Number sense in the transition from natural to rational numbers. In D.M. Gomez Rojas (Chair), Living apart together? The long and winding road from natural to rational number understanding. Symposium conducted at the biennial meeting of the European Association for Research on Learning and Instruction (EARLI)

Understanding rational numbers is of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, i.e. the tendency to (inappropriately) apply natural number properties in rational number tasks. Still, it has been shown that a good understanding of natural numbers is highly predictive for mathematics achievement in general, and for performance on rational number tasks in particular. In this study, we further investigated the relation between learners’ natural and rational number knowledge, specifically in cases where a natural number bias may occur. 140 sixth graders completed a symbolic and a non-symbolic natural number comparison task, two natural number line estimation tasks, and a rational number sense test. Learners’ natural and rational number knowledge were positively correlated. The relation was however fully mediated by learners’ general mathematics achievement, suggesting that there is no direct effect of learners’ natural number knowledge on their rational number knowledge.status: publishe