Top

Gepubliceerd in:

29-08-2017 | Original Article

Set size influences the relationship between ANS acuity and math performance: a result of different strategies?

Auteurs: Julia Felicitas Dietrich, Hans-Christoph Nuerk, Elise Klein, Korbinian Moeller, Stefan Huber

Gepubliceerd in: Psychological Research | Uitgave 3/2019

Abstract

Previous research has proposed that the approximate number system (ANS) constitutes a building block for later mathematical abilities. Therefore, numerous studies investigated the relationship between ANS acuity and mathematical performance, but results are inconsistent. Properties of the experimental design have been discussed as a potential explanation of these inconsistencies. In the present study, we investigated the influence of set size and presentation duration on the association between non-symbolic magnitude comparison and math performance. Moreover, we focused on strategies reported as an explanation for these inconsistencies. In particular, we employed a non-symbolic magnitude comparison task and asked participants how they solved the task. We observed that set size was a significant moderator of the relationship between non-symbolic magnitude comparison and math performance, whereas presentation duration of the stimuli did not moderate this relationship. This supports the notion that specific design characteristics contribute to the inconsistent results. Moreover, participants reported different strategies including numerosity-based, visual, counting, calculation-based, and subitizing strategies. Frequencies of these strategies differed between different set sizes and presentation durations. However, we found no specific strategy, which alone predicted arithmetic performance, but when considering the frequency of all reported strategies, arithmetic performance could be predicted. Visual strategies made the largest contribution to this prediction. To conclude, the present findings suggest that different design characteristics contribute to the inconsistent findings regarding the relationship between non-symbolic magnitude comparison and mathematical performance by inducing different strategies and additional processes.

vorige artikel Joint cognition and the role of human agency in random number choices

volgende artikel Within-person adaptivity in frugal judgments from memory

Alleen toegankelijk voor geautoriseerde gebruikers

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.CrossRef

Amthauer, R., Brocke, B., Liepmann, D., & Beauducel, A. (2007). I-S-T 2000 R: Intelligenz-Struktur-Test 2000 R. Göttingen: Hogrefe.

Anobile, G., Cicchini, G. M., & Burr, D. C. (2013). Separate mechanisms for perception of numerosity and density. Psychological Science, 25(1), 265–270. doi:10.1177/0956797613501520.CrossRefPubMed

Anobile, G., Turi, M., Cicchini, G., & Burr, D. (2015). Mechanisms for perception of numerosity or texture-density are governed by crowding-like effects. Journal of Vision, 15, 4.CrossRef

Ansari, D. (2012). Why the “symbol-grounding problem” for number symbols is still problematic. Current Anthropology, 53(2), 212–213. doi:10.1086/664818.CrossRef

Assel, M. A., Landry, S. H., Swank, P., Smith, K. E., & Steelman, L. M. (2003). Precursors to mathematical skills: Examining the roles of visual-spatial skills, executive processes, and parenting factors. Applied Developmental Science, 7(1), 27–38. doi:10.1207/S1532480XADS0701_3.CrossRef

Baayen, R. H., Davidson, D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subjects and items. Journal of Memory and Language, 59(4), 390–412. doi:10.1016/j.jml.2007.12.005.CrossRef

Baayen, R. H., & Milin, P. (2010). Analyzing reaction times. International Journal of Psychological Research, 3(2), 12–28.CrossRef

Barr, D. J., Levy, R., Scheepers, C., & Tily, H. J. (2013). Random effects structure for confirmatory hypothesis testing: Keep it maximal. Journal of Memory and Language, 68(3), 255–278. doi:10.1016/j.jml.2012.11.001.CrossRef

Bartelet, D., Vaessen, A., Blomert, L., & Ansari, D. (2014). What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency? Journal of Experimental Child Psychology, 117(1), 12–28. doi:10.1016/j.jecp.2013.08.010.CrossRefPubMed

Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models unsing lme4. Journal of Statistical Software, 67(1), 1–48. doi:10.18637/jss.v067.i01.CrossRef

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B (Methodological), 57(1), 289–300. Retrieved from http://www.jstor.org/stable/2346101.

Brankaer, C., Ghesquière, P., & De Smedt, B. (2014). Children’s mapping between non-symbolic and symbolic numerical magnitudes and its association with timed and untimed tests of mathematics achievement. PLoS One, 9(4), e93565. doi:10.1371/journal.pone.0093565.CrossRefPubMedPubMedCentral

Bull, R., & Scerif, G. (2001). Executive functioning as a predictor of children’s mathematics ability: Inhibition, switching, and working memory. Developmental Neuropsychology, 19(3), 273–293.CrossRef

Cantlon, J. F., Platt, M. L., & Brannon, E. M. (2009). Beyond the number domain. Trends in Cognitive Sciences, 13(2), 83–91. doi:10.1016/j.tics.2008.11.007.CrossRefPubMedPubMedCentral

Castronovo, J., & Göbel, S. M. (2012). Impact of high mathematics education on the number sense. PLoS One, 7(4), e33832. doi:10.1371/journal.pone.0033832.CrossRefPubMedPubMedCentral

Chang, C.-C., & Lin, C.-J. (2011). LIBSVM: A library for support vector machines. ACM Transactions on Intelligent Systems and Technology, 2(3), 1–27. doi:10.1145/1961189.1961199.CrossRef

Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance: A meta-analysis. Acta Psychologica, 148, 163–172. doi:10.1016/j.actpsy.2014.01.016.CrossRefPubMed

Cicchini, G. M., Anobile, G., Burr, D. C., Agrillo, C., Bisazza, A., Izard, V., & Tibber, M. S. (2016). Spontaneous perception of numerosity in humans. Nature Communications, 7, 12536. doi:10.1038/ncomms12536.CrossRefPubMedPubMedCentral

Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. ZDM, 47(5), 759–770. doi:10.1007/s11858-014-0655-2.CrossRef

Clayton, S., Gilmore, C., & Inglis, M. (2015). Dot comparison stimuli are not all alike: The effect of different visual controls on ANS measurement. Acta Psychologica, 161, 177–184.

Crutcher, R. J. (1994). Telling what we know: The use of verbal report methodologies in psychological research. Psychological Science, 5(5), 241. doi:10.1111/j.1467-9280.1994.tb00619.x.CrossRef

Cutini, S., Scatturin, P., Basso Moro, S., & Zorzi, M. (2014). Are the neural correlates of subitizing and estimation dissociable? An fNIRS investigation. Neuroimage, 85, 391–399. doi:10.1016/j.neuroimage.2013.08.027.CrossRefPubMed

De Oliveira Ferreira, F., Wood, G., Pinheiro-Chagas, P., Lonnemann, J., Krinzinger, H., Willmes, K., & Haase, V. G. (2012). Explaining school mathematics performance from symbolic and nonsymbolic magnitude processing: Similarities and differences between typical and low-achieving children. Psychology and Neuroscience, 5(1), 37–46.CrossRef

De Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children’s mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48–55. doi:10.1016/j.tine.2013.06.001.CrossRef

Defever, E., Reynvoet, B., & Gebuis, T. (2013). Task- and age-dependent effects of visual stimulus properties on children’s explicit numerosity judgments. Journal of Experimental Child Psychology, 116(2), 216–233. doi:10.1016/j.jecp.2013.04.006.CrossRefPubMed

Dehaene, S. (2001). Precis of the number sense. Mind and Language, 16(1), 16–36. doi:10.1111/1468-0017.00154.CrossRef

Dehaene, S. (2009). Origins of mathematical intuitions. Annals of the New York Academy of Sciences, 1156(1), 232–259. doi:10.1111/j.1749-6632.2009.04469.x.CrossRefPubMed

DeWind, N. K., Adams, G. K., Platt, M. L., & Brannon, E. M. (2015). Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition, 142, 247–265. doi:10.1016/j.cognition.2015.05.016.CrossRefPubMedPubMedCentral

Dietrich, J. F., Huber, S., Klein, E., Willmes, K., Pixner, S., & Moeller, K. (2016). A systematic investigation of accuracy and response time based measures used to index ANS acuity. PLoS One, 11(9), e0163076.CrossRef

Dietrich, J. F., Huber, S., Moeller, K., & Klein, E. (2015a). The influence of math anxiety on symbolic and non-symbolic magnitude processing. Frontiers in Psychology, 6, 1621. doi:10.3389/fpsyg.2015.01621.CrossRefPubMedPubMedCentral

Dietrich, J. F., Huber, S., & Nuerk, H.-C. (2015b). Methodological aspects to be considered when measuring the approximate number system (ANS)—a research review. Frontiers in Psychology, 6, 295. doi:10.3389/fpsyg.2015.00295.CrossRefPubMedPubMedCentral

Durgin, F. H. (1995). Texture density adaptation and the perceived numerosity and distribution of texture. Journal of Experimental Psychology: Human Perception and Performance, 21, 149–169.

Espy, K. A., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A., & Stern, T. E. (2004). The contribution of executive functions to emergent mathematic skills in preschool children. Developmental Neuropsychology, 26(1), 465–486.CrossRef

Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123(1), 53–72. doi:10.1016/j.jecp.2014.01.013.CrossRefPubMed

Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. doi:10.1016/j.tics.2004.05.002.CrossRefPubMed

Feigenson, L., Libertus, M. E., & Halberda, J. (2013). Links between the intuitive sense of number and formal mathematics ability. Child Development Perspectives, 7(2), 74–79. doi:10.1111/cdep.12019.CrossRefPubMedPubMedCentral

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(1), 136–148. doi:10.1111/desc.12013.CrossRefPubMed

Gandini, D., Lemaire, P., Anton, J.-L., & Nazarian, B. (2008a). Neural correlates of approximate quantification strategies in young and older adults: An fMRI study. Brain Research, 1246, 144–157. doi:10.1016/j.actpsy.2008.05.009.CrossRefPubMed

Gandini, D., Lemaire, P., & Dufau, S. (2008b). Older and younger adults’ strategies in approximate quantification. Acta Psychologica, 129(1), 175–189. doi:10.1016/j.actpsy.2008.05.009.CrossRefPubMed

Gebuis, T., & Reynvoet, B. (2011). Generating nonsymbolic number stimuli. Behavior Research Methods, 43(4), 981–986. doi:10.3758/s13428-011-0097-5.CrossRefPubMed

Gebuis, T., & Reynvoet, B. (2012). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648. doi:10.1037/a0026218.CrossRef

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), 1–9. doi:10.1371/journal.pone.0067374.CrossRef

Gilmore, C., Attridge, N., De Smedt, B., & Inglis, M. (2014). Measuring the approximate number system in children: Exploring the relationships among different tasks. Learning and Individual Differences, 29, 50–58. doi:10.1016/j.lindif.2013.10.004.CrossRef

Gilmore, C., Attridge, N., & Inglis, M. (2011). Measuring the approximate number system. The Quarterly Journal of Experimental Psychology, 64(11), 2099–2109. doi:10.1080/17470218.2011.574710.CrossRefPubMed

Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 8(3), 211–215. doi:10.2307/748522.CrossRef

Guillaume, M., Nys, J., Mussolin, C., & Content, A. (2013). Differences in the acuity of the approximate number system in adults: The effect of mathematical ability. Acta Psychologica, 144(3), 506–512. doi:10.1016/j.actpsy.2013.09.001.CrossRefPubMed

Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The relation between spatial skill and early number knowledge: The role of the linear number line. Developmental Psychology, 48(5), 1229–1241. doi:10.1037/a0027433.CrossRefPubMed

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, 109(28), 11116–11120. doi:10.1073/pnas.1200196109.CrossRef

Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455, 665–668. doi:10.1038/nature07246.CrossRefPubMed

Hothorn, T., Bretz, F., & Westfall, P. (2008). Simultaneous inference in general parametric models. Biometrical Journal, 50(3), 346–363. doi:10.1002/bimj.200810425.CrossRefPubMed

Inglis, M., Attridge, N., Batchelor, S., & Gilmore, C. (2011). Non-verbal number acuity correlates with symbolic mathematics achievement: But only in children. Psychonomic Bulletin & Review, 18(6), 1222–1229. doi:10.3758/s13423-011-0154-1.CrossRef

Inglis, M., & Gilmore, C. (2013). Sampling from the mental number line: How are approximate number system representations formed? Cognition, 129(1), 63–69. doi:10.1016/j.cognition.2013.06.003.CrossRefPubMed

Inglis, M., & Gilmore, C. (2014). Indexing the approximate number system. Acta Psychologica, 145, 147–155. doi:10.1016/j.actpsy.2013.11.009.CrossRefPubMed

Jaeger, T. F. (2008). Categorical data analysis: Away from ANOVAs (transformation or not) and towards logit mixed models. Journal of Memory and Language, 59(4), 434–446. doi:10.1016/j.jml.2007.11.007.CrossRefPubMedPubMedCentral

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning (Vol. 6). New York: Springer.CrossRef

Kaufman, E. L., Lord, M. W., Reese, T. W., & Volkmann, J. (1949). The discrimination of visual number. The American Journal of Psychology, 62(4), 498–525. doi:10.2307/1418556.CrossRefPubMed

Keller, L., & Libertus, M. (2015). Inhibitory control may not explain the link between approximation and math abilities in kindergarteners from middle class families. Frontiers in Psychology, 6, 685. doi:10.3389/fpsyg.2015.00685.CrossRefPubMedPubMedCentral

Kirk, E. P., & Ashcraft, M. H. (2001). Telling stories: The perils and promise of using verbal reports to study math strategies. Journal of Experimental Psychology. Learning, Memory, and Cognition, 27(1), 157–175. doi:10.1037/0278-7393.27.1.157.CrossRefPubMed

Kolkman, M. E., Kroesbergen, E. H., & Leseman, P. P. M. (2013). Early numerical development and the role of non-symbolic and symbolic skills. Learning and Instruction, 25, 95–103. doi:10.1016/j.learninstruc.2012.12.001.CrossRef

Kurdek, L. A., & Sinclair, R. J. (2001). Predicting reading and mathematics achievement in fourth-grade children from kindergarten readiness scores. Journal of Educational Psychology, 93(3), 451–455. doi:10.1037/0022-0663.93.3.451.CrossRef

Kuznetsova, A., Brockhoff, P. B., & Christensen, R. H. (2015). lmerTest: Tests in linear mixed effects models. Retrieved from http://cran.r-project.org/package=lmerTest.

Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174. doi:10.2307/2529310.CrossRefPubMed

Leibovich, T., & Henik, A. (2013). Magnitude processing in non-symbolic stimuli. Frontiers in Psychology, 4(June), 375. doi:10.3389/fpsyg.2013.00375.CrossRefPubMedPubMedCentral

Libertus, M. E., Feigenson, L., & Halberda, J. (2011). Preschool acuity of the approximate number system correlates with school math ability. Developmental Science, 14(6), 1292–1300. doi:10.1111/j.1467-7687.2011.01080.x.CrossRefPubMedPubMedCentral

Libertus, M. E., Woldorff, M. G., & Brannon, E. M. (2007). Electrophysiological evidence for notation independence in numerical processing. Behavioral and Brain Functions, 3, 1. doi:10.1186/1744-9081-3-1.CrossRefPubMedPubMedCentral

Lindskog, M., Winman, A., Juslin, P., & Poom, L. (2013). Measuring acuity of the approximate number system reliably and validly: The evaluation of an adaptive test procedure. Frontiers in Psychology, 4, 510. doi:10.3389/fpsyg.2013.00510.CrossRefPubMedPubMedCentral

Lipton, J. S., & Spelke, E. S. (2005). Preschool children’s mapping of number words to nonsymbolic numerosities. Child Development, 76(5), 978–988. doi:10.1111/j.1467-8624.2005.00891.x.CrossRefPubMed

Lonnemann, J., Linkersdörfer, J., Hasselhorn, M., & Lindberg, S. (2013). Developmental changes in the association between approximate number representations and addition skills in elementary school children. Frontiers in Psychology, 4, 783. doi:10.3389/fpsyg.2013.00783.CrossRefPubMedPubMedCentral

Luwel, K., & Verschaffel, L. (2003). Adapting strategy choices to situational factors: The effect of time pressure on children’s numerosity judgement strategies. Psychologica Belgica, 43, 269–295.

Luwel, K., Verschaffel, L., Onghena, P., & De Corte, E. (2003a). Flexibility in strategy use: Adaptation of numerosity judgement strategies to task characteristics. European Journal of Cognitive Psychology, 15(2), 247–266. doi:10.1080/09541440244000139.CrossRef

Luwel, K., Verschaffel, L., Onghena, P., & De Corte, E. (2003b). Strategic aspects of numerosity judgment: The effect of task characteristics. Experimental Psychology, 50(1), 63–75. doi:10.1026//1618-3169.50.1.63.CrossRefPubMed

Lyons, I. M., Ansari, D., & Beilock, S. L. (2015a). Qualitatively different coding of symbolic and nonsymbolic numbers in the human brain. Human Brain Mapping, 36(2), 475–488. doi:10.1002/hbm.22641.CrossRefPubMed

Lyons, I. M., Nuerk, H.-C., & Ansari, D. (2015b). 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(5), 1021–1035. doi:10.1037/xge0000094.CrossRef

Mandler, G., & Shebo, B. J. (1982). Subitizing: An analysis of its component processes. Journal of Experimental Psychology: General, 111(1), 1–22. doi:10.1037/0096-3445.111.1.1.CrossRef

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Preschoolers’ precision of the approximate number system predicts later school mathematics performance. PLoS One, 6, e23749. doi:10.1371/journal.pone.0023749.CrossRefPubMedPubMedCentral

Mazzocco, M. M. M., & Myers, G. F. (2003). Complexities in identifying and defining mathematics learning disability in the primary school-age years. Annals of Dyslexia, 53(1), 218–253. doi:10.1007/s11881-003-0011-7.CrossRefPubMedPubMedCentral

Mundy, E., & Gilmore, C. K. (2009). Children’s mapping between symbolic and nonsymbolic representations of number. Journal of Experimental Child Psychology, 103(4), 490–502. doi:10.1016/j.jecp.2009.02.003.CrossRefPubMed

Nieder, A. (2011). The neural code for number. In S. Dehaene & E. M. Brannon (Eds.), Space, time and number in the brain: Searching for the foundations of mathematical thought (pp. 103–118). London: Academic Press.CrossRef

Nieder, A. (2013). Coding of abstract quantity by “number neurons” of the primate brain. Journal of Comparative Physiology A, 199(1), 1–16.CrossRef

Nieder, A., & Dehaene, S. (2009). Representation of number in the brain. Annual Review of Neuroscience, 32, 185–208. doi:10.1146/annurev.neuro.051508.135550.CrossRefPubMed

Nieder, A., Freedman, D. J., & Miller, E. K. (2002). Representation of the quantity of visual items in the primate prefrontal cortex. Science, 297(5587), 1708–1711.CrossRef

Noël, M. P., & Rousselle, L. (2011). Developmental changes in the profiles of dyscalculia: an explanation based on a double exact-and-approximate number representation model. Frontiers in Human Neuroscience, 5, 165. doi:10.3389/fnhum.2011.00165.CrossRefPubMedPubMedCentral

Piazza, M. (2010). Neurocognitive start-up tools for symbolic number representations. Trends in Cognitive Sciences, 14(12), 542–551. doi:10.1016/j.tics.2010.09.008.CrossRefPubMed

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), 547–555CrossRef

Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta Psychologica, 140(1), 50–57. doi:10.1016/j.actpsy.2012.02.008.CrossRefPubMed

Ratcliff, R. (1993). Methods for dealing with reaction time outliers. Psychological Bulletin, 114(3), 510–532. doi:10.1037/0033-2909.114.3.510.CrossRefPubMed

Reuhkala, M. (2001). Mathematical skills in ninth-graders: Relationship with visuo-spatial abilities and working memory. Educational Psychology, 21(4), 387–399. doi:10.1080/01443410120090786.CrossRef

Revkin, S. K., Piazza, M., Izard, V., Cohen, L., & Dehaene, S. (2008). Does subitizing reflect numerical estimation? Psychological Science, 19(6), 607–614. doi:10.1111/j.1467-9280.2008.02130.x.CrossRefPubMed

Robinson, K. M. (2001). The validity of verbal reports in children’s subtraction. Journal of Educational Psychology, 93(1), 211–222. doi:10.1037/0022-0663.93.1.211.CrossRef

Russo, J. E., Johnson, E. J., & Stephens, D. L. (1989). The validity of verbal protocols. Memory & Cognition, 17(6), 759–769. doi:10.3758/BF03202637.CrossRef

Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2016). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science. doi:10.1111/desc.12372.CrossRefPubMed

Seyler, D. J., Kirk, E. P., & Ashcraft, M. H. (2003). Elementary Subtraction. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29(6), 1339–1352. doi:10.1037/0278-7393.29.6.1339.CrossRefPubMed

Singmann, H., Bolker, B., & Westfall, J. (2015). afex: Analysis of factorial experiments. Retrieved from http://cran.r-project.org/package=afex.

Smets, K., Sasanguie, D., Szücs, D., & Reynvoet, B. (2015). The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison. Journal of Cognitive Psychology, 27(3), 310–325. doi:10.1080/20445911.2014.996568.CrossRef

Smith-Chant, B. L., & LeFevre, J.-A. (2003). Doing as they are told and telling it like it is: Self-reports in mental arithmetic. Memory and Cognition, 31(4), 516–528. doi:10.3758/BF03196093.CrossRefPubMed

Soltész, F., Szucs, D., & Szucs, L. (2010). Relationships between magnitude representation, counting and memory in 4- to 7-year-old children: a developmental study. Behavioral and Brain Functions: BBF, 6, 13. doi:10.1186/1744-9081-6-13.CrossRefPubMed

St Clair-Thompson, H. L., & Gathercole, S. E. (2006). Executive functions and achievements in school: Shifting, updating, inhibition, and working memory. The Quarterly Journal of Experimental Psychology, 59(4), 745–759. doi:10.1080/17470210500162854.CrossRefPubMed

Szűcs, D., Nobes, A., Devine, A., Gabriel, F. C., & 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. doi:10.3389/fpsyg.2013.00444.CrossRefPubMedPubMedCentral

Trick, L. M., & Pylyshyn, Z. W. (1994). Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review, 101(1), 80–102. doi:10.1037/0033-295X.101.1.80.CrossRefPubMed

van den Berg, B. A., Reinders, M. J. T., de Ridder, D., & de Beer, T. A. P. (2015). Insight into neutral and disease-associated human genetic variants through interpretable predictors. PLoS One, 10(3), 1–17. doi:10.1371/journal.pone.0120729.CrossRef

van Marle, K., Chu, F. W., Li, Y., & Geary, D. C. (2014). Acuity of the approximate number system and preschoolers’ quantitative development. Developmental Science, 17(4), 492–505. doi:10.1111/desc.12143.CrossRefPubMed

Vanbinst, K., Ghesquière, P., & De Smedt, B. (2012). Numerical magnitude representations and individual differences in children’s arithmetic strategy use. Mind, Brain, and Education, 6(3), 129–136. doi:10.1111/j.1751-228X.2012.01148.x.CrossRef

Verguts, T., & Fias, W. (2004). Representation of number in animals and humans: A neural model. Journal of Cognitive Neuroscience, 16(9), 1493–1504. doi:10.1162/0898929042568497.CrossRefPubMed

Titel: Set size influences the relationship between ANS acuity and math performance: a result of different strategies?
Auteurs: Julia Felicitas Dietrich
Hans-Christoph Nuerk
Elise Klein
Korbinian Moeller
Stefan Huber
Publicatiedatum: 29-08-2017
Uitgeverij: Springer Berlin Heidelberg
Gepubliceerd in: Psychological Research / Uitgave 3/2019
Print ISSN: 0340-0727
Elektronisch ISSN: 1430-2772
DOI: https://doi.org/10.1007/s00426-017-0907-1

Bohn Stafleu van Loghum

Deel dit onderdeel of sectie (kopieer de link)

Abstract

Log in om toegang te krijgen

Andere artikelen Uitgave 3/2019

Within-person adaptivity in frugal judgments from memory

Humans show a higher preference for stimuli that are predictive relative to those that are predictable

Novel representations that support rule-based categorization are acquired on-the-fly during category learning

Do I need to have my hands free to understand hand-related language? Investigating the functional relevance of experiential simulations

Flexible coupling of covert spatial attention and motor planning based on learned spatial contingencies

Exploring the relationship between threat-related changes in anxiety, attention focus, and postural control