Swipe om te navigeren naar een ander artikel
Spatial–numerical associations (small numbers—left/lower space and large numbers—right/upper space) are regularly found in simple number categorization tasks. These associations were taken as evidence for a spatially oriented mental number line. However, the role of spatial–numerical associations during more complex number processing, such as counting or mental arithmetic is less clear. Here, we investigated whether counting is associated with a movement along the mental number line. Participants counted aloud upward or downward in steps of 3 for 45 s while looking at a blank screen. Gaze position during upward counting shifted rightward and upward, while the pattern for downward counting was less clear. Our results, therefore, confirm the hypothesis of a movement along the mental number line for addition. We conclude that space is not only used to represent number magnitudes but also to actively operate on numbers in more complex tasks such as counting, and that the eyes reflect this spatial mental operation.
Log in om toegang te krijgen
Met onderstaand(e) abonnement(en) heeft u direct toegang:
Alibali, M. W., & DiRusso, A. A. (1999). The function of gesture in learning to count: more than keeping track. Cognitive Development, 14(1), 37–56. CrossRef
Ashcraft, M. H., & Battaglia, J. (1978). Cognitive arithmetic: evidence for retrieval and decision processes in mental addition. Journal of Experimental Psychology Human Learning and Memory, 4(5), 527. CrossRef
Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). lme4: linear mixed-effects models using Eigen and S4. R package version 1.1- 8.
Campbell, J. I. D. (2005). Handbook of mathematical cognition. New York: Psychology Press.
Carlson, R. A., Ayraamides, M. N., Cary, M., & Strasberg, S. (2007). What do the hands externalize in simple arithmetic. Journal of Experimental Psychology Learning Memory and Cognition, 33, 747–756. CrossRef
Cassia, V. M., McCrink, K., de Hevia, M. D., Gariboldi, V., & Bulf, H. (under review). Operational momentum and size ordering in preverbal infants. Psychological Research.
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology General, 122(3), 371–396. CrossRef
Fias, W., & Fischer, M. H. (2005). Spatial representation of numbers. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition (pp. 43–54). New York: Psychology Press.
Fischer, M. H. (2012). A hierarchical view of grounded, embodied, and situated numerical cognition. Cognitive Processing, 13(1), 161–164. CrossRef
Fischer, M. H., & Brugger, P. (2011). When digits help digits: spatial–numerical associations point to finger counting as prime example of embodied cognition. Frontiers in Psychology, 2.
Fischer, M. H., & Rottmann, J. (2005). Do negative numbers have a place on the mental number line. Psychology Science, 47(1), 22–32.
Fischer, M. H., & Shaki, S. (2015). Measuring spatial-numerical associations: evidence for a purely conceptual link. Psychol Res. doi: 10.1007/s00426-015-0646-0
Freyd, J. J., & Finke, R. A. (1984). Representational momentum. Journal of Experimental Psychology Learning Memory and Cognition, 10(1), 126. CrossRef
Gao, X., Yan, H., & Sun, H. (2015). Modulation of microsaccade rate by task difficulty revealed through between- and within-trial comparisons. Journal of Vision, 15(3), 1–15. CrossRef
Göbel, S. M., Shaki, S., & Fischer, M. H. (2011). The cultural number line: a review of cultural and linguistic influences on the development of number processing. Journal of Cross Cultural Psychology, 42(4), 543–565. CrossRef
Grade, S., Lefèvre, N., & Pesenti, M. (2012). Influence of gaze observation on random number generation. Experimental Psychology, 60, 122–130. CrossRef
Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychological Review, 79(4), 329. CrossRef
Gross, J., Hudson, C., & Price, D. (2009). The long term costs of numeracy difficulties. London: Every Child a Chance Trust and KPMG.
Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Review Neuroscience, 6(6), 435–448. CrossRef
Kahneman, D., & Beatty, J. (1966). Pupil diameter and load on memory. Science, 154, 3. CrossRef
Kennedy, A. (1983). On looking into space. In K. Rayner (Ed.), Eye movements in reading: perceptual and language processes (pp. 237–251). New York: Academic Press.
Lakoff, G., & Johnson, M. (1980). Conceptual metaphor in everyday language. The Journal of Philosophy, 77(8), 453–486. CrossRef
Mock, J., Huber, S., Klein, E., Moeller, K. (under review). Insights into numerical cognition—considering eye-fixations in number processing and arithmetic. Psychological Research.
Myachykov, A., Ellis, R., Changeolosi, A., & Fischer, M. H. (under review). Ocular drift along the mental number line. Psychological Research.
Nakayama, M., Takahashi, K., & Shimizu, Y. (2002). The act of task difficulty and eye-movement frequency for the ‘Oculo-motor indices’. In Proceedings of the 2002 symposium on Eye tracking research and applications (pp. 37–42): ACM
Parsons, S., & Bynner, J. (2005). Does numeracy matter more?. London: National Research and Development Centre for Adult Literacy and Numeracy.
R Core Team. (2014). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
Ranzini, M., Lisi, M., Zorzi, M. (under review). Voluntary eye movements direct attention on the mental number space. Psychological Research.
Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 274. CrossRef
Singmann, H., & Bolker, M. (2014). afex: analysis of factorial experiments. R package version 0.12–135
Stocker, K., Hartmann, M., Martarelli, C., & Mast, F. W. (2015). Eye movements reveal mental scanning through time. Cognitive Science, 1-23. doi: 10.1111/cogs.12301
Van Gompel, R. P. G., Fischer, M. H., Murray, W., & Hill, R. L. (2007). Eye movements: a window on mind and brain. Oxford: Elsevier.
Walsh, V. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends Cognitive Science, 7(11), 483–488. CrossRef
Walsh, V. (2014). A theory of magnitude: the parts that sum to numbers. In R. C. Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition. Oxford: Oxford Universtiy Press.
Winter, B. (2013). Linear models and linear mixed effects models in R with linguistic applications. arXiv:1308.5499. http://arxiv.org/pdf/1308.5499.pdf
Winter, B., & Matlock, T. (2013). More is up … and right: random number generation along two axes. In M. Knauff, N. Pauen, N. Sebanz, & I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of the Cognitive Science Society (pp. 3789–3794). Austin: Cognitive Science Society.
Yu, X., Liu, J., Li, D., Cui, J., & Zhou, X. (under review). Dynamic mental number line in symple arithmetic. Psychological Research.
Zbrodoff, N. J., & Logan, G. D. (1990). On the relation between production and verification tasks in the psychology of simple arithmetic. Journal of Experimental Psychology Learning Memory and Cognition, 16(1), 83–97. CrossRef
- Counting is a spatial process: evidence from eye movements
Fred W. Mast
Martin H. Fischer
- Springer Berlin Heidelberg