Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners

In this study we longitudinally followed 201 upper elementary school learners in the crucial years of acquiring rational number understanding. Using latent transition analysis we investigated their conceptual change from an initial natural number based concept of a rational number towards a mathematically more correct one by characterizing the various intermediate states learners go through. Results showed that learners first develop an understanding of decimal numbers before they have an increased understanding of fractions. We also found that a first step in learners' rational number understanding is an increased understanding of the numerical size of rational numbers. Further, only a limited number of learners fully understand the dense structure of rational numbers at the end of elementary education.