In this dissertation I focus on (1) whether people process numerosity from concrete object arrays in an abstract manner, and (2) how they form abstract numerical representations. Abstractness is a key property of the mature number concept, as it enables humans to utilize numbers in any situation to solve complex problems, regardless of notation, modality, and dimension. The predominant view of numerical cognition assumes an inherent abstractness of numerosity representation, so that how humans develop abstract numerosity representation has not been properly examined. I considered and examined two alternative hypotheses that may explain the development of abstract numerosity processing through comparing the performances in numerical perception and numerical memory tasks of different age groups. In particular, I investigated (1) the effect of the visual properties of sets on adults and children’s numerosity perception, (2) the role of selective attention in non-symbolic numerical representation(s), and (3) the role of number words as young children’s potent attention cues.
In the first study, I conducted two experiments. In Experiment 1, I examined the effect of the dimensional structure of concrete object arrays on numerosity and object perception across two age groups, adults and 4-5-year-olds, based on Garner’s (1976) integral-separable distinction. I found that irrelevant changes in object features significantly interfered with both adults’ and children’s numerical perceptions. Counterintuitively, both adults and children, while in general exhibiting high accuracy in the numerical matching task, consistently exhibited larger object interference. This finding indicates that adults and children, even when they are fully engaged in numerical processing, consider object information as relevant for numerical judgments. In Experiment 2, I tested a possible explanation for adults’ integral numerosity perception by removing the time limit in presenting the stimuli; however, the results showed no significant differences from the results in Experiment 1. Taken together, the results in both experiments imply that numerosity perception processing are neither abstract nor domain-specific, which challenges the predominant view of the abstract innate number system.
In the second study, I conducted four experiments in which I considered and resolved a potential concern with relying on Garner’s (1976) paradigm for examining dimensional interactions as in Study 1. I investigated whether salient object change captured attention from numerical features prior to focused attention, leading to the formation of proto-objects (Rensink, 2002). If so, the memory trace of the decaying proto-objects would lead to inefficient and inaccurate numerical decisions. To compensate for this concern, I reinvestigated the effect of object features on numerical judgements by relying on recognition memory tasks and Signal Detection theory. I examined the role of selective attention in numerosity representations and explored the role of number words as potent attention cues in 4-5-year-old children’s numerosity representations.
The results of Experiment 3 showed a congruency effect in numerical memory across three age groups: adults, 8-9-year-olds, and 4-5-year-olds. The congruency effect in numerical memory sensitivity was particularly larger than that in object memory sensitivity, which was similar to the asymmetrical integral dimensions in Study 1. This asymmetry seemed to increase as the participants’ age increased.
In Experiments 4 and 5, I manipulated the direction of attention during training, and found that a dimension-biased instruction led to analytic perceptual processing for adults and older children, but not for young children. This result indicates that cued attention altered the form of participants’ representation of the target dimensions. Furthermore, the training effect was also asymmetrical between the numerical and object dimensions: numerosity-biased training demonstrated larger training effect than did object-biased training.
In Experiment 6, I explored the effect of number words on young children’s numerical representations by providing the labels of both dimensional properties during training. The result demonstrated that the verbal number-biased training increased the young children’s numerical memory sensitivity both on congruent and incongruent trials. Unexpectedly, the young children’s object sensitivity also increased, which indicates that the verbal number-biased training led young children to process numerosity in a more independent manner, but it also led them to more correctly encode and retain object information.
My investigation in Studies 1 and 2 led me to conclude that integral numerosity processing is a genuine property of numerical perception and representation. A new model that represents this non-abstract nature of numerosity processing is necessary for advancing our understanding of how humans develop abstract number concepts from their concrete environment.