Number comparison and number ordering as predictors of arithmetic performance in adults: Exploring the link between the two skills, and investigating the question of domain-specificity

References

• Arthur, W. Jr., & Day, D. V. (1994). Development of a short form for the Raven advanced progressive matrices test. Educational and Psychological Measurement, 54, 394–403. doi: 10.1177/0013164494054002013
   Google Scholar
• Attout, L., Fias, W., Salmon, E., & Majerus, S. (2014). Common neural substrates for ordinal representation in short-term memory, numerical and alphabetical cognition. PLoS One 9, e92049. doi: 10.1371/journal.pone.0092049
   Google Scholar
• Attout, L., & Majerus, S. (2015). Working memory deficits in developmental dyscalculia: The importance of serial order. Child Neuropsychology, 21, 432–450. doi: 10.1080/09297049.2014.922170
   Google Scholar
• Attout, L., Noël, M.-P., & Majerus, S. (2014). The relationship between working memory for serial order and numerical development: A longitudinal study. Developmental Psychology, 50, 1667–1679. doi: 10.1037/a0036496
   Google Scholar
• Berteletti, I., Lucangeli, D., & Zorzi, M. (2012). Representation of numerical and non-numerical order in children. Cognition, 124, 304–313. doi: 10.1016/j.cognition.2012.05.015
   Google Scholar
• Blair, C., & Razza, R. P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78, 647–663. doi: 10.1111/j.1467-8624.2007.01019.x
   Google Scholar
• Blazhenkova, O., & Kozhevnikov, M. (2009). The new object-spatial-verbal cognitive style model: Theory and measurement. Applied Cognitive Psychology, 23, 638–663. doi: 10.1002/acp.1473
   Google Scholar
• Bonato, M., Zorzi, M., & Umiltà, C. (2012). When time is space: Evidence for a mental time line. Neuroscience and Biobehavioral Reviews, 36, 2257–2273. doi: 10.1016/j.neubiorev.2012.08.007
   Google Scholar
• Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42, 189–201. doi: 10.1037/0012-1649.41.6.189
   Google Scholar
• Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19, 273–293. doi: 10.1207/S15326942DN1903_3
   Google Scholar
• Caplan, J. B. (2015). Order-memory and association-memory. Canadian Journal of Experimental Psychology, 69, 221–232. doi: 10.1037/cep0000052
   Google Scholar
• Casarotti, M., Michielin, M., Zorzi, M., & Umiltà, C. (2007). Temporal order judgment reveals how number magnitude affects visuospatial attention. Cognition, 102, 101–117. doi: 10.1016/j.cognition.2006.09.001
   Google Scholar
• Chiesi, F., Ciancaleoni, M., Galli, S., Morsanyi, K., & Primi, C. (2012). Item response theory analysis and differential item functioning across age, gender and country of a short form of the advanced progressive matrices. Learning and Individual Differences, 22, 390–396. doi: 10.1016/j.lindif.2011.12.007
   Google Scholar
• Colomé, À., & Noël, M. P. (2012). One first? Acquisition of the cardinal and ordinal uses of numbers in preschoolers. Journal of Experimental Child Psychology, 113, 233–247. doi: 10.1016/j.jecp.2012.03.005
   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. doi: 10.1037/0096-3445.122.3.371
   Google Scholar
• 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, 626–641.
   Google Scholar
• De Hevia, M. D., Vallar, G., & Girelli, L. (2008). Visualizing numbers in the mind's eye: The role of visuo-spatial processes in numerical abilities. Neuroscience & Biobehavioral Reviews, 32, 1361–1372. doi: 10.1016/j.neubiorev.2008.05.015
   Google Scholar
• De Smedt, B., Noël, M.P., Gilmore, C., & Ansari, D. (2013). The relationship between symbolic and non-symbolic numerical magnitude processing and the typical and atypical development of mathematics: A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2, 48–55. doi: 10.1016/j.tine.2013.06.001
   Google Scholar
• Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology, 82, 64–81. doi: 10.1348/2044-8279.002002
   Google Scholar
• Di Bono, M. G., & Zorzi, M. (2013). The spatial representation of numerical and non-numerical ordered sequences: Insights from a random generation task. Quarterly Journal of Experimental Psychology, 66, 2348–2362. doi: 10.1080/17470218.2013.779730
   Google Scholar
• 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, 1854–1859. doi: 10.1177/0956797613479610
   Google Scholar
• van Dijck, J. P., & Fias, W. (2011). A working memory account for spatial-numerical associations. Cognition, 119, 114–119. doi: 10.1016/j.cognition.2010.12.013
   Google Scholar
• van Dijck, J. P., Gevers, W., & Fias, W. (2009). Numbers are associated with different types of spatial information depending on the task. Cognition, 113, 248–253. doi: 10.1016/j.cognition.2009.08.005
   Google Scholar
• Fairbanks, B. A. Jr. (1969). Experiments on the temporal aspects of number perception. Dissertation Abstracts International, 30, 403.
   Google Scholar
• Fias, W., Lammertyn, J., Caessens, B., & Orban, G. A. (2007). Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. Journal of Neuroscience, 27, 8952–8956. doi: 10.1523/JNEUROSCI.2076-07.2007
   Google Scholar
• Franklin, M. S., Jonides, J., & Smith, E. E. (2009). Processing of order information for numbers and months. Memory & Cognition, 37, 644–654. doi: 10.3758/MC.37.5.644
   Google Scholar
• Friedman, W. J. (1983). Image and verbal processes in reasoning about the months of the year. Journal of Experimental Psychology: Learning, Memory, and Cognition, 9, 650–666.
   Google Scholar
• Friedman, W. J. (1984). Analog and semantic models of judgments about the months of the year. Memory and Cognition, 12, 306–313. doi: 10.3758/BF03197680
   Google Scholar
• Friedman, W. J. (1986). The development of children’s knowledge of temporal structure. Child Development, 57, 1386–1400. doi: 10.2307/1130418
   Google Scholar
• Friedman, W. J. (1989). The representation of temporal structure in children, adolescents and adults. In I. Levin & D. Zakay (Eds.), Time and human cognition: A life-span perspective (pp. 259–304). Amsterdam: North-Holland.
   Google Scholar
• Friedman, W. J. (1992). The development of children’s representations of temporal structure. In F. Macar, V. Pouthas, & W. J. Friedman (Eds.), Time, actions and cognition: Towards bridging the gap (pp. 67–75). Dordrecht, The Netherlands: Kluwer.
   Google Scholar
• Fuhs, M. W., & McNeil, N. M. (2013). ANS acuity and mathematics ability in preschoolers from low-income homes: Contributions of inhibitory control. Developmental Science, 16, 136–148. doi: 10.1111/desc.12013
   Google Scholar
• Gevers, W., Reynvoet, B., & Fias, W. (2003). The mental representation of ordinal sequences is spatially organized. Cognition, 87, B87–B95. doi: 10.1016/S0010-0277(02)00234-2
   Google Scholar
• Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N. … Inglis, M. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLOS ONE, 8(6), e67374. doi: 10.1371/journal.pone.0067374
   Google Scholar
• Goffin, C., & Ansari, D. (2016). Beyond magnitude: Judging ordinality of symbolic number is unrelated to magnitude comparison and independently relates to individual differences in arithmetic. Cognition, 150, 68–76. doi: 10.1016/j.cognition.2016.01.018
   Google Scholar
• Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668. doi: 10.1038/nature07246
   Google Scholar
• Hurst, M., Monahan, K. L., Heller, E., & Cordes, S. (2014). 123s and ABCs: Developmental shifts in logarithmic-to-linear responding reflect fluency with sequence values. Developmental Science, 17, 892–904. doi: 10.1111/desc.12165
   Google Scholar
• Jou, J. (2003). Multiple number and letter comparison: Directionality and accessibility in numeric and alphabetic memories. The American Journal of Psychology, 116, 543–579. doi: 10.2307/1423660
   Google Scholar
• Jou, J., & Aldridge, J. W. (1999). Memory representation of alphabetic position and interval information. Journal of Experimental psychology: Learning, Memory, and Cognition, 25, 680–701.
   Google Scholar
• Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schonmann, C., Plangger, F., … . von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57, 782–795. doi: 10.1016/j.neuroimage.2011.01.070
   Google Scholar
• Laski, E. V., & Siegler, R. S. (2007). Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 78, 1723–1743. doi: 10.1111/j.1467-8624.2007.01087.x
   Google Scholar
• Lewandowsky, S., & Murdock Jr, B. B. (1989). Memory for serial order. Psychological Review, 96, 25–57. doi: 10.1037/0033-295X.96.1.25
   Google Scholar
• Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121, 256–261. doi: 10.1016/j.cognition.2011.07.009
   Google Scholar
• Lyons, I. M., & Beilock, S. L. (2013). Ordinality and the nature of symbolic numbers. Journal of Neuroscience, 33, 17052–61. doi: 10.1523/JNEUROSCI.1775-13.2013
   Google Scholar
• Lyons, I. M., Nuerk, H. C., & Ansari, D. (2015). Rethinking the implications of numerical ratio effects for understanding the development of representational precision and numerical processing across formats. Journal of Experimental Psychology: General, 144, 1021–1035. doi: 10.1037/xge0000094
   Google Scholar
• Lyons, I. M., Price, G. R., Vaessen, A., Blomert, L., & Ansari, D. (2014). Numerical predictors of arithmetic success in Grades 1–6. Developmental Science, 17, 714–726. doi: 10.1111/desc.12152
   Google Scholar
• Maloney, E. A., Risko, E. F., Preston, F., Ansari, D., & Fugelsang, J. (2010). Challenging the reliability and validity of cognitive measures: The case of the numerical distance effect. Acta Psychologica, 134, 154–161. doi: 10.1016/j.actpsy.2010.01.006
   Google Scholar
• Morsanyi, K., Devine, A., Nobes, A., & Szucs, D. (2013). The link between logic, mathematics and imagination. Evidence from children with developmental dyscalculia and mathematically gifted children. Developmental Science, 16, 542–553. doi: 10.1111/desc.12048
   Google Scholar
• Morsanyi, K., Primi, C., Handley, S.J., Chiesi, F., & Galli, S. (2012). Are systemizing and autistic traits related to talent and interest in mathematics and engineering? Testing some of the central claims of the empathizing-systemizing theory. British Journal of Psychology, 103, 472–496. doi: 10.1111/j.2044-8295.2011.02089.x
   Google Scholar
• Moyer, R. S., & Landauer, T. K. (1967). Time required for judgments of numerical inequality. Nature, 215, 1519–1520. doi: 10.1038/2151519a0
   Google Scholar
• Myers, R. (1990). Classical and modern regression with applications (2nd ed.). Boston, MA: Duxbury.
   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, 33–41. doi: 10.1016/j.cognition.2010.03.012
   Google Scholar
• Preacher, K. J., & Hayes, A. F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavioral Research Methods, 40, 879–891. doi: 10.3758/BRM.40.3.879
   Google Scholar
• Preacher, K. J., & Kelley, K. (2011). Effect size measures for mediation models: Quantitative strategies for communicating indirect effects. Psychological Methods, 16, 93–115. doi: 10.1037/a0022658
   Google Scholar
• Raven, J. C. (1938). Progressive matrices: A perceptual test of intelligence. London: H. K. Lewis.
   Google Scholar
• Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 274–278. doi: 10.1037/h0028573
   Google Scholar
• Rubinsten, O., & Sury, D. (2011). Processing ordinality and quantity: The case of developmental dyscalculia. PLoS ONE, 6, e24079. doi: 10.1371/journal.pone.0024079
   Google Scholar
• Sasanguie, D., Defever, E., Van den Bussche, E., & Reynvoet, B. (2011). The reliability of and the relation between non-symbolic numerical distance effects. Acta Psychologica, 136, 73–80. doi: 10.1016/j.actpsy.2010.10.004
   Google Scholar
• Seymour, P. H. K. (1980). Internal representations of months: An experimental analysis of spatial forms. Psychological Research, 42, 255–273. doi: 10.1007/BF00308532
   Google Scholar
• Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–250. doi: 10.1111/1467-9280.02438
   Google Scholar
• Swanson, H. L. (2011). Working memory, attention, and mathematical problem solving: A longitudinal study of elementary school children. Journal of Educational Psychology, 103, 821–837. doi: 10.1037/a0025114
   Google Scholar
• Szűcs, D., Nobes, A., Devine, A., Gabriel, F., & Gebuis, T. (2013). Visual stimulus parameters seriously compromise the measurement of approximate number system acuity and comparative effects between adults and children. Frontiers in Psychology, 4, 444.
   Google Scholar
• Turconi, E., Campbell, J. I. D., & Seron, X. (2006). Numerical order and quantity processing in number comparison. Cognition, 98, 273–285. doi: 10.1016/j.cognition.2004.12.002
   Google Scholar
• Van Opstal, F., Gevers, W., De Moor, W., & Verguts, T. (2008). Dissecting the symbolic distance effect: Comparison and priming effects in numerical and nonnumerical orders. Psychonomic Bulletin & Review, 15, 419–425. doi: 10.3758/PBR.15.2.419
   Google Scholar
• Van Opstal, F., & Verguts, T. (2011). The origins of the numerical distance effect: The same–different task. Journal of Cognitive Psychology, 23, 112–20. doi: 10.1080/20445911.2011.466796
   Google Scholar
• Verguts, T., & Van Opstal, F. (2005). Dissociation of the distance effect and size effect in one-digit numbers. Psychonomic Bulletin & Review, 12, 925–930. doi: 10.3758/BF03196787
   Google Scholar
• Vogel, S. E., Remark, A., & Ansari, D. (2015). Differential processing of symbolic numerical magnitude and order in first-grade children. Journal of Experimental Child Psychology, 129, 26–39. doi: 10.1016/j.jecp.2014.07.010
   Google Scholar
• Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson tests of achievement. Itasca, IL: Riverside Publishing.
   Google Scholar
• Zorzi, M., Di Bono, M. G., & Fias, W. (2011). Distinct representations of numerical and nonnumerical order in the human intraparietal sulcus revealed by multivariate pattern recognition. NeuroImage, 56, 674–680. doi: 10.1016/j.neuroimage.2010.06.035
   Google Scholar