Abstract
Previous studies have found decomposed processes, as well as holistic processes, in the representation of two-digit numbers. The present study investigated the influence of task instruction on such processes. Participants completed both magnitude and parity tasks in one of three instructional conditions, where they were asked to either consider two-digit numbers as a whole or to focus on one specific digit. In two experiments, we found that when participants were asked to consider the two digits as an integrated number, they always exhibited a unit–decade compatibility effect, indicating a failure of selective attention on the digit relevant to the given task. However, the mere presence of the neighboring digit is not a sufficient condition for the compatibility effect: when participants were explicitly asked to process a specific digit, their success/failure to selectively ignore the irrelevant digit depended on task requirements. Further, computer mouse tracking indicated that the locus of the compatibility effect was related to late response-related processing. The results signify the deep involvement of top-down processes in unit–decade binding for two-digit number representation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Castronovo, J., & Crollen, V. (2011). Numerical comparison of two-digit numbers: How differences at encoding can involve differences in processing. Journal of Cognitive Psychology, 23(1), 8–17. https://doi.org/10.1080/20445911.2011.445985.
Cohen-Kdoshay, O., & Meiran, N. (2007). The representation of instructions in working memory leads to autonomous response activation: Evidence from the first trials in the flanker paradigm. The Quarterly Journal of Experimental Psychology, 60(8), 1140–1154. https://doi.org/10.1080/1747021060089674.
De Jong, R., Liang, C.-C., & Lauber, E. (1994). Conditional and unconditional automaticity: A dual-process model of effects of spatial stimulus–response correspondence. Journal of Experimental Psychology: Human Perception and Performance, 20(4), 731–750. https://doi.org/10.1037/0096-1523.20.4.731.
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. https://doi.org/10.1037/0096-1523.16.3.626.
DeWolf, M., Grounds, M. A., Bassok, M., & Holyoak, K. J. (2014). Magnitude comparison with different types of rational numbers. Journal of Experimental Psychology: Human Perception and Performance, 40(1), 71–82. https://doi.org/10.1037/a0032916.
Dotan, D., & Dehaene, S. (2013). How do we convert a number into a finger trajectory? Cognition, 129(3), 512–529. https://doi.org/10.1016/j.cognition.2013.07.007.
Erb, C. D., Moher, J., Sobel, D. M., & Song, J.-H. (2016). Reach tracking reveals dissociable processes underlying cognitive control. Cognition, 152, 114–126. https://doi.org/10.1016/j.cognition.2016.03.015.
Faulkenberry, T. J. (2014). Hand movements reflect competitive processing in numerical cognition. Canadian Journal of Experimental Psychology, 68(3), 147–151. https://doi.org/10.1037/cep0000021.
Faulkenberry, T. J. (2016). Testing a direct mapping versus competition account of response dynamics in number comparison. Journal of Cognitive Psychology,. https://doi.org/10.1080/20445911.2016.1191504.
Faulkenberry, T. J., Cruise, A., & Shaki, S. (2017). Reversing the manual digit bias in two-digit number comparison. Experimental Psychology, 64(3), 191–204. https://doi.org/10.1027/1618-3169/a000365.
Faulkenberry, T. J., Cruise, A., Lavro, D., & Shaki, S. (2016). Response trajectories capture the continuous dynamics of the size congruity effect. Acta Psychologica, 163, 114–123. https://doi.org/10.1016/j.actpsy.2015.11.010.
Faulkenberry, T. J., Hartmann, M., & Witte, M. (2018). Tracking the continuous dynamics of numerical processing: A brief review and editorial. Journal of Numerical Cognition. https://doi.org/10.31234/osf.io/pruz7
Faulkenberry, T. J., Montgomery, S. A., & Tennes, S.-A. N. (2015). Response trajectories reveal the temporal dynamics of fraction representations. Acta Psychologica, 159, 100–107. https://doi.org/10.1016/j.actpsy.2015.05.013.
Fischer, M. H., & Hartmann, M. (2014). Pushing forward in embodied cognition: May we mouse the mathematical mind? Frontiers in Psychology, 5, 1315. https://doi.org/10.3389/fpsyg.2014.01315.
Freeman, J. B., & Ambady, N. (2009). Motions of the hand expose the partial and parallel activation of stereotypes. Psychological Science, 20(10), 1183–1188. https://doi.org/10.1111/j.1467-9280.2009.02422.x.
Freeman, J. B., & Ambady, N. (2010). MouseTracker: Software for studying real-time mental processing using a computer mouse-tracking method. Behavior Research Methods, 42(1), 226–241. https://doi.org/10.3758/BRM.42.1.226.
Freeman, J. B., Dale, R., & Farmer, T. A. (2011). Hand in motion reveals mind in motion. Frontiers in Psychology, 2, 59. https://doi.org/10.3389/fpsyg.2011.00059.
Ganor-Stern, D., Tzelgov, J., & Ellenbogen, R. (2007). Automaticity and two-digit numbers. Journal of Experimental Psychology: Human Perception and Performance, 33(2), 483–496. https://doi.org/10.1037/0096-1523.33.2.483.
Gevers, W., Verguts, T., Reynvoet, B., Caessens, B., & Fias, W. (2006). Numbers and space: A computational model of the SNARC effect. Journal of Experimental Psychology: Human Perception and Performance, 32(1), 32–44. https://doi.org/10.1037/0096-1523.32.1.32.
Herrera, A., Macizo, P., & Semenza, C. (2008). The role of working memory in the association between number magnitude and space. Acta Psychologica, 128(2), 225–237. https://doi.org/10.1016/j.actpsy.2008.01.002.
Hinrichs, J. V., Yurko, D. S., & Hu, J.-M. (1981). Two-digit number comparison: Use of place information. Journal of Experimental Psychology: Human Perception and Performance, 7(4), 890–901. https://doi.org/10.1037/0096-1523.7.4.890.
Kallai, A. Y., & Tzelgov, J. (2012). The place-value of a digit in multi-digit numbers is processed automatically. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38(5), 1221–1233. https://doi.org/10.1037/a0027635.
Kiesel, A., Steinhauser, M., Wendt, M., Falkenstein, M., Jost, K., Philipp, A. M., et al. (2010). Control and interference in task switching: A review. Psychological Bulletin, 136(5), 849.
Klein, E., Bahnmueller, J., Mann, A., Pixner, S., Kaufmann, L., Nuerk, H.-C., et al. (2013). Language influences on numerical development Inversion effects on multi-digit number processing. Frontiers in Psychology, 4, 480. https://doi.org/10.3389/fpsyg.2013.00480.
Kornblum, S., Hasbroucq, T., & Osman, A. (1990). Dimensional overlap: Cognitive basis for stimulus-response compatibility—a model and taxonomy. Psychological Review, 97(2), 253–270. https://doi.org/10.1037/0033-295x.97.2.253.
Liefooghe, B., De Houwer, J., & Wenke, D. (2013). Instruction-based response activation depends on task preparation. Psychonomic Bulletin and Review, 20(3), 481–487. https://doi.org/10.3758/s13423-013-0374-7.
Logan, G. D., Taylor, S. E., & Etherton, J. L. (1996). Attention in the acquisition and expression of automaticity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22(3), 620–638. https://doi.org/10.1037/0278-7393.22.3.620.
Macizo, P., & Herrera, A. (2011). Cognitive control in number processing: Evidence from the unit–decade compatibility effect. Acta Psychologica, 136(1), 112–118. https://doi.org/10.1016/j.actpsy.2010.008.
Macizo, P., Herrera, A., Paolieri, D., & Román, P. (2010). Is there cross-language modulation when bilinguals process number words? Applied Psycholinguistics, 31(04), 651–669. https://doi.org/10.1017/s0142716410000184.
Moeller, K., Klein, E., Nuerk, H.-C., & Willmes, K. (2013). Magnitude representation in sequential comparison of two-digit numbers is not holistic either. Cognitive Processing, 14(1), 51–62. https://doi.org/10.1007/s10339-012-0535-z.
Moeller, K., Nuerk, H.-C., & Willmes, K. (2009). Internal number magnitude representation is not holistic, either. European Journal of Cognitive Psychology, 21(5), 672–685. https://doi.org/10.1080/09541440802311899.
Morey, R. D. (2008). Confidence intervals from normalized data: A correction to cousineau (2005). Tutorial in Quantitative Methods for Psychology, 4(2), 61–64.
Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. Nature, 215(5109), 1519–1520. https://doi.org/10.1038/2151519a0.
Mussolin, C., & Noël, M.-P. (2008). Automaticity for numerical magnitude of two-digit arabic numbers in children. Acta Psychologica, 129(2), 264–272. https://doi.org/10.1016/j.actpsy.2008.08.001.
Nuerk, H.-C., & Willmes, K. (2005). On the magnitude representations of two-digit numbers. Psychology Science, 47(1), 52–72.
Nuerk, H.-C., Bauer, F., Krummenacher, J., Heller, D., & Willmes, K. (2005). The power of the mental number line: How the magnitude of unattended numbers affects performance in an eriksen task. Psychology Science, 47(1), 34–50.
Nuerk, H.-C., Moeller, K., & Willmes, K. (2014). Multi-digit number processing. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford handbook of numerical cognition (pp. 106–139). Oxford, UK: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.021
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. https://doi.org/10.1027/2151-2604/a000041.
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. https://doi.org/10.1016/s0010-0277(01)00142-1.
Nuerk, H.-C., Weger, U., & Willmes, K. (2005). Language effects in magnitude comparison: Small, but not irrelevant. Brain and Language, 92(3), 262–277. https://doi.org/10.1016/j.bandl.2004.06.107.
Ratinckx, E., Brysbaert, M., & Fias, W. (2005). Naming two-digit arabic numerals: Evidence from masked priming studies. Journal of Experimental Psychology: Human Perception and Performance, 31(5), 1150–1163. https://doi.org/10.1037/0096-1523.31.5.1150.
Reynvoet, B., Notebaert, K., & Van den Bussche, E. (2011). The processing of two-digit numbers depends on task instructions. Zeitschrift Für Psychologie, 219(1), 37–41. https://doi.org/10.1027/2151-2604/a000044.
Ruitenberg, M. F. L., Duthoo, W., Santens, P., Seidler, R. D., Notebaert, W., & Abrahamse, E. L. (2016). Sequence learning in parkinson’s disease: Focusing on action dynamics and the role of dopaminergic medication. Neuropsychologia, 93, 30–39. https://doi.org/10.1016/j.neuropsychologia.2016.09.027.
Santens, S., Goossens, S., & Verguts, T. (2011). Distance in motion: Response trajectories reveal the dynamics of number comparison. PloS One, 6(9), e25429. https://doi.org/10.1371/journal.pone.0025429.
Sobel, K. V., Puri, A. M., & Faulkenberry, T. J. (2016). Bottom-up and top-down attentional contributions to the size congruity effect. Attention, Perception, and Psychophysics, 78(5), 1324–1336. https://doi.org/10.3758/s13414-016-1098-3.
Sobel, K. V., Puri, A. M., Faulkenberry, T. J., & Dague, T. D. (2017). Visual search for conjunctions of physical and numerical size shows that they are processed independently. Journal of Experimental Psychology: Human Perception and Performance, 43(3), 444–453. https://doi.org/10.1037/xhp0000323.
Song, J.-H., & Nakayama, K. (2008). Numeric comparison in a visually-guided manual reaching task. Cognition, 106(2), 994–1003. https://doi.org/10.1016/j.cognition.2007.03.014.
Spivey, M. J., Grosjean, M., & Knoblich, G. (2005). Continuous attraction toward phonological competitors. Proceedings of the National Academy of Sciences, 102(29), 10393–10398. https://doi.org/10.1073/pnas.0503903102.
Steinborn, M. B., Langner, R., & Huestegge, L. (2017). Mobilizing cognition for speeded action: Try-harder instructions promote motivated readiness in the constant-foreperiod paradigm. Psychological Research, 81(6), 1135–1151. https://doi.org/10.1007/s00426-016-0810-1.
Strauss, S., Woodgate, P. J., Sami, S. A., & Heinke, D. (2015). Choice reaching with a LEGO arm robot (CoRLEGO): The motor system guides visual attention to movement-relevant information. Neural Networks, 72, 3–12. https://doi.org/10.1016/j.neunet.2015.10.005.
van Dijck, J.-P., Gevers, W., & Fias, W. (2009). Numbers are associated with different types of spatial information depending on the task. Cognition, 113(2), 248–253. https://doi.org/10.1016/j.cognition.2009.08.005.
Vandierendonck, A., Liefooghe, B., & Verbruggen, F. (2010). Task switching: Interplay of reconfiguration and interference control. Psychological Bulletin, 136(4), 601–626. https://doi.org/10.1037/a0019791.
Verguts, T., & De Moor, W. (2005). Two-digit comparison: Decomposed, holistic, or hybrid? Experimental Psychology, 52(3), 195–200. https://doi.org/10.1027/1618-3169.52.3.195.
Wenke, D., & Frensch, P. A. (2005). The influence of task instruction on action coding: Constraint setting or direct coding? Journal of Experimental Psychology: Human Perception and Performance, 31(4), 803–819. https://doi.org/10.1037/0096-1523.31.4.803.
Wenke, D., Gaschler, R., & Nattkemper, D. (2005). Instruction-induced feature binding. Psychological Research, 71(1), 92–106. https://doi.org/10.1007/s00426-005-0038-y.
Zorzi, M., & Umiltà, C. (1995). A computational model of the Simon effect. Psychological Research, 58(3), 193–205. https://doi.org/10.1007/bf00419634.
Acknowledgements
The authors would like to thank Brie Heidingsfelder, Jonathan Herring, Heather Hill, and Kate Shaw for their assistance with data collection. We would also like to thank Michael Steinborn and an anonymous reviewer for their helpful comments on an earlier version of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committees and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.
Informed consent
Informed consent was obtained from all individual participants included in the study.
Additional information
This paper was written in RMarkdown, with code for data analysis integrated into the manuscript text. The RMarkdown script and data are open and freely available at https://git.io/vhU7z.
Rights and permissions
About this article
Cite this article
Faulkenberry, T.J., Cruise, A. & Shaki, S. Task instructions modulate unit–decade binding in two-digit number representation. Psychological Research 84, 424–439 (2020). https://doi.org/10.1007/s00426-018-1057-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00426-018-1057-9