Skip to main content
main-content
Top

Tip

Swipe om te navigeren naar een ander artikel

Gepubliceerd in: Psychological Research 3/2016

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

Log in om toegang te krijgen
share
DELEN

Deel dit onderdeel of sectie (kopieer de link)

  • Optie A:
    Klik op de rechtermuisknop op de link en selecteer de optie “linkadres kopiëren”
  • Optie B:
    Deel de link per e-mail

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.

Met onderstaand(e) abonnement(en) heeft u direct toegang:

BSL Psychologie Totaal

Met BSL Psychologie Totaal blijf je als professional steeds op de hoogte van de nieuwste ontwikkelingen binnen jouw vak. Met het online abonnement heb je toegang tot een groot aantal boeken, protocollen, vaktijdschriften en e-learnings op het gebied van psychologie en psychiatrie. Zo kun je op je gemak en wanneer het jou het beste uitkomt verdiepen in jouw vakgebied.

Voetnoten
1
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.
 
2
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.
 
3
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.
 
Literatuur
go back to reference 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/​0272498024400078​3. PubMedCrossRef 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/​0272498024400078​3. PubMedCrossRef
go back to reference 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 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
go back to reference *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 *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
go back to reference *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 *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
go back to reference *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. *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.
go back to reference 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 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
go back to reference Dearborn, W. F. (1906). The psychology of reading. Psychology and Scientific Methods: Archives of Philosophy. 4. Dearborn, W. F. (1906). The psychology of reading. Psychology and Scientific Methods: Archives of Philosophy. 4.
go back to reference 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., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology, 122(3), 371–396. CrossRef
go back to reference Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83–120. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical Cognition, 1, 83–120.
go back to reference 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., 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
go back to reference Dehaene, S., & Mehler, J. (1992). Cross-linguistic regularities in the frequency of number words. Cognition, 43, 1–29. PubMedCrossRef Dehaene, S., & Mehler, J. (1992). Cross-linguistic regularities in the frequency of number words. Cognition, 43, 1–29. PubMedCrossRef
go back to reference Delabarre, E. B. (1898). A method of recording eye-movements. The American Journal of Psychology, 9(4), 572–574. CrossRef Delabarre, E. B. (1898). A method of recording eye-movements. The American Journal of Psychology, 9(4), 572–574. CrossRef
go back to reference 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 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
go back to reference Dobel, C., Diesendruck, G., & Bölte, J. (2007). How writing system and age influence spatial representations of actions. Psychological Science, 18(6), 487–491. PubMedCrossRef Dobel, C., Diesendruck, G., & Bölte, J. (2007). How writing system and age influence spatial representations of actions. Psychological Science, 18(6), 487–491. PubMedCrossRef
go back to reference 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 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
go back to reference Dodge, R., & Cline, T. S. (1901). The angle velocity of eye movements. Psychological Research, 8(2), 145–157. Dodge, R., & Cline, T. S. (1901). The angle velocity of eye movements. Psychological Research, 8(2), 145–157.
go back to reference Duchowski, A. T. (2007). Eye tracking methodology: Theory and practice. London: Springer. Duchowski, A. T. (2007). Eye tracking methodology: Theory and practice. London: Springer.
go back to reference *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 *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
go back to reference Erdmann, B., & Dodge, R. (1898). Psychologische Untersuchungen über das Lesen. Halle: Niemeyer. Erdmann, B., & Dodge, R. (1898). Psychologische Untersuchungen über das Lesen. Halle: Niemeyer.
go back to reference 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 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
go back to reference *Gielen, I., Brysbaert, M., & Dhondt, A. (1991). The syllable-length effect in number processing is task-dependent, 50(87), 449–458. *Gielen, I., Brysbaert, M., & Dhondt, A. (1991). The syllable-length effect in number processing is task-dependent, 50(87), 449–458.
go back to reference 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 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
go back to reference 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. (2015). Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition? Cognitive Processing, 16, 245–248. PubMedCrossRef
go back to reference *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. *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.
go back to reference *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. *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.
go back to reference Hendee, W. R., & Wells, P. N. T. (1997). The perception of visual information. New York: Springer Verlag. CrossRef Hendee, W. R., & Wells, P. N. T. (1997). The perception of visual information. New York: Springer Verlag. CrossRef
go back to reference 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 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
go back to reference Hess, E. H., & Polt, J. M. (1964). Pupil size in relation to mental activity during simple problem-solving. Science, 143, 1190–1192. PubMedCrossRef Hess, E. H., & Polt, J. M. (1964). Pupil size in relation to mental activity during simple problem-solving. Science, 143, 1190–1192. PubMedCrossRef
go back to reference 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. 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.
go back to reference *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., 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
go back to reference *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 *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
go back to reference Huey, E. B. (1898). Preliminary experiments in the physiology and psychology of reading. The American Journal of Psychology, 9(4), 575–586. CrossRef Huey, E. B. (1898). Preliminary experiments in the physiology and psychology of reading. The American Journal of Psychology, 9(4), 575–586. CrossRef
go back to reference 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. (1984). Two stages of word processing during eye fixations in reading of prose. Journal of Verbal Learning and Verbal Behaviour, 23, 612–624. CrossRef
go back to reference 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. (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.
go back to reference *Irwin, D. E., & Thomas, L. E. (2007). The effect of saccades on number processing. Perception and Psychophysics, 69(3), 450–458. PubMedCrossRef *Irwin, D. E., & Thomas, L. E. (2007). The effect of saccades on number processing. Perception and Psychophysics, 69(3), 450–458. PubMedCrossRef
go back to reference 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/​1747021070140065​7.​Children. CrossRef 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/​1747021070140065​7.​Children. CrossRef
go back to reference Just, M. A., & Carpenter, P. A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87(4), 329–354. PubMedCrossRef Just, M. A., & Carpenter, P. A. (1980). A theory of reading: From eye fixations to comprehension. Psychological Review, 87(4), 329–354. PubMedCrossRef
go back to reference 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, 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.
go back to reference *Kowler, E., & Steinman, R. M. (1977). The role of small saccades in counting. Vision Research, 17, 141–146. PubMedCrossRef *Kowler, E., & Steinman, R. M. (1977). The role of small saccades in counting. Vision Research, 17, 141–146. PubMedCrossRef
go back to reference Land, M. F., & Tatler, B. W. (2009). Loking and acting: Vision and eye movements in natural behaviour. New York: Oxford University Press. CrossRef Land, M. F., & Tatler, B. W. (2009). Loking and acting: Vision and eye movements in natural behaviour. New York: Oxford University Press. CrossRef
go back to reference Landolt, E. (1891). Nouvelles recherches sur la physiologie des mouvements des yeux. Archives D’ophthalmologie, 11, 385–395. Landolt, E. (1891). Nouvelles recherches sur la physiologie des mouvements des yeux. Archives D’ophthalmologie, 11, 385–395.
go back to reference *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. *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.
go back to reference Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271–290. CrossRef Lipton, J. S., & Spelke, E. S. (2004). Discrimination of large and small numerosities by human infants. Infancy, 5(3), 271–290. CrossRef
go back to reference *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 *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
go back to reference 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. 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.
go back to reference 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. 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.
go back to reference 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 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
go back to reference *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/​1747021080194674​0. CrossRef *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/​1747021080194674​0. CrossRef
go back to reference 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., 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.
go back to reference 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., 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.
go back to reference 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., Weger, U., & Willmes, K. (2002b). A unit-decade compatibility effect in German number words. Current Psychology Letters: Behaviour, Brain, & Cognition, 2, 19–38.
go back to reference 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. 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.
go back to reference 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 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
go back to reference *Pynte, J. (1974). Readiness for pronunciation during the reading process. Perception and Psychophysics, 16(1), 110–112. CrossRef *Pynte, J. (1974). Readiness for pronunciation during the reading process. Perception and Psychophysics, 16(1), 110–112. CrossRef
go back to reference Rayner, K. (1975). The perceptual span and peripheral cues in reading. Cognitive Psychology, 7, 65–81. CrossRef Rayner, K. (1975). The perceptual span and peripheral cues in reading. Cognitive Psychology, 7, 65–81. CrossRef
go back to reference Rayner, K., & Pollatsek, A. (1989). The psychology of reading. Englewood Cliffs, NJ: Prentice Hall. Rayner, K., & Pollatsek, A. (1989). The psychology of reading. Englewood Cliffs, NJ: Prentice Hall.
go back to reference 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. 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.
go back to reference Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83(2), 274–278. CrossRef Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83(2), 274–278. CrossRef
go back to reference 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 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
go back to reference Robinson, D. A. (1968). The oculomotor control system: A review. Proceedings of the IEEE, 56(6), 1032–1049. CrossRef Robinson, D. A. (1968). The oculomotor control system: A review. Proceedings of the IEEE, 56(6), 1032–1049. CrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference *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, 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.
go back to reference *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. *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.
go back to reference *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 *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
go back to reference 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 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
go back to reference 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 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
go back to reference *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 *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
go back to reference *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 *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
go back to reference *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 *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
go back to reference 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 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
go back to reference 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. 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.
go back to reference 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 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
go back to reference Xu, F., & Spelke, E. S. (2000). Large number discrimination in human infants. Cognition, 74, B1–B11. PubMedCrossRef Xu, F., & Spelke, E. S. (2000). Large number discrimination in human infants. Cognition, 74, B1–B11. PubMedCrossRef
go back to reference Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88–101. PubMedCrossRef Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88–101. PubMedCrossRef
go back to reference Yu, X., Liu, J., Li, D., Cui, J., & Zhou, X. (in press). Dynamic mental number line in simple arithmetic. Psychological Research. Yu, X., Liu, J., Li, D., Cui, J., & Zhou, X. (in press). Dynamic mental number line in simple arithmetic. Psychological Research.
go back to reference 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 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
go back to reference 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 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
Metagegevens
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