On the relation between the mental number line and arithmetic competencies

Abstract

In this study, we aimed at investigating whether it is indeed the spatial magnitude representation that links number line estimation performance to other basic numerical and arithmetic competencies. Therefore, estimations of 45 fourth-graders in both a bounded and a new unbounded number line estimation task (with only a start-point and a unit given) were correlated with their performance in a variety of tasks including addition, subtraction, and number magnitude comparison. Assuming that both number line tasks assess the same underlying mental number line representation, unbounded number line estimation should also be associated with other basic numerical and arithmetic competencies. However, results indicated that children's estimation performance in the bounded but not the unbounded number line estimation task was correlated significantly with numerical and arithmetic competencies. We conclude that unbounded and bounded number line estimation tasks do not assess the same underlying spatial–numerical representation. Rather, the observed association between bounded number line estimation and numerical/arithmetic competencies may be driven by additional numerical processes (e.g., proportion judgement, addition/subtraction) recruited to solve the task.

Keywords:

• Mental number line
• Number line estimation
• Proportion judgement
• Arithmetic competencies
• Numerical processes