The mental number line, the external number line, and elementary school mathematics

This paper is concerned with studies on magnitude estimations that strived to explain the underlying mental representation(s) of magnitudes by using a number line estimation paradigm, in which participants are usually asked to mark the position of numbers on an external number line (e.g., from 1 to 100). Based on a brief description and discussion of several studies done in our own centers as well as recent work done by others, we propose a taxonomy by which those studies can be classified, which helps to explain why it is so difficult drawing general conclusions, and we suggest perspectives for future research on magnitude estimations, which might abandon the hunt for ‘the mathematical function’ (linear, logarithmic, power) that explains estimations best and turns, instead, to investigate the underlying estimation strategies and ways of their improvement. In doing so, we also question some fundamental assumptions underlying the use of this paradigm, namely that estimations are a probate instrument to tap the underlying mental representation.status: publishe