Humans possess a numerical intuition that allows them to manipulate large non-symbolic quantities. This ability has been broadly assessed with the help of number comparison tasks involving simultaneously displayed arrays. Many authors pointed out that the manipulation (or the lack thereof) of non-numerical features deeply impacts performance in these tasks, but the specific nature of this influence is not clear. This study investigates the interaction between numerical and non-numerical quantity judgement tasks. Adult participants performed five distinct comparison tasks, each based on a target dimension: numerosity, total area, dot size, convex hull, and mean occupancy. We manipulated the relation between the target and the other dimensions to measure their respective influence on task performance. Results showed that total area and convex hull substantially affected numerosity comparisons. The number of dots conversely acted as an informative dimension when participants had to make a decision based on the total area or the convex hull. Our results illustrate that adults flexibly use non-target dimensions as visual cues to perform comparison judgements. Overall, this suggests that the influence found in numerical comparison tasks is explicit and deliberate rather than due to implicit visual integration processes.
Abreu-MendozaR. A.Soto-AlbaE. E.Arias-TrejoN. (2013). Area vs. density: Influence of visual variables and cardinality knowledge in early number comparison. Frontiers in Psychology, 4, e805. https://doi.org/10.3389/fpsyg.2013.00805
2.
AllïkJ.TuulmetsT. (1991). Occupancy model of perceived numerosity. Perception & Psychophysics, 49(4), 303–314.
3.
AnobileG.CicchiniG. M.BurrD. C. (2014). Separate mechanisms for perception of numerosity and density. Psychological Science, 25(1), 265–270. https://doi.org/10.1177/0956797613501520
4.
AnobileG.GuerriniG.BurrD. C.MontiM.Del LuccheseB.CicchiniG. M. (2019). Spontaneous perception of numerosity in pre-school children. Proceedings of the Royal Society B: Biological Sciences, 286(1906), e20191245. https://doi.org/10.1098/rspb.2019.1245
5.
AnobileG.TuriM.CicchiniG. M.BurrD. C. (2015). Mechanisms for perception of numerosity or texture-density are governed by crowding-like effects. Journal of Vision, 15(5), e4. https://doi.org/10.1167/15.5.4
CavdarogluS.KnopsA. (2019). Evidence for a posterior parietal cortex contribution to spatial but not temporal numerosity perception. Cerebral Cortex, 29(7), 2965–2977. https://doi.org/10.1093/cercor/bhy163
8.
CicchiniG. M.AnobileG.BurrD. C. (2016). Spontaneous perception of numerosity in humans. Nature Communications, 7, e12536. https://doi.org/10.1038/ncomms12536
DehaeneS. (2003). The neural basis of the Weber-Fechner law: A logarithmic mental number line. Trends in Cognitive Sciences, 7(4), 145–147. https://doi.org/10.1016/S1364-6613(03)00055-X
12.
DehaeneS.ChangeuxJ. P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5(4), 390–407. https://doi.org/10.1162/jocn.1993.5.4.390
13.
DehaeneS.IzardV.PiazzaM. (2005). Control over non-numerical parameters in numerosity experiments [Unpublished manuscript]. http://www.unicog.org
14.
De VosT. (1992). Test voor het vaststellen van het rekenvaardigheidsniveau der elementaire bewerkingen (automatisering) voor het basis en voortgezet onderwijs: Handleiding [Test to determine the mathematics ability level for elementary operations (automatization) in primary and secondary education: Manual]. Berkhout.
15.
DeWindN. K.AdamsG. K.PlattM. L.BrannonE. M. (2015). Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition, 142, 247–265. https://doi.org/10.1016/j.cognition.2015.05.016
16.
DietrichJ. F.HuberS.KleinE.WillmesK.PixnerS.MoellerK. (2016). A systematic investigation of accuracy and response time based measures used to index ANS acuity. PLOS ONE, 11(9), e0163076. https://doi.org/10.1371/journal.pone.0163076
17.
FaulF.ErdfelderE.LangA.-G.BuchnerA. (2007). G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences. Behavior Research Methods, 39(2), 175–191.
18.
FeigensonL. (2011). Predicting sights from sounds: 6-month-olds’ intermodal numerical abilities. Journal of Experimental Child Psychology, 110(3), 347–361. https://doi.org/10.1016/j.jecp.2011.04.004
FerrignoS.Jara-EttingerJ.PiantadosiS. T.CantlonJ. F. (2017). Universal and uniquely human factors in spontaneous number perception. Nature Communications, 8, e13968. https://doi.org/10.1038/ncomms13968
21.
FoltzG. S.PoltrockS. E.PottsG. R. (1984). Mental comparison of size and magnitude: Size congruity effects. Journal of Experimental Psychology: Learning, Memory and Cognition, 10(3), 442–453.
22.
GebuisT.Cohen KadoshR.GeversW. (2016). Sensory-integration system rather than approximate number system underlies numerosity processing: A critical review. Acta Psychologica, 171, 17–35. https://doi.org/10.1016/j.actpsy.2016.09.003
GebuisT.ReynvoetB. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648. https://doi.org/10.1037/a0026218
25.
GilmoreC.AttridgeN.ClaytonS.CraggL.JohnsonS.MarlowN.. . .InglisM. (2013). Individual differences in inhibitory control, not non-verbal number acuity, correlate with mathematics achievement. PLOS ONE, 8(6), e67374. https://doi.org/10.1371/journal.pone.0067374
26.
GilmoreC.AttridgeN.InglisM. (2011). Measuring the approximate number system. Quarterly Journal of Experimental Psychology, 64(11), 2099–2109. https://doi.org/10.1080/17470218.2011.574710
27.
GilmoreC.CraggL.HoganG.InglisM. (2016). Congruency effects in dot comparison tasks: Convex hull is more important than dot area. Journal of Cognitive Psychology, 28(8), 923–931. https://doi.org/10.1080/20445911.2016.1221828
28.
GimbertF.GentazE.CamosV.MazensK. (2016). Children’s approximate number system in haptic modality. Perception, 45(1–2), 44–55. https://doi.org/10.1177/0301006615614448
29.
GuillaumeM.NysJ.MussolinC.ContentA. (2013). Differences in the acuity of the Approximate Number System in adults: The effect of mathematical ability. Acta Psychologica, 144(3), 506–512. https://doi.org/10.1016/j.actpsy.2013.09.001
30.
GuillaumeM.SchiltzC.Van RinsveldA. (2020). NASCO: A new method and program to generate dot arrays for non-symbolic number comparison tasks. Journal of Numerical Cognition, 6(1), 129–147. https://doi.org/10.5964/jnc.v6i1.231
31.
GuillaumeM.Van RinsveldA. (2018). Comparing numerical comparison tasks: A meta-analysis of the variability of the Weber fraction relative to the generation algorithm. Frontiers in Psychology, 9, e1694. https://doi.org/10.3389/fpsyg.2018.01694
32.
HalberdaJ.MazzoccoM. M.FeigensonL. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668. https://doi.org/10.1038/nature07246
33.
HurewitzF.GelmanR.SchnitzerB. (2006). Sometimes area counts more than number. Proceedings of the National Academy of Sciences, 103(51), 19599–19604. https://doi.org/10.1073/pnas.0609485103
KobayashiT.HirakiK.HasegawaT. (2005). Auditory–visual intermodal matching of small numerosities in 6-month-old infants. Developmental Science, 8(5), 409–419.
LeibovichT.KatzinN.HarelM.HenikA. (2017). From “sense of number” to “sense of magnitude”: The role of continuous magnitudes in numerical cognition. Behavioral and Brain Sciences, 40, e164. https://doi.org/10.1017/S0140525X16000960
38.
LiptonJ. S.SpelkeE. S. (2003). Origins of number sense: Large-number discrimination in human infants. Psychological Science, 14(5), 396–401.
39.
LourencoS. F.BonnyJ. W. (2017). Representations of numerical and non-numerical magnitude both contribute to mathematical competence in children. Developmental Science, 20(4), e12418. https://doi.org/10.1111/desc.12418
40.
LourencoS. F.BonnyJ. W.FernandezE. P.RaoS. (2012). Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence. Proceedings of the National Academy of Sciences, 109(46), 18737–18742. https://doi.org/10.1073/pnas.1207212109
41.
NysJ.ContentA. (2012). Judgement of discrete and continuous quantity in adults: Number counts!Quarterly Journal of Experimental Psychology, 65(4), 675–690. https://doi.org/10.1080/17470218.2011.619661
42.
OdicD.HalberdaJ. (2015). Eye movements reveal distinct encoding patterns for number and cumulative surface area in random dot arrays. Journal of Vision, 15(15), e5. https://doi.org/10.1167/15.15.5
43.
PeirceJ.GrayJ. R.SimpsonS.MacAskillM.HochenbergerR.SogoH.. . .LindelovJ. K. (2019). PsychoPy2: Experiments in behavior made easy. Behavior Research Methods, 51(1), 195–203. https://doi.org/10.3758/s13428-018-01193-y
44.
PiazzaM.IzardV.PinelP.Le BihanD.DehaeneS. (2004). Tuning curves for approximate numerosity in the human intraparietal sulcus. Neuron, 44(3), 547–555. https://doi.org/10.1016/j.neuron.2004.10.014
45.
PicaP.LemerC.IzardV.DehaeneS. (2004). Exact and approximate arithmetic in an Amazonian Indigene Group. Science, 306, 499–503.
46.
PomerantzJ. R. (1983). Global and local precedence: Selective attention in form and motion perception. Journal of Experimental Psychology: General, 112(4), 516–540.
47.
RoquetA.LemaireP. (2019). Strategy variability in numerosity comparison task: A study in young and older adults. Open Psychology, 1(1), 152–167. https://doi.org/10.1515/psych-2018-0011
48.
SaltiM.KatzinN.KatzinD.LeibovichT.HenikA. (2017). One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks. Behavior Research Methods, 49(3), 1120–1127. https://doi.org/10.3758/s13428-016-0772-7
49.
SchneiderM.BeeresK.CobanL.MerzS.Susan SchmidtS.StrickerJ.De SmedtB. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. https://doi.org/10.1111/desc.12372
50.
SchwenkC.SasanguieD.KuhnJ. T.KempeS.DoeblerP.HollingH. (2017). (Non-)symbolic magnitude processing in children with mathematical difficulties: A meta-analysis. Research in Developmental Disabilities, 64, 152–167. https://doi.org/10.1016/j.ridd.2017.03.003
51.
SmetsK.GebuisT.DefeverE.ReynvoetB. (2014). Concurrent validity of approximate number sense tasks in adults and children. Acta Psychologica, 150, 120–128. https://doi.org/10.1016/j.actpsy.2014.05.001
52.
SmetsK.MoorsP.ReynvoetB. (2016). Effects of presentation type and visual control in numerosity discrimination: Implications for number processing?Frontiers in Psychology, 7, e66. https://doi.org/10.3389/fpsyg.2016.00066
53.
SmetsK.SasanguieD.SzücsD.ReynvoetB. (2015). The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison. Journal of Cognitive Psychology, 27(3), 310–325. https://doi.org/10.1080/20445911.2014.996568
van OeffelenM. P.VosP. G. (1982). A probabilistic model for the discrimination of visual number. Perception & Psychophysics, 32(2), 163–170. https://doi.org/10.3758/BF03204275
57.
WalshV. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483–488. https://doi.org/10.1016/j.tics.2003.09.002
58.
Xenidou-DervouI.De SmedtB.van der SchootM.van LieshoutE. C. D. M. (2013). Individual differences in kindergarten math achievement: The integrative roles of approximation skills and working memory. Learning and Individual Differences, 28, 119–129. https://doi.org/10.1016/j.lindif.2013.09.012
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
