Abstract
This article explores the effect of external representations on numeric tasks. Through several minor modifications on the previously reported two-digit number comparison task, we obtained different results. Rather than holistic comparison, we found parallel comparison. We argue that this difference was a reflection of different representational forms: The comparison was based on internal representations in previous studies but on external representations in our present study. This representational effect is discussed under a framework of distributed number representations. We propose that in numerical tasks involving external representations, numbers should be considered as distributed representations, and the behaviour in these tasks should be considered as the interactive processing of internal and external information through the interplay of perceptual and cognitive processes. We suggest that theories of number representations and process models of numerical cognition should consider external representations as an essential component.
Acknowledgments
This research was in part supported by Grants N00014-95-1-0241, N00014-96-1-0472, and N00014-01-1-0074 from the Office of Naval Research, Cognitive and Neural Sciences Technology Division. We would like to thank Gwen Hall for his assistance in the experiments.
Notes
AICi = −2 ln(MLi ) + 2ni , where MLi is the maximum likelihood for model i, and ni is the number of free parameters in the model. The criterion prescribes that the model that minimizes the AIC should be chosen. AIC can be rewritten as a function of sum squared error (SSE ): AICi = N ln(SSEi ) + 2ni + (−N ln N + N −1 + N ln 2π), where SSEi is the sum squared error for model i, ni is the number of free parameters in the model, and N is the number of observations (I. J. Myung, personal communication, 1996). The latter equation was used in the present study.