Geometric Aspects of Number Line Estimations

Number lines are implicitly embedded in nature. Yet researchers use them for measuring number sense as if they are processed purely through numerical reasoning. We argue that number line estimation tasks are done both by numerical and geometric reasoning. The purpose of this research was to investigate the relationships among mathematics achievement, geometry achievement, spatial skills, and number line estimations. A total of 142 fourth graders were administered 5 different tests: 2 curriculum-based math achievement tests, a spatial visualization test, a number line estimation test, and the Raven Standard Progresive Matrices test. Results showed; estimation accuracy of the relative magnitude of numbers on an empty number line has more to do with geometry achievement and diagrammatic reasoning rather than with numerical or arithmetic reasoning. It seems that number line estimation tasks may constitute an interplay between number and shape. Therefore, we conclude that using multiple external representations of numbers, such as spatial, symbolic, and verbal could be useful in developing a more robust number sense.