Can approximate mental calculation account for operational momentum in addition and subtraction?

REFERENCES

• Agrillo, C., Dadda, M., & Bisazza, A. (2007). Quantity discrimination in female mosquitofish. Animal Cognition, 10(1), 63–70. doi:10.1007/s10071-006-0036-5
   PubMed Web of Science ®Google Scholar
• Agrillo, C., Piffer, L., & Adriano, A. (2013). Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM. Behavioral and Brain Functions, 9(1), 26. doi:10.1186/1744-9081-9-26
   PubMed Web of Science ®Google Scholar
• Agrillo, C., Piffer, L., & Bisazza, A. (2010). Large number discrimination by mosquitofish. PLoS One, 5(12), e15232. doi:10.1371/journal.pone.0015232
   PubMed Web of Science ®Google Scholar
• Casarotti, M., Michielin, M., Zorzi, M., & Umiltà, C. (2007). Temporal order judgment reveals how number magnitude affects visuospatial attention. Cognition, 102(1), 101–117. doi:10.1016/j.cognition.2006.09.001
   PubMed Web of Science ®Google Scholar
• Chen, Q., & Verguts, T. (2012). Spatial intuition in elementary arithmetic: A neurocomputational account. PLoS One, 7(2), e31180. doi:10.1371/journal.pone.0031180
   PubMed Web of Science ®Google Scholar
• Dadda, M., Piffer, L., Agrillo, C., & Bisazza, A. (2009). Spontaneous number representation in mosquitofish. Cognition, 112(2), 343–348. doi:10.1016/j.cognition.2009.05.009
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7(4), 145–147.
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (2011). The number sense: How the mind creates mathematics (2nd ed.). New York: Oxford University Press.
   Google Scholar
• Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of.Experimental Psychology: General, 122, 371–396.
   Web of Science ®Google Scholar
• Dehaene, S., Izard, V., & Piazza, M. (2005). Control over non-numerical parameters in numerosity experiments. Retrieved from http://www.unicog.org/pm/pmwiki.php/Main/Arithmetics
   Google Scholar
• Dehaene, S., Spelke, E. S., Pinel, P., Stanescu, R., & Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284(5416), 970–974.
   PubMed Web of Science ®Google Scholar
• Emmerton, J., & Renner, J. C. (2006). Scalar effects in the visual discrimination of numerosity by pigeons. Learning & Behavior, 34(2), 176–192.
   PubMed Web of Science ®Google Scholar
• Fias, W., & Verguts, T. (2004). The mental number line: Exact and approximate. Trends in Cognitive Sciences, 8(10), 447–448.
   PubMed Web of Science ®Google Scholar
• Fischer, M. H., Castel, A. D., Dodd, M. D., & Pratt, J. (2003). Perceiving numbers causes spatial shifts of attention. Nature Neuroscience, 6(6), 555–556.
   PubMed Web of Science ®Google Scholar
• Galfano, G., Rusconi, E., & Umiltà, C. (2006). Number magnitude orients attention, but not against one's will. Psychonomic Bulletin & Review, 13(5), 869–874.
   PubMed Web of Science ®Google Scholar
• Gebuis, T. & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43(4), 981–986.
   PubMed Web of Science ®Google Scholar
• Gilmore, C. K., McCarthy, S. E., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and mathematics achievement in the first year of formal schooling. Cognition, 115(3), 394–406.
   PubMed Web of Science ®Google Scholar
• Halberda, J., Ly, R., Wilmer, J. B., Naiman, D. Q., & Germine, L. (2012). Number sense across the lifespan as revealed by a massive Internet-based sample. Proceedings of the National Academy of Sciences of the USA, 109(28), 11116–11120.doi:10.1073/pnas.1200196109
   PubMed Web of Science ®Google Scholar
• Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668.
   PubMed Web of Science ®Google Scholar
• Izard, V., & Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221–1247.
   PubMed Web of Science ®Google Scholar
• Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences of the USA, 106(25), 10382–10385.
   PubMed Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• Knops, A., Viarouge, A., & Dehaene, S. (2009). Dynamic representations underlying symbolic and nonsymbolic calculation: Evidence from the operational momentum effect. Attention, Perception & Psychophysics, 71(4), 803–821.
   PubMed Web of Science ®Google Scholar
• Knops, A., Zitzmann, S., & McCrink, K. (2013). Examining the presence and determinants of operational momentum in childhood. Frontiers in Psychology, 4(325). doi:10.3389/fpsyg.2013.00325
   PubMed Web of Science ®Google Scholar
• McCrink, K., Dehaene, S., & Dehaene-Lambertz, G. (2007). Moving along the number line: Operational momentum in nonsymbolic arithmetic. Perception & Psychophysics, 69(8), 1324–1333.
   PubMed Web of Science ®Google Scholar
• Meck, W. H., & Church, R. M. (1983). A mode control model of counting and timing processes. Journal of Experimental Psychology: Animal Behavior Processes, 9(3), 320–334.
   PubMed Web of Science ®Google Scholar
• Merten, K., & Nieder, A. (2009). Compressed scaling of abstract numerosity representations in adult humans and monkeys. Journal of Cognitive Neuroscience, 21(2), 333–346.
   PubMed Web of Science ®Google Scholar
• Nicholls, M. E. R., Loftus, A. M., & Gevers, W. (2008). Look, no hands: A perceptual task shows that number magnitude induces shifts of attention. Psychonomic Bulletin & Review, 15(2), 413–418. doi:10.3758/pbr.15.2.413
   PubMed Web of Science ®Google Scholar
• Nieder, A. (2012). Supramodal numerosity selectivity of neurons in primate prefrontal and posterior parietal cortices. Proceedings of the Natonal Academy of Sciences of the USA, 109(29), 11860–11865. doi:10.1073/pnas.1204580109
   PubMed Web of Science ®Google Scholar
• Nieder, A., & Miller, E. K. (2003). Coding of cognitive magnitude: Compressed scaling of numerical information in the primate prefrontal cortex. Neuron, 37(1), 149–157.
   PubMed Web of Science ®Google Scholar
• van Oeffelen, M. P., & Vos, P. G. (1982). A probabilistic model for the discrimination of visual number. Perception & Psychophysics, 32(2), 163–170.
   PubMedGoogle Scholar
• Park, J., & Brannon, E. M. (2013). Training the approximate number system improves math proficiency. Psychological Science, 24(10), 2013–2019. doi:10.1177/0956797613482944
   PubMed Web of Science ®Google Scholar
• Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542–551.
   PubMed Web of Science ®Google Scholar
• Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., … Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.
   PubMed Web of Science ®Google Scholar
• Piazza, M., Izard, V., Pinel, P., Le Bihan, D., & Dehaene, S. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555. doi:10.1016/j.neuron.2004.10.014
   PubMed Web of Science ®Google Scholar
• Pinhas, M., & Fischer, M. H. (2008). Mental movements without magnitude? A study of spatial biases in symbolic arithmetic. Cognition, 109(3), 408–415.
   PubMed Web of Science ®Google Scholar
• 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
   PubMed Web of Science ®Google Scholar
• Shaki, S., Fischer, M. H., & Petrusic, W. M. (2009). Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review, 16(2), 328–331. doi:10.3758/PBR.16.2.328
   PubMed Web of Science ®Google Scholar
• Stoianov, I., & Zorzi, M. (2012). Emergence of a 'visual number sense' in hierarchical generative models. Nature Neuroscience, 15(2), 194–196. doi:10.1038/nn.2996
   PubMed Web of Science ®Google Scholar
• Xu, F., & Spelke, E. S. (2000). Large number discrimination in 6-month-old infants. Cognition, 74(1), B1–B11.
   PubMed Web of Science ®Google Scholar
• Xu, F., Spelke, E. S., & Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88–101.
   PubMed Web of Science ®Google Scholar
• Zorzi, M., Bonato, M., Treccani, B., Scalambrin, G., Marenzi, R., & Priftis, K. (2012). Neglect impairs explicit processing of the mental number line. Frontiers in Human Neuroscience, 6, 125. doi:10.3389/fnhum.2012.00125
   PubMed Web of Science ®Google Scholar
• Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417(6885), 138–139.
   PubMed Web of Science ®Google Scholar