Abstract
Recent evidence has shown that, like adults and children, 9-month-old infants manifest an operational momentum (OM) effect during non-symbolic arithmetic, whereby they overestimate the outcomes to addition problems, and underestimate the outcomes to subtraction problems. Here we provide the first evidence that OM occurs for transformations of non-numerical magnitudes (i.e., spatial extent) during ordering operations. Twelve-month-old infants were tested in an ordinal task in which they detected and represented ascension or descension in physical size, and then responded to ordinal sequences that exhibited greater or lesser sizes. Infants displayed longer looking time to the size change whose direction violated the operational momentum experienced during habituation (i.e., the smaller sequence in the ascension condition and the larger sequence in the descension condition). The presence of momentum for ordering size during infancy suggests that continuous quantities are represented spatially during the first year of life.
Similar content being viewed by others
References
Boroditsky, L., Fuhrman, O., & McCormick, K. (2011). Do English and Mandarin speakers think about time differently? Cognition, 118, 123–129. doi:10.1016/j.cognition.2010.09.010.
Brannon, E. M. (2002). The development of ordinal numerical knowledge in infancy. Cognition, 83, 223–240. doi:10.1016/S0010-0277(02)00005-7.
Bulf, H., de Hevia, M. D., & Macchi Cassia, V. (2014). Are numbers, size and brightness equally efficient in orienting visual attention? Evidence from an eye-tracking study. PLoS One, 9, e99499. doi:10.1371/journal.pone.0099499.
Bulf, H., de Hevia, M. D., & Macchi Cassia, V. (2015a). Small on the left, large on the right: numbers orient visual attention onto space in preverbal infants. Developmental Science,. doi:10.1111/desc.12315.
Bulf, H., Gariboldi, V., de Hevia, M. D., & Macchi Cassia, V. (2015b). Left-to-right spatial orientation facilitates learning of abstract rules in 7-month-old infants. Poster presented at the Budapest CEU Conference on Cognitive Development. Budapest, January.
Casasanto, D. (2010). Space for Thinking. In V. Evans & P. Chilton (Eds.), Language, cognition, and space: state of the art and new directions (pp. 453–478). London: Equinox Publishing.
de Hevia, M. D., Girelli, L., Addabbo, M., & Macchi Cassia, V. (2014a). Human infants’ preference for left-to-right oriented increasing numerical sequences. PLoS One, 9, e96412. doi:10.1371/journal.pone.0096412.
de Hevia, M. D., Girelli, L., & Macchi Cassia, V. M. (2012). Minds without language represent number through space: origins of the mental number line. Frontiers in Psychology, 3, 466. doi:10.3389/fpsyg.2012.00466.
de Hevia, M. D., Izard, V., Coubart, A., Spelke, E. S., & Streri, A. (2014b). Representations of space, time and number in neonates. Proceedings of the National Academy of Sciences USA, 111, 4809–4813. doi:10.1073/pnas.1323628111.
de Hevia, M. D., & Spelke, E. S. (2010). Number-space mapping in human infants. Psychological Science, 21, 653–660. doi:10.1177/0956797610366091.
Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371–396. doi:10.1037/0096-3445.122.3.371.
Fedden, S., & Boroditsky, L. (2012). Spatialization of time in Mian. Frontiers in Psychology, 3, 485. doi:10.3389/fpsyg.2012.00485.
Feigenson, L. (2007). The equality of quantity. Trends in Cognitive Sciences, 11, 185–187. doi:10.1016/j.tics.2007.01.006.
Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6, 555–556. doi:10.1038/nn1066.
Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor bias induced by number perception. Experimental Psychology, 51, 91–97. doi:10.1027/1618-3169.51.2.91.
Freyd, J. J. (1987). Dynamic mental representation. Psychological Review, 94, 427–438. doi:10.1037/0033-295X.94.4.427.
Freyd, J. J., & Finke, R. A. (1984). Representational momentum. Journal of Experimental Psychology. Learning, Memory, and Cognition, 10, 126–132.
Gevers, W., Reynvoet, B., & Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition, 87, B87–B95. doi:10.1016/S0010-0277(02)00234-2.
Goebel, S. M., Shaki, S., & Fischer, M. H. (2011). Cultural effects on the mental number line. Journal of Cross-Cultural Psychology, 42, 541–542. doi:10.1177/0022022111406251.
Hartmann, M., Mast, F. W., & Fischer, M. H. (2015). Counting is a spatial process: Evidence from eye movements. Psychological Research. doi:10.1007/s00426-015-0722-5.
Hubbard, T. L. (2005). Representational momentum and related displacements in spatial memory: a review of the findings. Psychonomic Bulletin & Review, 12, 822–851. doi:10.3758/BF03196775.
Hubbard, T. L. (2014). Forms of momentum across space: representational, operational, and attentional. Psychonomic Bulletin Review, 1, 1371–1403. doi:10.3758/s13423-014-0624-3.
Hubbard, E. M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435–448. doi:10.1038/nrn1684.
Katz, C., & Knops, A. (2014). Operational momentum in approximate multiplication and division? PLoS One, 9, e104777. doi:10.1371/journal.pone.0104777.
Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009a). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324, 1583–1585. doi:10.1126/science.1171599.
Knops, A., Viarouge, A., & Dehaene, S. (2009b). Dynamic representations underlying symbolic and nonsymbolic calculation: evidence from the operational momentum effect. Attention, Perception, & Psychophysics, 71, 803–821. doi:10.3758/APP.71.4.803.
Knops, A., Zitzmann, S., & McCrink, K. (2013). Examining the presence and determinants of operational momentum in childhood. Frontiers in Psychology, 4, 325. doi:10.3389/fpsyg.2013.00325.
Lourenco, S. F., & Longo, M. R. (2010). General magnitude representation in human infants. Psychological Science, 21, 873–881. doi:10.1177/0956797610370158.
Macchi Cassia, V., de Hevia, M. D., Picozzi, M., & Girelli, L. (2012). Increasing magnitude counts more: asymmetrical processing of ordinality in 4-month-old infants. Cognition, 124, 183–193. doi:10.1016/j.cognition.2012.05.004.
McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: the case for operational momentum. Perception and Psychophysics, 69, 1324–1333.
McCrink, K., & Opfer, J. E. (2014). Development of spatial-numerical associations. Current Directions in Psychological Science, 23, 439–445. doi:10.1177/0963721414549751.
McCrink, K., & Wynn, K. (2009). Operational momentum in large-number addition and subtraction by 9-month-olds. Journal of Experimental Child Psychology, 103, 400–408. doi:10.1016/j.jecp.2009.01.013.
Mock, J., Huber, S., Klein, E., & Moeller, K. (2016). Insights into numerical cognition—considering eye-fixations in number processing and arithmetic. Psychological Research. doi:10.1007/s00426-015-0739-9.
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgement of inequality. Nature, 215, 1519–1520. doi:10.1038/2151519a0.
Myachykov, A., Ellis, R., Cangelosi , A., & Fischer, M. H. (2016). Ocular drift along the mental number line. Psychological Research. doi:10.1007/s00426-015-0731-4.
Nuerk, H. C., Patro, K., Cress, U., Schild, U., Friedrich, C. K., & Göbel, S. M. (2015). How space-number associations may be created in preliterate children: six distinct mechanisms. Frontiers in Psychology, 6, 215. doi:10.3389/fpsyg.2015.00215.
Opfer, J. E., Thompson, C. A., & Furlong, J. E. (2010). Early development of spatial-numeric associations: evidence from spatial and quantitative performance of preschoolers. Developmental Science, 13, 761–771. doi:10.1111/j.1467-7687.2009.00934.x.
Pinel, P., Piazza, M., Le Bihan, D., & Dehaene, S. (2004). Distributed and overlapping cerebral representations of number, size, and luminance during comparative judgments. Neuron, 41, 983–993.
Pinhas, M., & Fischer, M. (2008). Mental movements with magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109, 408–415. doi:10.1016/j.cognition.2008.09.003.
Previtali, P., de Hevia, M. D., & Girelli, L. (2010). Placing order in space: the SNARC effect in serial learning. Experimental Brain Research, 201, 599–605. doi:10.1007/s00221-009-2063-3.
Ranzini, M., Lisi, M., & Zorzi, M. (2016). Voluntary eye movements direct attention on the mental number space. Psychological Research. doi:10.1007/s00426-015-0741-2.
Rao, H., Han, S., Jiang, Y., Xue, Y., Gu, H., Cui, Y., & Gao, D. (2004). Engagement of the prefrontal cortex in representational momentum: an fMRI study. NeuroImage, 23, 98–103. doi:10.1016/j.neuroimage.2004.05.016.
Ren, P., Nicholls, M. E. R., Ma, Y., & Chen, L. (2011). Size matters: non-numerical magnitude affects the spatial coding of response. PLoS One, 6, e23553. doi:10.1371/journal.pone.0023553.
Rusconi, E., Kwan, B., Giordano, B., Umiltà, C., & Butterworth, B. (2006). Spatial representation of pitch height: the SMARC effect. Cognition, 99, 113–129. doi:10.1016/j.cognition.2005.01.004.
Srinivasan, M., & Carey, S. (2010). The long and the short of it: on the nature and origin of functional overlap between representations of space and time. Cognition, 116, 217–241. doi:10.1016/j.cognition.2010.05.005.
Vallesi, A., Binns, M. A., & Shallice, T. (2008). An effect of spatial–temporal association of response codes: understanding the cognitive representations of time. Cognition, 107, 501–527. doi:10.1016/j.cognition.2007.10.011.
Van Opstal, F., Fias, W., Peigneux, P., & Verguts, T. (2009). The neural representation of extensively trained sequences. NeuroImage, 47, 367–375. doi:10.1016/j.neuroimage.2009.04.035.
Walsh, V. A. (2003). A theory of magnitude: common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7, 483–488. doi:10.1016/j.tics.2003.09.002.
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750. doi:10.1038/358749a0.
Yu, X., Liu, J., Li, D., Liu, H., Cui, J., & Zhou, X. (2015). Dynamic mental number line in simple arithmetic. Psychological Research. doi:10.1007/s00426-015-0730-5.
Zebian, S. (2005). Linkages between number concepts, spatial thinking and directionality of writing: the SNARC effect and the REVERSE SNARC effect in English and in Arabic monoliterates, biliterates and illiterate Arabic speakers. Journal of Cognition and Culture, 5, 165–190.
Acknowledgments
The authors are indebted to parents and infants who donated their time to participate in the study. The authors also thank Carlo Toneatto for invaluable contribution in programming the experiment, and Simona Quirito and Marika Cometti for help in recruiting and testing infants. This work was partially supported by award R15-HD077518-01A1 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development to the second author. MDdH was supported by a Marie Curie IntraEuropean Fellowship for Career Development (SpaNum 272633).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Macchi Cassia, V., McCrink, K., de Hevia, M.D. et al. Operational momentum and size ordering in preverbal infants. Psychological Research 80, 360–367 (2016). https://doi.org/10.1007/s00426-016-0750-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00426-016-0750-9