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08-12-2015 | Original Article

Dynamic mental number line in simple arithmetic

Auteurs: Xiaodan Yu, Jie Liu, Dawei Li, Hang Liu, Jiaxin Cui, Xinlin Zhou

Gepubliceerd in: Psychological Research | Uitgave 3/2016

Abstract

Studies have found that spatial-numerical associations could extend to arithmetic. Addition leads to rightward shift in spatial attention while subtraction leads to leftward shift (e.g., Knops et al. 2009; McCrink et al. 2007; Pinhas & Fischer 2008), which is consistent with the hypothesis of static mental number line (MNL) for arithmetic. The current investigation tested the hypothesis of dynamic mental number line which was shaped by the relative magnitudes of two operands in simple arithmetic. Horizontal and vertical electrooculograms (HEOG and VEOG) during simple arithmetic were recorded. Results showed that the direction of eye movements was dependent on the relative magnitudes of two operands. Subtraction was associated with larger rightward eye movements than addition (Experiment 1), and smaller-operand-first addition (e.g., 2+9) was associated with larger rightward eye movement than larger-operand-first addition (e.g., 9+2) only when the difference of two operands was large (Experiment 2). The results suggest that the direction of the mental number line could be dynamic during simple arithmetic, and that the eyes move along the dynamic mental number line to search for solutions.

vorige artikel Counting is a spatial process: evidence from eye movements

volgende artikel Processing multi-digit numbers: a translingual eye-tracking study

Bächtold, D., Baumüller, M., & Brugger, P. (1998). Stimulus-response compatibility in representational space. Neuropsychologia, 36(8), 731–735. doi: 10.1016/S0028-3932(98)00002-5. CrossRefPubMed

Butterworth, B., Zorzi, M., Girelli, L., & Jonckheere, A. R. (2001). Storage and retrieval of addition facts: the role of number comparison. Q. J. Exp. Psychol. Sect. A., 54(4), 1005–1029. doi: 10.1080/713756007. CrossRef

Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. J. Exp. Psychol. Gen., 122(3), 371–396. doi: 10.1037/0096-3445.122.3.371. CrossRef

Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nat. Neurosci., 6(6), 555–556. doi: 10.1038/nn1066. CrossRefPubMed

Fischer, M. H., Fias, MH: Spatial representation of numbers. In: The handbook of mathematical cognition, Psychology Press, New York (2005).

Fischer, M. H., Mills, R. A., & Shaki, S. (2010). How to cook a SNARC: number placement in text rapidly changes spatial–numerical associations. Brain Cogn., 72(3), 333–336. doi: 10.1016/j.bandc.2009.10.010. CrossRefPubMed

Fischer, M. H., & Shaki, S. (2014). Spatial associations in numerical cognition–from single digits to arithmetic. Q. J. Exp. Psychol., 67(8), 1461–1483. doi: 10.1080/17470218.2014.927515. CrossRef

Galton, F. (1880a). Visualised numerals. Nature, 21, 252–256. CrossRef

Galton, F. (1880b). Visualised numerals. Nature, 21, 494–495. CrossRef

Groen, G. J., & Parkman, J. M. (1972). A chronometric analysis of simple addition. Psychol Rev, 79(4), 329–343. doi: 10.1037/h0032950. CrossRef

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

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

Hartmann, M., Mast, F. W., Fischer, M. H: (in press). Counting is a spatial process: evidence from eye movements. Psychol. Res. doi: 10.1007/s00426-015-0722-5.

Hung, Y., Hung, D. L., Tzeng, O. J.-L., & Wu, D. H. (2008). Flexible spatial mapping of different notations of numbers in Chinese readers. Cognition, 106(3), 1441–1450. doi: 10.1016/j.cognition.2007.04.017. CrossRefPubMed

Klein, E., Huber, S., Nuerk, H. C., & Moeller, K. (2014). Operational momentum affects eye fixation behaviour. Q. J. Exp. Psychol., 67(8), 1614–1625. doi: 10.1080/17470218.2014.902976. CrossRef

Knops, A., Dehaene, S., Berteletti, I., & Zorzi, M. (2014). Can approximate mental calculation account for operational momentum in addition and subtraction? Q. J. Exp. Psychol., 67(8), 1541–1556. doi: 10.1080/17470218.2014.890234. CrossRef

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. CrossRefPubMed

Knops, A., Zitzmann, S., & McCrink, K. (2013). Examining the presence and determinants of operational momentum in childhood. Front. Psychol., 4, 325. doi: 10.3389/fpsyg.2013.00325. CrossRefPubMedPubMedCentral

Lugli, L., Baroni, G., Anelli, F., Borghi, A. M., Nicoletti, R.: Counting is easier while experiencing a congruent motion. (2013) doi: 10.1371/journal.pone.0064500.

Masson, N., & Pesenti, M. (2014). Attentional bias induced by solving simple and complex addition and subtraction problems. Q. J Exp. Psychol., 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. Percept. Psychophys., 69(8), 1324–1333. doi: 10.3758/BF03192949. CrossRefPubMed

McCrink, K., & Wynn, K. (2009). Operational momentum in large-number addition and subtraction by 9-month-olds. J. Exp. Child Psychol., 103(4), 400–408. doi: 10.1016/j.jecp.2009.01.013. CrossRefPubMed

Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215, 1519–1520. doi: 10.1038/2151519a0. CrossRefPubMed

Myachykov, A., Ellis, R., Changelosi, A., Fischer, M. H.: (in press). Ocular drift along the mental number line. Psychol. Res.

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

Ranzini, M., Lisi, M., Zorzi, M.: (in press). Voluntary eye movements direct attention on the mental number space. Psychol. Res.

Restle, F. (1970). Speed of adding and comparing numbers. J. Exp. Psychol., 83(2p1), 274–278. doi: 10.1037/h0028573. CrossRef

Ristic, J., Wright, A., & Kingstone, A. (2006). The number line effect reflects top-down control. Psychon. Bull. Rev., 13(5), 862–868. doi: 10.3758/BF03194010. CrossRefPubMed

Schwarz, W., & Keus, I. M. (2004). Moving the eyes along the mental number line: comparing SNARC effects with saccadic and manual responses. Percept. Psychophys., 66(4), 651–664. doi: 10.3758/BF03194909. CrossRefPubMed

Shaki, S., & Fischer, M. H. (2008). Reading space into numbers—a cross-linguistic comparison of the SNARC effect. Cognition, 108(2), 590–599. doi: 10.1016/j.cognition.2008.04.001. CrossRefPubMed

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

Shaki, S., Sery, N., & Fischer, M. H. (2015). 1+ 2 is more than 2+ 1: violations of commutativity and identity axioms in mental arithmetic. J. Cognit. Psychol., 27(4), 471–477. doi: 10.1080/20445911.2014.973414. CrossRef

Wiemers, M., Bekkering, H., & Lindemann, O. (2014). Spatial interferences in mental arithmetic: evidence from the motion-arithmetic compatibility effect. Q. J. Exp. Psychol., 67(8), 1557–1570. doi: 10.1080/17470218.2014.889180. CrossRef

Wood, G., Willmes, K., Nuerk, H., & Fischer, M. H. (2008). On the cognitive link between space and number: a meta-analysis of the SNARC effect. Psychol. Sci. Q., 50(4), 489–525.

Woods, S. S., Resnick, L. B., & Groen, G. J. (1975). An experimental test of five process models for subtraction. J. Educ. Psychol, 67(1), 17–21. doi: 10.1037/h0078666. CrossRef

Yang, T., Chen, C., Zhou, X., Xu, J., Dong, Q., & Chen, C. (2014). Development of spatial representation of numbers: a study of the SNARC effect in Chinese children. J. Exp. Child Psychol., 117, 1–11. doi: 10.1016/j.jecp.2013.08.011. CrossRefPubMed

Zebian, S. (2005). Linkages between number concepts, spatial thinking, and directionality of writing: the SNARC effect and the reverse SNARC effect in English and Arabic monoliterates, biliterates, and illiterate Arabic speakers. J. Cognit. Cult., 5(1), 165–190. doi: 10.1163/1568537054068660. CrossRef

Zhou, X., Chen, C., Dong, Q., Zhang, H., Zhou, R., Zhao, H., & Guo, Y. (2006). Event-related potentials of single-digit addition, subtraction, and multiplication. Neuropsychologia, 44(12), 2500–2507. doi: 10.1016/j.neuropsychologia.2006.04.003. CrossRefPubMed

Zhou, X., Chen, C., Qiao, S., Chen, C., Chen, L., Lu, N., & Dong, Q. (2009). Event-related potentials for simple arithmetic in Arabic digits and Chinese number words: a study of the mental representation of arithmetic facts through notation and operation effects. Brain Res., 1302, 212–224. doi: 10.1016/j.brainres.2009.09.024. CrossRefPubMed

Zhou, X., Chen, C., Zang, Y., Dong, Q., Chen, C., Qiao, S., & Gong, Q. (2007). Dissociated brain organization for single-digit addition and multiplication. Neuroimage, 35(2), 871–880. doi: 10.1016/j.neuroimage.2006.12.017. CrossRefPubMed

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. Q. J. Exp. Psychol., 65(4), 661–674. doi: 10.1080/17470218.2011.616213. CrossRef

Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: neglect disrupts the mental number line. Nature, 417(6885), 138–139. doi: 10.1038/417138a. CrossRefPubMed

Titel: Dynamic mental number line in simple arithmetic
Auteurs: Xiaodan Yu
Jie Liu
Dawei Li
Hang Liu
Jiaxin Cui
Xinlin Zhou
Publicatiedatum: 08-12-2015
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/s00426-015-0730-5

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