Response trajectories reveal the temporal dynamics of fraction representations

Previous studies on mental arithmetic with fractions have been equivocal with respect to the nature of mental representations that are formed with fractions. It is not clear from present evidence whether fractions form perceptual primitives independent from components or whether component magnitudes must be processed in addition to the holistic magnitude. In the present study, we attempt to resolve this issue by using computer mouse-tracking. We analyzed the dynamics of participants' hand movements as they compared presented fractions to 1/2. We found that before settling to the correct answer, hand trajectories showed competitive influences of component magnitude and overall fraction magnitude, but the influence of components happened much earlier. These data support the idea that in fraction comparison, component magnitudes and holistic magnitude are processed together in a continuous, competitive manner.