A generalized fraction: an entity smaller than one on the mental number line.
The representation of fractions in long-term memory (LTM) was investigated by examining the automatic processing of such numbers in a physical comparison task, and their intentional processing in a numerical comparison task. The size congruity effect (SiCE) served as a marker of automatic processing and consequently as an indicator of the access to the primitives of numerical representation in LTM. Mixed pairs composed of a natural number and a fraction showed both a SiCE and a distance effect. The SiCE for mixed pairs was stable across relative sizes of natural numbers compared to the fraction digits (Experiment 4). However, comparing pairs of fractions revealed a strong influence of fractional components: An inverse SiCE was found for pairs of unit fractions (Experiment 1), while no SiCE was found for pairs of non-unit fractions (Experiments 2-3). This leads to the conclusions that: (1) there are no unique representations of distinct fraction values in LTM, and (2) there is a representation of a "generalized fraction" as an "entity smaller than one" that emerges from the notational structure common to all fractions.
Kallai
Arava Y
AY
Learning Research and Development Center, Department of Psychology, University of Pittsburgh, PA, USA. kallai@pitt.edu
Tzelgov
Joseph
J
D032882:Comprehension; D005260:Female; D005793:Generalization, Psychological; D006801:Humans; D008297:Male; D008433:Mathematics; D008568:Memory; D011340:Problem Solving; D011597:Psychomotor Performance; D011930:Reaction Time; D012858:Size Perception