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04-02-2016 | Review

Insights into numerical cognition: considering eye-fixations in number processing and arithmetic

Auteurs: J. Mock, S. Huber, E. Klein, K. Moeller

Gepubliceerd in: Psychological Research | Uitgave 3/2016

Abstract

Considering eye-fixation behavior is standard in reading research to investigate underlying cognitive processes. However, in numerical cognition research eye-tracking is used less often and less systematically. Nevertheless, we identified over 40 studies on this topic from the last 40 years with an increase of eye-tracking studies on numerical cognition during the last decade. Here, we review and discuss these empirical studies to evaluate the added value of eye-tracking for the investigation of number processing. Our literature review revealed that the way eye-fixation behavior is considered in numerical cognition research ranges from investigating basic perceptual aspects of processing non-symbolic and symbolic numbers, over assessing the common representational space of numbers and space, to evaluating the influence of characteristics of the base-10 place-value structure of Arabic numbers and executive control on number processing. Apart from basic results such as reading times of numbers increasing with their magnitude, studies revealed that number processing can influence domain-general processes such as attention shifting—but also the other way round. Domain-general processes such as cognitive control were found to affect number processing. In summary, eye-fixation behavior allows for new insights into both domain-specific and domain-general processes involved in number processing. Based thereon, a processing model of the temporal dynamics of numerical cognition is postulated, which distinguishes an early stage of stimulus-driven bottom-up processing from later more top-down controlled stages. Furthermore, perspectives for eye-tracking research in numerical cognition are discussed to emphasize the potential of this methodology for advancing our understanding of numerical cognition.

vorige artikel Exploring the numerical mind by eye-tracking: a special issue

volgende artikel Operational momentum and size ordering in preverbal infants

Besides the reading times of numerals, eye-tracking was also employed to investigate the readability of different number formats which seem to differ with regard to their comprehensibility. Rello, Bautista, Baeza-Yates, Gerv, and Herv (2013) found that participants with dyslexia improved in text comprehension when digits and percentages were used instead of number words and fractions, respectively.

While further investigating the mental representation of arithmetic facts, Zhou, Zhao, Chen, and Zhou (2012) employed horizontal electrooculography (HEOG) in single-digit addition and multiplication problems. This method only provides information about the horizontal direction (i.e., left/right) of eye-movements. In their HEOG data the authors found converging evidence for a preferred operand order in the representation of arithmetic facts. In particular, the HEOG data indicated that participants preferentially fixated the larger operand first. Again relying on HEOG, Yu, Liu, Li, Cui, & Zhou (in press, in this issue) showed that the direction of eye movements in mental arithmetic is influenced by the relative magnitude of the operands.

Please note that there is an ongoing debate on whether symbolic and non-symbolic presentation formats address the same underlying representation of numbers or not (e.g., Cohen Kadosh & Walsh, 2009 for an overview and discussion). However, this is beyond the scope of this article.

Alameda, J. R., Cuetos, F., & Brysbaert, M. (2003). The number 747 is named faster after seeing Boeing than after seeing Levi’s: Associative priming in the processing of multidigit Arabic numerals. The Quarterly Journal of Experimental Psychology. A, Human Experimental Psychology, 56(747), 1009–1019. doi: 10.1080/02724980244000783. PubMedCrossRef

Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278–291. doi: 10.1038/nrn2334. PubMedCrossRef

Ansari, D., Garcia, N., Lucas, E., Hamon, K., & Dhital, B. (2005). Neural correlates of symbolic number processing in children and adults. NeuroReport, 16(16), 1769–1773. doi: 10.1097/01.wnr.0000183905.23396.f1. PubMedCrossRef

Bahnmueller, J., Huber, S., Nuerk, H.-C., Göbel, S. M., & Moeller, K. (2015). Processing multi-digit numbers: a translingual eye tracking study. Psychological Research. doi: 10.1007/s00426-015-0729-y. PubMed

Barth, H. C., & Paladino, A. M. (2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14(1), 125–135. doi: 10.1111/j.1467-7687.2010.00962.x. PubMedCrossRef

Blythe, H. I., Liversedge, S. P., Joseph, H. S. S. L., White, S. J., & Rayner, K. (2009). Visual information capture during fixations in reading for children and adults. Vision Research, 49(12), 1583–1591. doi: 10.1016/j.visres.2009.03.015. PubMedPubMedCentralCrossRef

Botvinick, M. M., Braver, T. S., Barch, D. M., Carter, C. S., & Cohen, J. D. (2001). Conflict monitoring and cognitive control. Psychological Review, 108(3), 624–652. PubMedCrossRef

*Brysbaert, M. (1995). Arabic number reading: On the nature of the numerical scale and the origin of phonological recoding. Journal of Experimental Psychology, 124(4), 434–452. CrossRef

*Bulf, H., Cassia, V. M., & De Hevia, M. D. (2014). Are numbers, size and brightness equally efficient in orienting visual attention? Evidence from an eye-tracking study. PLoS ONE, 9(6), e99499. doi: 10.1371/journal.pone.0099499. PubMedPubMedCentralCrossRef

*Bulf, H., de Hevia, M. D., & Macchi Cassia, V. (2015). Small on the left, large on the right: Numbers orient visual attention onto space in preverbal infants. Developmental Science. doi: 10.1111/desc.12315. PubMed

Burr, D., & Ross, J. (2008). A visual sense of number. Current Biology, 18(6), 425–428. doi: 10.1016/j.cub.2008.02.052. PubMedCrossRef

Calvo, M. G., & Meseguer, E. (2002). Eye movements and processing stages in reading: Relative contribution of visual, lexical, and contextual factors. The Spanish Journal of Psychology, 5(1), 66–77. doi: 10.1017/S1138741600005849. PubMedCrossRef

*Ceulemans, A., Loeys, T., Hoppenbrouwers, K., & Desoete, A. (2014). To be or not to be: An informative non-symbolic numerical magnitude processing study about small versus large numbers in infants. Journal of Special Education and Rehabilitation, 15(1–2), 75–90. doi: 10.2478/jser-2014-0005.

Clifton, C., Staub, A., & Rayner, K. (2007). Eye movements in reading words and sentences. In R. P. G. van Gompel, M. H. Fischer, W. S. Murray, & R. L. Hill (Eds.), Eye movements: A window on mind and brain (pp. 341–372). Oxford: Elsevier Ltd. CrossRef

Cohen Kadosh, R., & Walsh, V. (2009). Numerical representation in the parietal lobes: Abstract or not abstract? The Behavioral and Brain Sciences, 32(3–4), 313–373. doi: 10.1017/S0140525X09990938. PubMedCrossRef

*De Corte, E., Verschaffel, L., & Pauwels, A. (1990). Influence of the semantic structure of word problems on second graders’ eye movements. Journal of Educational Psychology, 82(2), 359–365. doi: 10.1037/0022-0663.82.2.359. CrossRef

De Hevia, M. D., Girelli, L., Addabbo, M., & Cassia, V. M. (2014a). Human infants’ preference for left-to-right oriented increasing numerical sequences. PLoS ONE. doi: 10.1371/journal.pone.0096412.

De Hevia, M. D., Girelli, L., & Cassia, V. M. (2012). Minds without language represent number through space: Origins of the mental number line. Frontiers in Psychology, 3, 1–4. doi: 10.3389/fpsyg.2012.00466. CrossRef

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 of the United States of America, 111(13), 4809–4813. doi: 10.1073/pnas.1323628111. PubMedPubMedCentralCrossRef

Dearborn, W. F. (1906). The psychology of reading. Psychology and Scientific Methods: Archives of Philosophy. 4.

Dehaene, S. (2005). Evolution of human cortical circuits for reading and arithmetic: The “neuronal recycling” hypothesis. In S. Dehaene, J.-R. Duhamel, M. D. Hauser, & G. Rizzolatti (Eds.), From monkey brain to human brain (pp. 133–157). Cambridge, MA: MIT Press. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.57.9491&rep=rep1&type=pdf

Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology, 122(3), 371–396. CrossRef

Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83–120.

Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16(3), 626–641. PubMed

Dehaene, S., & Mehler, J. (1992). Cross-linguistic regularities in the frequency of number words. Cognition, 43, 1–29. PubMedCrossRef

Delabarre, E. B. (1898). A method of recording eye-movements. The American Journal of Psychology, 9(4), 572–574. CrossRef

Den Buurman, R., Roersema, T., & Gerrissen, J. F. (1981). Eye movements and the perceptual span in reading. Reading Research Quarterly, 16(2), 227–235. doi: 10.1016/0022-0965(86)90037-8. CrossRef

Deubel, H., & Schneider, W. X. (1996). Saccade target selection and object recognition: Evidence for a common attentional mechanism. Vision Research, 36(12), 1827–1837. doi: 10.1016/0042-6989(95)00294-4. PubMedCrossRef

Deutsch, A., Frost, R., Pelleg, S., Pollatsek, A., & Rayner, K. (2003). Early morphological effects in reading: Evidence from parafoveal preview benefit in Hebrew. Psychonomic Bulletin & Review, 10(2), 415–422. doi: 10.3758/BF03196500. CrossRef

Dobel, C., Diesendruck, G., & Bölte, J. (2007). How writing system and age influence spatial representations of actions. Psychological Science, 18(6), 487–491. PubMedCrossRef

Dockeray, F. C., & Pillsbury, W. B. (1910). The span of vision in reading and the legibility of letters. Journal of Educational Psychology, 1(3), 123–131. CrossRef

Dodge, R., & Cline, T. S. (1901). The angle velocity of eye movements. Psychological Research, 8(2), 145–157.

Dooley, C. M. (2010). Young children’s approaches to books: The emergence of comprehension. The Reading Teacher, 64(2), 120–130. doi: 10.1598/RT.64.2.4. CrossRef

Duchowski, A. T. (2007). Eye tracking methodology: Theory and practice. London: Springer.

Engbert, R., Nuthmann, A., Richter, E. M., & Kliegl, R. (2005). SWIFT: A dynamical model of saccade generation during reading. Psychological Review, 112(4), 777–813. doi: 10.1037/0033-295X.112.4.777. PubMedCrossRef

*Epelboim, J., & Suppes, P. (2001). A model of eye movements and visual working memory during problem solving in geometry. Vision Research, 41(12), 1561–1574. PubMedCrossRef

Erdmann, B., & Dodge, R. (1898). Psychologische Untersuchungen über das Lesen. Halle: Niemeyer.

Fattorini, E., Pinto, M., Rotondaro, F., & Doricchi, F. (2015). Perceiving numbers does not cause automatic shifts of spatial attention. Cortex. doi: 10.1016/j.cortex.2015.09.007

Feng, G., Miller, K., Shu, H., & Zhang, H. (2009). Orthography and the development of reading processes: An eye-movement study of Chinese and English. Child Development, 80(3), 720–735. doi: 10.1111/j.1467-8624.2009.01293.x. PubMedCrossRef

Fischer, M. H., & Shaki, S. (2014). 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. PubMedCrossRef

*Fischer, M. H., Warlop, N., Hill, R. L., & Fias, W. (2004). Oculomotor bias induced by number perception. Experimental Psychology, 51(2), 91–97. doi: 10.1027/1618-3169.51.2.91. PubMedCrossRef

Fuchs, A. F. (1967). Saccadic and smooth pursuit eye movements in the monkey. Journal of Physiology, 191, 609–631. PubMedPubMedCentralCrossRef

Galfano, G., Rusconi, E., & Umiltà, C. (2003). Automatic activation of multiplication facts: Evidence from the nodes adjacent to the product. Quarterly Journal of Experimental Psychology, 56(1), 31–61. PubMedCrossRef

*Gandini, D., Lemaire, P., & Dufau, S. (2008). Older and younger adults’ strategies in approximate quantification. Acta Psychologica, 129(1), 175–189. doi: 10.1016/j.actpsy.2008.05.009. PubMedCrossRef

Ganor-Stern, D., & Weiss, N. (2015). Tracking practice effects in computation estimation. Psychological Research. doi: 10.1007/s00426-015-0720-7. PubMed

Gebuis, T., Gevers, W., & Cohen Kadosh, R. (2014). Topographic representation of high-level cognition: Numerosity or sensory processing? Trends in Cognitive Sciences, 18(1), 1–3. doi: 10.1016/j.tics.2013.10.002. PubMedCrossRef

*Gielen, I., Brysbaert, M., & Dhondt, A. (1991). The syllable-length effect in number processing is task-dependent, 50(87), 449–458.

Ginsburg, V., & Gevers, W. (2015). Spatial coding of ordinal information in short- and long-term memory. Frontiers in Human Neuroscience, 9(5), 1–10. doi: 10.3389/fnhum.2015.00008.

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. doi: 10.1177/0022022111406251. CrossRef

*Godau, C., Wirth, M., Hansen, S., Haider, H., & Gaschler, R. (2014). From marbles to numbers—Estimation influences looking patterns on arithmetic problems. Psychology, 05(02), 127–133. doi: 10.4236/psych.2014.52020. CrossRef

*Green, H. J., Lemaire, P., & Dufau, S. (2007). Eye movement correlates of younger and older adults’ strategies for complex addition. Acta Psychologica, 125(3), 257–278. doi: 10.1016/j.actpsy.2006.08.001. PubMedCrossRef

Hartmann, M. (2015). Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition? Cognitive Processing, 16, 245–248. PubMedCrossRef

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. PubMedCrossRef

Hartmann, M., Mast, F. W., & Fischer, M. H. (2015a). Counting is a spatial process: Evidence from eye movements. Psychological Research. doi: 10.1007/s00426-015-0722-5. PubMed

*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(January), 1–8. doi: 10.3389/fpsyg.2015.00012.

Harvey, B. M., Klein, B. P., Petridou, N., & Dumoulin, S. O. (2013). Topographic representation of numerosity in the human parietal cortex. Science, 341(2013), 1123–1126. doi: 10.1126/science.1239052. PubMedCrossRef

*Hegarty, M., Mayer, R. E., & Green, C. E. (1992). Comprehension of arithmetic word problems: Evidence from students’ eye fixations. Journal of Educational Psychology, 84(1), 76–84. doi: 10.1037/0022-0663.84.1.76. CrossRef

*Heine, A., Thaler, V., Tamm, S., Hawelka, S., Schneider, M., Torbeyns, J., et al. (2010). What the eyes already “know”: Using eye movement measurement to tap into children’s implicit numerical magnitude representations. Infant and Child Development, 19(2), 175–186. doi: 10.1002/icd.

Hendee, W. R., & Wells, P. N. T. (1997). The perception of visual information. New York: Springer Verlag. CrossRef

Henderson, J. M. (1992). Object identification in context: The visual processing of natural scenes. Canadian Journal of Psychology, 46(3), 319–341. doi: 10.1037/h0084325. PubMedCrossRef

Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory & Cognition, 10(4), 389–395. doi: 10.3758/BF03202431. CrossRef

Hess, E. H., & Polt, J. M. (1964). Pupil size in relation to mental activity during simple problem-solving. Science, 143, 1190–1192. PubMedCrossRef

Hoffman, J. E., & Subramaniam, B. (1995). The role of visual attention in saccadic eye movements. Perception and Psychophysics, 57(6), 787–795. doi: 10.3758/BF03206794. PubMedCrossRef

Holmqvist, K., Nyström, M., Andersson, R., Dewhurst, R., Jarodzka, H., & van de Weijer, J. (2011). Eye tracking: A comprehensive guide to methods and measures. New York: Oxford University Press.

Hubbard, T. L. (2014). Forms of momentum across space: Representational, operational, and attentional. Psychonomic Bulletin & Review. doi: 10.3758/s13423-014-0624-3.

*Huber, S., Klein, E., Willmes, K., Nuerk, H.-C., & Moeller, K. (2014a). Decimal fraction representations are not distinct from natural number representations—Evidence from a combined eye-tracking and computational modeling approach. Frontiers in Human Neuroscience, 8, 172. doi: 10.3389/fnhum.2014.00172. PubMedPubMedCentral

*Huber, S., Mann, A., Nuerk, H. C., & Moeller, K. (2014b). Cognitive control in number magnitude processing: Evidence from eye-tracking. Psychological Research, 78(4), 539–548. doi: 10.1007/s00426-013-0504-x. PubMedCrossRef

*Huber, S., Moeller, K., & Nuerk, H.-C. (2014c). Adaptive processing of fractions—Evidence from eye-tracking. Acta Psychologica, 148, 37–48. doi: 10.1016/j.actpsy.2013.12.010. PubMedCrossRef

*Huber, S., Cornelsen, S., Moeller, K., & Nuerk, H.-C. (2015). Towards a model framework of generalized parallel componential processing of multi-symbol numbers. Journal of Experimental Psychology: Learning, Memory, and Cognition, 41, 732–745. doi: 10.1037/xlm0000043. PubMed

Huey, E. B. (1898). Preliminary experiments in the physiology and psychology of reading. The American Journal of Psychology, 9(4), 575–586. CrossRef

Inhoff, A. W. (1984). Two stages of word processing during eye fixations in reading of prose. Journal of Verbal Learning and Verbal Behaviour, 23, 612–624. CrossRef

Inhoff, A. W. (1985). The effect of factivity on lexical retrieval and postlexical processes during eye fixations in reading. Journal of Psycholinguistic Research, 14(1), 45–56. doi: 10.1007/BF01067473. PubMedCrossRef

Irwin, D. E. (2004). Fixation location and fixation duration as indices of cognitive processing. In J. M. Henderson & F. Ferreira (Eds.), The interface of language, vision, and action: Eye movements and the visual world (pp. 105–133). New York: Psychology Press.

*Irwin, D. E., & Thomas, L. E. (2007). The effect of saccades on number processing. Perception and Psychophysics, 69(3), 450–458. PubMedCrossRef

Joseph, H. S. S. L., Liversedge, S. P., Blythe, H. I., White, S. J., Gathercole, S. E., & Rayner, K. (2008). Children’s and adults’ processing of anomaly and implausibility during reading: Evidence from eye movements. Quarterly Journal of Experimental Psychology, 61(5), 708–723. doi: 10.1080/17470210701400657.Children. CrossRef

Joseph, H. S. S. L., Liversedge, S. P., Blythe, H. I., White, S. J., & Rayner, K. (2009). Word length and landing position effects during reading in children and adults. Vision Research, 49(16), 2078–2086. doi: 10.1016/j.visres.2009.05.015. PubMedCrossRef

Just, M. A., & Carpenter, P. A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87(4), 329–354. PubMedCrossRef

Klein, R. M. (1980). Does oculomotor readiness mediate cognitive control of visual attention? In R. S. Nickerson (Ed.), Attention and performance VIII (pp. 259–276). Hillsdale, NJ: Lawrence Erlbaum.

*Klein, E., Huber, S., Nuerk, H.-C., & Moeller, K. (2014). Operational momentum affects eye fixation behaviour. The Quarterly Journal of Experimental Psychology, 67(8), 1614–1625. doi: 10.1080/17470218.2014.902976. PubMedCrossRef

Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324(5934), 1583–1585. doi: 10.1126/science.1171599. PubMedCrossRef

*Kowler, E., & Steinman, R. M. (1977). The role of small saccades in counting. Vision Research, 17, 141–146. PubMedCrossRef

Laeng, B., Sirois, S., & Gredeback, G. (2012). Pupillometry: A window to the preconscious? Perspectives on Psychological Science, 7(1), 18–27. doi: 10.1177/1745691611427305. PubMedCrossRef

Land, M. F., & Tatler, B. W. (2009). Loking and acting: Vision and eye movements in natural behaviour. New York: Oxford University Press. CrossRef

Landolt, E. (1891). Nouvelles recherches sur la physiologie des mouvements des yeux. Archives D’ophthalmologie, 11, 385–395.

*Landy, D. H., Jones, M. N., & Goldstone, R. L. (2008). How the appearance of an operator affects its formal precedence. In Proceedings of the thirtieth annual conference of the cognitive science society, 2109–2114.

Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271–290. CrossRef

*Loetscher, T., Bockisch, C. J., & Brugger, P. (2008). Looking for the answer: The mind’s eye in number space. Neuroscience, 151(3), 725–729. doi: 10.1016/j.neuroscience.2007.07.068. PubMedCrossRef

*Loetscher, T., Bockisch, C. J., Nicholls, M. E. R., & Brugger, P. (2010). Eye position predicts what number you have in mind. Current Biology, 20(6), 264–265. CrossRef

Macchia Cassia, V., McCrink, K., De Hevia, M. D., Gariboldi, V., & Bulf, H. (under review). Operational momentum and size ordering in preverbal infants. Psychological Research.

Macizo, P., & Herrera, A. (2011). Cognitive control in number processing: Evidence from the unit-decade compatibility effect. Acta Psychologica, 136(1), 112–118. doi: 10.1016/j.actpsy.2010.10.008. PubMedCrossRef

Macizo, P., & Herrera, A. (2013). The processing of Arabic numbers is under cognitive control. Psychological Research, 77(5), 651–658. doi: 10.1007/s00426-012-0456-6. PubMedCrossRef

McConkie, G. W., Zola, D., Grimes, J., Kerr, P. W., Bryant, N. R., & Wolff, P. M. (1991). Children’s eye movements during reading. In J. F. Stein (Ed.), Vision and visual dyslexia (pp. 251–262). London: Macmillan.

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. PubMedCrossRef

*Merkley, R., & Ansari, D. (2010). Using eye tracking to study numerical cognition: The case of the ratio effect. Experimental Brain Research, 206(4), 455–460. doi: 10.1007/s00221-010-2419-8. PubMedCrossRef

*Meyerhoff, H. S., Moeller, K., Debus, K., & Nuerk, H. C. (2012). Multi-digit number processing beyond the two-digit number range: A combination of sequential and parallel processes. Acta Psychologica, 140(1), 81–90. doi: 10.1016/j.actpsy.2011.11.005. PubMedCrossRef

*Milosavljevic, M., Madsen, E., Koch, C., & Rangel, A. (2011). Fast saccades toward numbers: Simple number comparisons can be made in as little as 230 ms. Journal of Vision, 11(4), 1–12. doi: 10.1167/11.4.4.Introduction. CrossRef

*Moeller, K., Fischer, M. H., Nuerk, H.-C., & Willmes, K. (2009a). Eye fixation behaviour in the number bisection task: Evidence for temporal specificity. Acta Psychologica, 131(3), 209–220. doi: 10.1016/j.actpsy.2009.05.005. PubMedCrossRef

*Moeller, K., Fischer, M. H., Nuerk, H.-C., & Willmes, K. (2009b). Sequential or parallel decomposed processing of two-digit numbers? Evidence from eye-tracking. Quarterly Journal of Experimental Psychology, 62(2), 323–334. doi: 10.1080/17470210801946740. CrossRef

*Moeller, K., Klein, E., & Nuerk, H.-C. (2011a). (No) small adults: Children’s processing of carry addition problems. Developmental Neuropsychology, 36(6), 702–720. doi: 10.1080/87565641.2010.549880. PubMedCrossRef

*Moeller, K., Klein, E., & Nuerk, H.-C. (2011b). Three processes underlying the carry effect in addition—Evidence from eye tracking. British Journal of Psychology, 102(3), 623–645. doi: 10.1111/j.2044-8295.2011.02034.x. PubMedCrossRef

*Moeller, K., Neuburger, S., Kaufmann, L., Landerl, K., & Nuerk, H. C. (2009c). Basic number processing deficits in developmental dyscalculia: Evidence from eye tracking. Cognitive Development, 24(4), 371–386. doi: 10.1016/j.cogdev.2009.09.007. CrossRef

Myachykov, A., Ellis, R., Changelosi, A., & Fischer, M. H. (2015). Ocular drift along the mental number line. Psychological Research. doi: 10.1007/s00426-015-0731-4.

Noton, D., & Stark, L. (1971). Scanpaths in eye movements during pattern perception. Science, 171, 308–311. doi: 10.1126/science.171.3968.308. PubMedCrossRef

Nuerk, H.-C., Geppert, B. E., van Herten, M., & Willmes, K. (2002a). On the impact of different number representations in the number bisection task. Cortex, 38(5), 691–715. doi: 10.1016/S0010-9452(08)70038-8. PubMedCrossRef

Nuerk, H.-C., Moeller, K., Klein, E., Willmes, K., & Fischer, M. H. (2011). Extending the mental number line. Zeitschrift Für Psychologie, 219(1), 3–22. doi: 10.1027/2151-2604/a000041. CrossRef

Nuerk, H.-C., Moeller, K., & Willmes, K. (2015a). Multi-digit number processing: overview, conceptual clarifications, and language influences. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 106–139). Oxford: Oxford University Press.

Nuerk, H.-C., Patro, K., Cress, U., Schild, U., Friedrich, C. K., & Göbel, S. M. (2015b). How space-number associations may be created in preliterate children: Six distinct mechanisms. Frontiers in Psychology,. doi: 10.3389/fpsyg.2015.00215.

Nuerk, H.-C., Weger, U., & Willmes, K. (2001). Decade breaks in the mental number line? Putting the tens and units back in different bins. Cognition, 82(1), B25–B33. doi: 10.1016/S0010-0277(01)00142-1. PubMedCrossRef

Nuerk, H.-C., Weger, U., & Willmes, K. (2002b). A unit-decade compatibility effect in German number words. Current Psychology Letters: Behaviour, Brain, & Cognition, 2, 19–38.

Nuerk, H.-C., & Willmes, K. (2005). On the magnitude representations of two-digit numbers Three models of two-digit magnitude representation. Psychology Science, 47(1), 52–72.

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. PubMedCrossRef

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

Poltrock, S. E., & Schwartz, D. R. (1984). Comparative judgments of multidigit numbers. Journal of Experimental Psychology. Learning, Memory, and Cognition, 10(1), 32–45. CrossRef

Porter, G., Troscianko, T., & Gilchrist, I. D. (2007). Effort during visual search and counting: Insights from pupillometry. Quarterly Journal of Experimental Psychology, 60(2), 211–229. doi: 10.1080/17470210600673818. CrossRef

*Pynte, J. (1974). Readiness for pronunciation during the reading process. Perception and Psychophysics, 16(1), 110–112. CrossRef

Ranzini, M., Lisi, M., & Zorzi, M. (2015). Voluntary eye movements direct attention on the mental number space. Psychological Research. doi: 10.1007/s00426-015-0741-2.

Rayner, K. (1975). The perceptual span and peripheral cues in reading. Cognitive Psychology, 7, 65–81. CrossRef

Rayner, K. (1998). Eye movements in reading and information processing: 20 years of research. Psychological Bulletin, 124(3), 372–422. doi: 10.1037//0033-2909.124.3.372. PubMedCrossRef

Rayner, K. (2009). Eye movements and attention in reading, scene perception, and visual search. Quarterly journal of experimental psychology (2006) (Vol. 62). doi: 10.1080/17470210902816461

Rayner, K., & Pollatsek, A. (1989). The psychology of reading. Englewood Cliffs, NJ: Prentice Hall.

Reichle, E. D., Rayner, K., & Pollatsek, A. (2003). The E–Z reader model of eye-movement control in reading: Comparisons to other models. Behavioral and Brain Sciences, 26, 445–476. doi: 10.1017/S0140525X03000104. PubMedCrossRef

Rello, L., Bautista, S., Baeza-Yates, R., Gerv, P., & Herv, R. (2013). One half or 50%? An eye-tracking study of number representation readability. Human-Computer Interaction, 8120, 229–245.

Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83(2), 274–278. CrossRef

*Rinaldi, L., Brugger, P., Bockisch, C. J., Bertolini, G., & Girelli, L. (2015). Keeping an eye on serial order: Ocular movements bind space and time. Cognition, 142, 291–298. doi: 10.1016/j.cognition.2015.05.022. PubMedCrossRef

Rivera, S. M., Reiss, A. L., Eckert, M. A., & Menon, V. (2005). Developmental changes in mental arithmetic: Evidence for increased functional specialization in the left inferior parietal cortex. Cerebral Cortex, 15(11), 1779–1790. doi: 10.1093/cercor/bhi055. PubMedCrossRef

Robinson, D. A. (1968). The oculomotor control system: A review. Proceedings of the IEEE, 56(6), 1032–1049. CrossRef

Ross, J., & Burr, D. C. (2010). Vision senses number directly. Journal of Vision, 10(2), 10.1–10.8. doi: 10.1167/10.2.10. CrossRef

Rugani, R., Vallortigara, G., Priftis, K., & Regolin, L. (2015). Number-space mapping in the newborn chick resembles humans’ mental number line. Science, 347(6221), 534–536. PubMedCrossRef

*Ruiz Fernández, S., Rahona, J. J., Hervás, G., Vázquez, C., & Ulrich, R. (2011). Number magnitude determines gaze direction: Spatial-numerical association in a free-choice task. Cortex, 47(5), 617–620. doi: 10.1016/j.cortex.2010.10.006. PubMedCrossRef

Saffran, J. R., Aslin, R. N., & Newport, E. L. (1996). Statistical learning by 8-month-old infants. Science, 274, 1926–1928. doi: 10.1126/science.274.5294.1926. PubMedCrossRef

Salman, M. S., Sharpe, J. A., Eizenman, M., Lillakas, L., Westall, C., To, T., et al. (2006). Saccades in children. Vision Research, 46(8–9), 1432–1439. doi: 10.1016/j.visres.2005.06.011. PubMedCrossRef

Schleger, F., Landerl, K., Muenssinger, J., Draganova, R., Reinl, M., Kiefer-Schmidt, I., et al. (2014). Magnetoencephalographic signatures of numerosity discrimination in fetuses and neonates. Developmental Neuropsychology, 39(4), 316–329. PubMedCrossRef

*Schleifer, P., & Landerl, K. (2011). Subitizing and counting in typical and atypical development. Developmental Science, 14(2), 280–291. doi: 10.1111/j.1467-7687.2010.00976.x. PubMedCrossRef

*Schneider, M., Heine, A., Thaler, V., Torbeyns, J., De Smedt, B., Verschaffel, L., et al. (2008). A validation of eye movements as a measure of elementary school children’s developing number sense. Cognitive Development, 23(3), 424–437. doi: 10.1016/j.cogdev.2008.07.002.

*Schneider, E., Maruyama, M., Dehaene, S., & Sigman, M. (2012). Eye gaze reveals a fast, parallel extraction of the syntax of arithmetic formulas. Cognition, 125(3), 475–490. doi: 10.1016/j.cognition.2012.06.015. PubMedCrossRef

*Schot, W. D., van Viersen, S., van‘t Noordende, J. E., Slot, E. M., & Kroesbergen, E. H. (2015). Strategiegebruik op de getallenlijntaak geanalyseerd met behulp van eye-tracking. Pedagogische Studien, 92(1), 55–69.

*Schwarz, W., & Keus, I. M. (2004). Moving the eyes along the mental number line: Comparing SNARC effects with saccadic and manual responses. Perception and Psychophysics, 66(4), 651–664. PubMedCrossRef

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(2), 287–294. doi: 10.1111/ejn.12395. PubMedCrossRef

Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250. doi: 10.1111/1467-9280.02438. PubMedCrossRef

Simon, O., Mangin, J.-F., Cohen, L., Le Bihan, D., & Dehaene, S. (2002). Topographical layout of hand, eye, calculation, and language-related areas in the human parietal lobe. Neuron, 33, 475–487. PubMedCrossRef

*Sophian, C., & Crosby, M. E. (2008). What eye fixation patterns tell us about subitizing. Developmental Neuropsychology, 33(3), 394–409. doi: 10.1080/87565640801982460. PubMedCrossRef

*Sullivan, J. L., Juhasz, B. J., Slattery, T. J., & Barth, H. C. (2011). Adults’ number-line estimation strategies: Evidence from eye movements. Psychonomic Bulletin & Review 18(3), 557–563. doi: 10.3758/s13423-011-0081-1. CrossRef

*Suppes, P., Cohen, M., Laddaga, R., Anliker, J., & Floyd, R. (1983). A procedural theory of eye movements in doing arithmetic. Journal of Mathematical Psychology, 27(4), 341–369. CrossRef

*Susac, A., Bubic, A., Kaponja, J., Planinic, M., & Palmovic, M. (2014). Eye movements reveal students’ strategies in simple equation solving. International Journal of Science and Mathematics Education, 12(3), 555–577. doi: 10.1007/s10763-014-9514-4. CrossRef

Traxler, M. J., Pickering, M. J., Communication, H., Kingdom, U., Liversedge, S., Rayner, K., & Re-, H. C. (1996). Plausibility and the processing of unbounded dependencies: An eye-tracking study. Journal of Memory and Language, 35, 454–475. doi: 10.1006/jmla.1996.0025. CrossRef

van Dijck, J.-P., Abrahamse, E. L., Majerus, S., & Fias, W. (2013). Spatial attention interacts with serial order retrieval from verbal working memory. Psychological Science, 24(9), 1854–1859. doi: 10.1177/0956797613479610. PubMedCrossRef

van Dijck, J.-P., & Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition, 119(1), 114–119. doi: 10.1016/j.cognition.2010.12.013. PubMedCrossRef

*van Viersen, S., Slot, E. M., Kroesbergen, E. H., van’t Noordende, J. E., & Leseman, P. P. M. (2013). The added value of eye-tracking in diagnosing dyscalculia: A case study. Frontiers in Psychology, 4, 679. doi: 10.3389/fpsyg.2013.00679. PubMedPubMedCentral

van’t Noordende, J. E., van Hoogmoed, A. E., Schot, W. D., & Kroesbergen, E. H. (2015). Number line estimation strategies in childrenwith mathematical learning difficulties measured by eye tracking. Psychological Research. doi: 10.1007/s00426-015-0736-z.

Varma, S., & Karl, S. R. (2013). Understanding decimal proportions: Discrete representations, parallel access, and privileged processing of zero. Cognitive Psychology, 66(3), 283–301. PubMedCrossRef

Wood, G., Willmes, K., Nuerk, H.-C., & Fischer, M. H. (2008). On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly, 50(4), 489–525. doi: 10.1027/1618-3169.52.3.187.

Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750. PubMedCrossRef

Xu, F., & Spelke, E. S. (2000). Large number discrimination in human infants. Cognition, 74, B1–B11. PubMedCrossRef

Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88–101. PubMedCrossRef

Yu, X., Liu, J., Li, D., Cui, J., & Zhou, X. (in press). Dynamic mental number line in simple arithmetic. Psychological Research.

Zangemeister, W. H., Shermant, K., & Stark, L. (1995). Evidence for a global scanpath strategy in viewing abstract compared to realistic images. Neuropsychologia, 33(8), 1009–1025. PubMedCrossRef

Zhao, M., Gersch, T. M., Schnitzer, B. S., Dosher, B. A., & Kowler, E. (2012). Eye movements and attention: The role of pre-saccadic shifts of attention in perception, memory and the control of saccades. Vision Research, 74, 40–60. doi: 10.1016/j.visres.2012.06.017. PubMedPubMedCentralCrossRef

Zhou, F., Zhao, Q., Chen, C., & Zhou, X. (2012). Mental representations of arithmetic facts: Evidence from eye movement recordings supports the preferred operand-order-specific representation hypothesis. The Quarterly Journal of Experimental Psychology, 65(4), 661–674. doi: 10.1080/17470218.2011.616213. PubMedCrossRef

Titel: Insights into numerical cognition: considering eye-fixations in number processing and arithmetic
Auteurs: J. Mock
S. Huber
E. Klein
K. Moeller
Publicatiedatum: 04-02-2016
Uitgeverij: Springer Berlin Heidelberg
Gepubliceerd in: Psychological Research / Uitgave 3/2016
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-015-0739-9

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