as an essential stepping-stone toward success in more difficult proportional reasoning problems with many-to-many correspondences. Third, exploratory analyses revealed that the large individual differences in children's development of proportional reasoning abilities were associated with socioeconomic status, language, spatial abilities, and numerical abilities. Theoretical, methodological, and educational implications are discussed.