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25-11-2015 | Original Article | Uitgave 3/2016

Counting is a spatial process: evidence from eye movements

Tijdschrift:: Psychological Research > Uitgave 3/2016

Auteurs:: Matthias Hartmann, Fred W. Mast, Martin H. Fischer

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Abstract

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.

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Meer informatie

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

Altmann, G. T. (2004). Language-mediated eye movements in the absence of a visual world: the ‘blank screen paradigm’. Cognition, 93(2), B79–B87. doi: 10.1016/j.cognition.2004.02.005. CrossRefPubMed

Andin, J., Fransson, P., Rönnberg, J., & Rudner, M. (2015). Phonology and arithmetic in the language–calculation network. Brain and Language, 143, 97–105. CrossRefPubMed

Anelli, F., Lugli, L., Baroni, G., Borghi, A. M., & Nicoletti, R. (2014). Walking boosts your performance in making additions and subtractions. Frontiers in Psychology, 5, 1459. CrossRefPubMedPubMedCentral

Ashcraft, M. H. (1992). Cognitive arithmetic: a review of data and theory. Cognition, 44(1–2), 75–106. CrossRefPubMed

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

Barrouillet, P., & Lépine, R. (2005). Working memory and children’s use of retrieval to solve addition problems. Journal of Experimental Child Psychology, 91(3), 183–204. CrossRefPubMed

Barsalou, L. W. (2008). Grounded cognition. Annual Review of Psychology, 59, 617–645. doi: 10.1146/annurev.psych.59.103006.093639. CrossRefPubMed

Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). lme4: linear mixed-effects models using Eigen and S4. R package version 1.1- 8.

Binda, P., & Murray, S. O. (2015). Keeping a large-pupilled eye on high-level visual processing. Trends Cognitive Science, 19(1), 1–3. doi: 10.1016/j.tics.2014.11.002. CrossRef

Brandt, S. A., & Stark, L. W. (1997). Spontaneous eye movements during visual imagery reflect the content of the visual scene. Journal of Cognitive Neuroscience, 9(1), 27–38. doi: 10.1162/jocn.1997.9.1.27. CrossRefPubMed

Butterworth, B., Zorzi, M., Girelli, L., & Jonckheere, A. R. (2001). Storage and retrieval of addition facts: the role of number comparison. The Quarterly Journal of Experimental Psychology Section A, 54(4), 1005–1029. doi: 10.1080/713756007. CrossRef

Campbell, J. I. D. (1994). Architectures for numerical cognition. Cognition, 53(1), 1–44. doi: 10.1016/0010-0277(94)90075-2. CrossRefPubMed

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

Casasanto, D., & Boroditsky, L. (2008). Time in the mind: using space to think about time. Cognition, 106(2), 579–593. doi: 10.1016/j.cognition.2007.03.004. CrossRefPubMed

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.

Corbetta, M., Akbudak, E., Conturo, T. E., Snyder, A. Z., Ollinger, J. M., Drury, H. A., et al. (1998). A common network of functional areas for attention and eye movements. Neuron, 21(4), 761–773. CrossRefPubMed

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

Ehrlichman, H., & Micic, D. (2012). Why do people move their eyes when they think? Current Directions in Psychological Science, 21(2), 96–100. doi: 10.1177/0963721412436810. 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. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44(4), 386–392. CrossRefPubMed

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. (2014a). Spatial associations in numerical cognition-from single digits to arithmetic. The Quarterly Journal of Experimental Psychology, 67(8), 1461–1483. doi: 10.1080/17470218.2014.927515. CrossRefPubMed

Fischer, M. H., & Shaki, S. (2014b). Spatial biases in mental arithmetic. The Quarterly Journal of Experimental Psychology, 67(8), 1457–1460. doi: 10.1080/17470218.2014.927516. CrossRefPubMed

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

Ganor-Stern, D., Pinhas, M., Kallai, A., & Tzelgov, J. (2010). Holistic representation of negative numbers is formed when needed for the task. The Quarterly Journal of Experimental Psychology, 63(10), 1969–1981. CrossRefPubMed

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

Gevers, W., Santens, S., Dhooge, E., Chen, Q., Bossche, L., Fias, W., et al. (2010). Verbal-spatial and visuospatial coding of number-space interactions. Journal of Experimental Psychology General, 139, 180–190. CrossRefPubMed

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

Grant, E. R., & Spivey, M. J. (2003). Eye movements and problem solving: guiding attention guides thought. Psychological Science, 14(5), 462–466. CrossRefPubMed

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.

Hartmann, M. (2015). Numbers in the eye of the beholder: what do eye movements reveal about numerical cognition? Cognitive Processing, 16(1), 245–248. doi: 10.1007/s10339-015-0716-7. CrossRefPubMed

Hartmann, M., Farkas, R., & Mast, F. W. (2012a). Self-motion perception influences number processing: evidence from a parity task. Cognitive Processing, 13(1), 189–192. doi: 10.1007/s10339-012-0484-6. CrossRef

Hartmann, M., & Fischer, M. H. (2014). Pupillometry: the eyes shed fresh light on the mind. Current Biology, 24(7), R281–R282. doi: 10.1016/j.cub.2014.02.028. CrossRefPubMed

Hartmann, M., Gashaj, V., Stahnke, A., & Mast, F. (2014a). There is more than “more is up”: hand and foot responses reverse the vertical association of number magnitudes. Journal of Experimental Psychology Human Perception and Performance, 40(4), 1401–1414. doi: 10.1037/a0036686. CrossRefPubMed

Hartmann, M., Grabherr, L., & Mast, F. W. (2012b). Moving along the mental number line: interactions between whole-body motion and numerical cognition. Journal of Experimental Psychology Human Perception and Performance, 38(6), 1416–1427. doi: 10.1037/a0026706. CrossRefPubMed

Hartmann, M., Martarelli, C., Mast, F. W. (2014b). Eye movements during mental time travel follow a diagonal line. Conscious Cogn, 30, 201–209. CrossRefPubMed

Hartmann, M., Mast, F. W., & Fischer, M. H. (2015). Spatial biases during mental arithmetic: evidence from eye movements on a blank screen. Frontiers in Psychology, 6, 12. doi: 10.3389/fpsyg.2015.00012. CrossRefPubMedPubMedCentral

Holmes, K. J., & Lourenco, S. F. (2012). Orienting numbers in mental space: horizontal organization trumps vertical. The Quarterly Journal of Experimental Psychology, 65(6), 1044–1051. doi: 10.1080/17470218.2012.685079. CrossRefPubMed

Hubbard, T. L. (2014). Forms of momentum across space: representational, operational, and attentional. Psychonomic Bulletin Review, 21(6), 1371–1403. CrossRefPubMed

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

Huette, S., Winter, B., Matlock, T., Ardell, D. H., & Spivey, M. (2014). Eye movements during listening reveal spontaneous grammatical processing. Frontiers in Psychology, 5, 410. doi: 10.3389/fpsyg.2014.00410. CrossRefPubMedPubMedCentral

Ito, Y., & Hatta, T. (2004). Spatial structure of quantitative representation of numbers: evidence from the SNARC effect. Memory Cognition, 32(4), 662–673. CrossRefPubMed

Johansson, R., Holsanova, J., & Holmqvist, K. (2006). Pictures and spoken descriptions elicit similar eye movements during mental imagery, both in light and in complete darkness. Cognitive Science, 30(6), 1053–1079. doi: 10.1207/s15516709cog0000_86. CrossRefPubMed

Johansson, R., & Johansson, M. (2014). Look here, eye movements play a functional role in memory retrieval. Psychological Science, 25(1), 236–242. doi: 10.1177/0956797613498260. CrossRefPubMed

Kahneman, D., & Beatty, J. (1966). Pupil diameter and load on memory. Science, 154, 3. CrossRef

Kahneman, D., Tursky, B., Shapiro, D., & Crider, A. (1969). Pupillary, heart rate, and skin resistance changes during a mental task. Journal of Experimental Psychology, 79, 164–167. CrossRefPubMed

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.

Kinsbourne, M. (1972). Eye and head turning indicates cerebral lateralization. Science, 176(4034), 539–541. CrossRefPubMed

Knops, A., Dehaene, S., Berteletti, I., & Zorzi, M. (2014). Can approximate mental calculation account for operational momentum in addition and subtraction? The Quarterly Journal of Experimental Psychology (Hove), 67(8), 1541–1556. doi: 10.1080/17470218.2014.890234. CrossRef

Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: evidence from the operational momentum effect. Attention Perception Psychophysics, 71(4), 803–821. doi: 10.3758/APP.71.4.803. CrossRef

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. CrossRefPubMedPubMedCentral

Lakoff, G., & Johnson, M. (1980). Conceptual metaphor in everyday language. The Journal of Philosophy, 77(8), 453–486. CrossRef

Lavie, N. (2005). Distracted and confused? Selective attention under load. Trends in Cognitive Science, 9(2), 75–82. doi: 10.1016/j.tics.2004.12.004. CrossRef

Lepsien, J., Griffin, I. C., Devlin, J. T., & Nobre, A. C. (2005). Directing spatial attention in mental representations: interactions between attentional orienting and working-memory load. Neuroimage, 26(3), 733–743. doi: 10.1016/j.neuroimage.2005.02.026. CrossRefPubMed

Loetscher, T., Bockisch, C. J., Nicholls, M. E., & Brugger, P. (2010). Eye position predicts what number you have in mind. Current Biology, 20(6), R264–R265. doi: 10.1016/j.cub.2010.01.015. CrossRefPubMed

Lugli, L., Baroni, G., Anelli, F., Borghi, A. M., & Nicoletti, R. (2013). Counting is easier while experiencing a congruent motion. PLoS One, 8(5), e64500. CrossRefPubMedPubMedCentral

Marghetis, T., Nunez, R., & Bergen, B. K. (2014). Doing arithmetic by hand: hand movements during exact arithmetic reveal systematic, dynamic spatial processing. The Quarterly Journal of Experimental Psychology (Hove), 67(8), 1579–1596. doi: 10.1080/17470218.2014.897359. CrossRef

Martarelli, C. S., & Mast, F. W. (2011). Preschool children’s eye-movements during pictorial recall. British Journal of Developmental Psychology, 29(Pt 3), 425–436. doi: 10.1348/026151010X495844. CrossRefPubMed

Masson, N., & Pesenti, M. (2014). Attentional bias induced by solving simple and complex addition and subtraction problems. The Quarterly Journal of Experimental Psychology (Hove), 67(8), 1514–1526. doi: 10.1080/17470218.2014.903985. CrossRef

McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: operational momentum in nonsymbolic arithmetic. Perception and Psychophysics, 69(8), 1324–1333. CrossRefPubMed

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., Cangelosi, A., Ellis, R., & Fischer, M. H. (2015a). The ocular resonance effect in spatial-numerical mapping. Acta Psychologica, 161, 162–169. CrossRefPubMed

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.

Pinhas, M., & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109(3), 408–415. doi: 10.1016/j.cognition.2008.09.003. CrossRefPubMed

Pinhas, M., Shaki, S., & Fischer, M. H. (2014). Heed the signs: operation signs have spatial associations. The Quarterly Journal of Experimental Psychology (Hove), 67(8), 1527–1540. doi: 10.1080/17470218.2014.892516. CrossRef

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

Shaki, S., & Fischer, M. H. (2012). Multiple spatial mappings in numerical cognition. Journal of Experimental Psychology Human Perception and Performance, 38(3), 804. CrossRefPubMed

Shaki, S., & Fischer, M. H. (2014). Random walks on the mental number line. Experimental Brain Research, 232, 43–49. CrossRefPubMed

Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin Review, 16(2), 328–331. doi: 10.3758/PBR.16.2.328. CrossRefPubMed

Sheliga, B. M., Riggio, L., & Rizzolatti, G. (1994). Orienting of attention and eye movements. Experimental Brain Research, 98(3), 507–522. CrossRefPubMed

Siegenthaler, E., Costela, F. M., McCamy, M. B., Di Stasi, L. L., Otero-Millan, J., Sonderegger, A., et al. (2014). Task difficulty in mental arithmetic affects microsaccadic rates and magnitudes. European Journal of Neuroscience, 39, 287–294. CrossRefPubMed

Singmann, H., & Bolker, M. (2014). afex: analysis of factorial experiments. R package version 0.12–135

Spivey, M. J., & Geng, J. J. (2001). Oculomotor mechanisms activated by imagery and memory: eye movements to absent objects. Psychological Research, 65(4), 235–241. CrossRefPubMed

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

Tzelgov, J., Ganor-Stern, D., & Maymon-Schreiber, K. (2009). The representation of negative numbers: exploring the effects of mode of processing and notation. The Quarterly Journal of Experimental Psychology, 62(3), 605–624. CrossRefPubMed

Van Gompel, R. P. G., Fischer, M. H., Murray, W., & Hill, R. L. (2007). Eye movements: a window on mind and brain. Oxford: Elsevier.

Varma, S., & Schwartz, D. L. (2011). The mental representation of integers: an abstract-to-concrete shift in the understanding of mathematical concepts. Cognition, 121, 363–385. CrossRefPubMed

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.

Wiemers, M., Bekkering, H., & Lindemann, O. (2014). Spatial interferences in mental arithmetic: evidence from the motion-arithmetic compatibility effect. The Quarterly Journal of Experimental Psychology, 67(8), 1557–1570. doi: 10.1080/17470218.2014.889180. CrossRefPubMed

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., Marghetis, T., & Matlock, T. (2015a). Of magnitudes and metaphors: explaining cognitive interactions between space, time, and number. Cortex, 64, 209–224. CrossRefPubMed

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.

Winter, B., Matlock, T., Shaki, S., & Fischer, M. H. (2015b). Mental number space in three dimensions. Neuroscience and Biobehavioral Reviews, 57, 209–219. CrossRefPubMed

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

Titel: Counting is a spatial process: evidence from eye movements
Auteurs:: Matthias Hartmann
Fred W. Mast
Martin H. Fischer
Publicatiedatum: 25-11-2015
DOI: https://doi.org/10.1007/s00426-015-0722-5
Uitgeverij: Springer Berlin Heidelberg
Tijdschrift: Psychological Research An International Journal of Perception, Attention, Memory, and Action
Uitgave 3/2016
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772

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