The log–linear response function of the bounded number-line task is unrelated to the psychological representation of quantity

Abstract

The bounded number-line task has been used extensively to assess the numerical competence of both children and adults. One consistent finding has been that young children display a logarithmic response function, whereas older children and adults display a more linear response function. Traditionally, these log–linear functions have been interpreted as providing a transparent window onto the nature of the participants’ psychological representations of quantity (termed here a direct response strategy). Here we show that the direct response strategy produces the log–linear response function regardless of whether the psychological representation of quantity is compressive or expansive. Simply put, the log–linear response function results from task constraints rather than from the psychological representation of quantities. We also demonstrate that a proportion/subtraction response strategy produces response patterns that almost perfectly correlate with the psychological representation of quantity. We therefore urge researchers not to interpret the log–linear response pattern in terms of numerical representation.