Proceedings of the Annual Meeting of the Cognitive Science Society

The number-line task is a widely used task in diverse fields of study. In the task, a given number that varies every trial isestimated on a continuum flanked with 0 and an upper-bound number. An upper-bound of a number-line is often arbitrarilyselected by researchers, although this design variable has been shown to affect the non-linearity in estimates. Examiningestimates of varying given numbers (design variable 1) with varying upper-bound numbers (design variable 2) can be costlybecause adding a new design dimension into a number-line task could drastically increase the number of trials requiredfor examining the underlying representation of number. The present study aims to conduct a number-line task with thegiven number and the upper-bound being the design variables. A design optimization algorithm, Gaussian Process ActiveLearning (GPAL), made this new paradigm feasible without increasing the number of trials, by presenting only the mostinformative combinations of the design variables every trial. Our experimental data showed that the non-linearity of thenumber-line estimates increases with the upper-bound of the number line. The degree of non-linearity could predict a mathskill (i.e., addition proficiency), but only when the upper-bound was relatively large. The observed range-dependency of thenumber-line estimates would not be fully explored without systematically manipulating the upper-bound as an additionaldesign variable. As in the present number-line task, GPAL would be a useful tool for the research problems that requiremultidimensional design experiments to be solved.