The number line placement task, in which individuals are presented with a target number and mark where it would belocated along a number line, has played an important role in the investigation of numerical cognition. However, recentwork suggests that different factors may influence performance on the task, making it a poor proxy for mental represen-tation of number. In this study, adults completed a computer-based number line placement task with either standard ornon-standard endpoints. Consistent with previous research, responses in the standard condition were best fit by a linearmodel, while responses in the non-standard condition were best fit by a logarithmic model. In addition, eye-trackingdata revealed different looking patterns between conditions, including greater fixations on and more frequent alternationbetween endpoints in the non-standard condition and a leftward bias in the standard condition. This behavior may reflectdifferences in number familiarity and strategy use.

Re-representation is a crucial component of structure mappingtheory, allowing individuals to notice structural commonalitiesbetween situations that do not initially have identical relationalrepresentations. Despite its theoretical importance, however, thisconcept has been the subject of very little empirical work. In twoexperiments, we find that a case’s participation in one comparisonsystematically changes its perceived similarity to new cases, in apattern consistent with re-representation. Additional work rules outalternative explanations based on relational priming.