Absolute or Relative Size: What Do We Perceive When We Look at a Glass That Is Half Full?

Given that both children and adults struggle with fractions in mathematics education, we investigated the processing of nonsymbolic fractions in a continuous form of part-of-the-whole. Continuous features of nonsymbolic numbers (e.g., the size of dots in an array) were found to influence numerosity judgment, but it should be noted that the (continuous) size of a part can be processed relative to a whole or as an absolute size. This study tested which of these size types (i.e., absolute and relative) influences comparison of parts. In two Stroop-like comparison tasks, we measured the interference of each size type on the processing of the other. In Experiment 1, stimuli were three-dimensional-like partially filled glasses of water. In both tasks, congruent trials (in which the larger absolute size was also the larger part-of-the-whole) were processed more efficiently than incongruent trials (in which the larger absolute size was the smaller part-of-the-whole). In Experiment 2, where stimuli were two-dimensional rectangles, this result was replicated under improved experimental control. We conclude that both absolute size and relative size of a part are automatically processed.