Associations between inhibition and arithmetic fact retrieval
Associations between inhibition and arithmetic fact retrieval
Te impulsief om te rekenen?
Rekenvaardigheden zijn cruciaal in onze moderne westerse samenleving. Overal worden we omringd door cijfers en hoeveelheden en wanneer je hier goed mee overweg kan, heb je vaak een streepje voor. Maar waarom is rekenen voor sommige een spelletje en voor anderen een levenslange strijd?
Veel wetenschappelijk onderzoek zoekt het antwoord op die vraag in de vaardigheid om getallen en hoeveelheden te verwerken. Maar wat als veel algemenere cognitieve factoren ook een belangrijke rol spelen? Aandachtig zijn, tussenstappen kunnen onthouden, een rekenstrategie kiezen, … : het zijn allemaal algemeen bekende, belangrijke cognitieve vaardigheden die we nodig hebben wanneer we rekenen. Inhibitie is minder gekend bij het brede publiek, maar zou hier ook een belangrijke rol in kunnen spelen.
Inhibitie is de cognitieve vaardigheid om je aandacht, gedrag en/of gedachten te onderdrukken in functie van het geven van een meer gepaste reactie. We kennen het allemaal: je krijgt een cadeau, maar vinden het maar niets. Toch zeggen we – althans de meesten onder ons – overtuigend ‘dank u wel’. Op dat moment inhiberen we de minder gepaste reactie ‘wat een stom cadeau’ in functie van de meer gepaste reactie ‘bedankt voor het cadeau’. Maar ook op veel onbewuster niveau speelt inhibitie een rol. Wanneer je het kleurwoord rood geschreven ziet staan in gele inkt en je gevraagd wordt enkel de kleur van de inkt te benoemen, ondervinden velen onder ons dat dit niet zo eenvoudig is als het op het eerste zicht lijkt. We lezen automatisch het woord rood, waardoor het een heel stuk moeilijker wordt om dat antwoord te onderdrukken – te inhiberen – en het meer gepaste antwoord ‘geel’ te geven.
Mensen die moeite hebben met inhibitievaardigheden worden vaak impulsief genoemd. Impulsief gedrag is een kernsymptoom van kinderen en jongeren met ADHD en laat dat nu net een groep zijn die vaak moeite heeft met rekenen. Er lijkt dus een samenhang te zijn tussen een tekort aan inhibitievaardigheden en rekenmoeilijkheden.
We gingen met een wetenschappelijk onderzoek bij een honderdtal normaal ontwikkelende kinderen na of we deze samenhang terugvinden in de gewone populatie. Indien dat zo zou zijn, opent dit deuren voor nieuwe wetenschappelijk onderbouwde diagnostische tests en remediëringsprogramma’s voor rekenen. Zo zouden we kinderen met rekenmoeilijkheden bijvoorbeeld wetenschappelijk onderbouwde games kunnen laten spelen om hun inhibitievaardigheden te oefenen en op die manier hun rekenvaardigheden te trainen.
De kinderen deden in dit onderzoek verschillende taakjes waarin hun inhibitievaardigheden gemeten werden en enkele taakjes waarin zij moesten hoofdrekenen. We gingen na of kinderen die goed scoorden op de inhibitietaakjes ook goed scoorden op de taakjes die peilden naar rekenvaardigheden en vice versa. Uit het onderzoek kwam geen samenhang naar voor tussen de taakjes die peilden naar de twee vaardigheden. We kunnen dus niet stellen dat inhibitievaardigheden een belangrijke rol spelen bij het rekenen en er is dus ook geen reden om te zeggen dat een impulsief kind, bijvoorbeeld met een diagnose ADHD, daarom perse problemen zal hebben met rekenen. Het oefenen op inhibitievaardigheden met computergames kan kinderen dus wel een leuke tijd bezorgen, maar geen betere rekenvaardigheden. Het onderzoek bevestigde wel dat de vaardigheid om getallen en hoeveelheden te verwerken een zeer belangrijke rol speelt bij rekenvaardigheden.
Om na te gaan wie al dan niet streepje voor heeft bij rekenen kan je dus helaas niet op het volgende feestje afgaan op het criterium hoe goed hij is in beleefd ‘bedankt’ zeggen wanneer hij een ongewenst cadeautje krijgt. Tenzij hij natuurlijk uitzinnig blij wordt met een rekenmachine als cadeau…
Allan, N. P., Hume, L. E., Allan, D. M., Farrington, A. L., & Lonigan, C. J. (2014). Relations between inhibitory control and the development of academic skills in preschool and kindergarten: a meta-analysis. Developmental Psychology, 50(10), 2368-2379. doi: 10.1037/a0037493
Allan, N. P., Lonigan, C. J., & Wilson, S. B. (2013). Psychometric evaluation of the Children’s Behavior Questionnaire – Very Short Form in preschool children using parent and teacher report. Early Childhood Research Quarterly, 28, 302-313. doi: 10.1016/j.ecresq.2012.07.009
Ancker, J. S., & Kaufman, D. (2007). Rethinking health numeracy: A multidisciplinary literature review. Journal of the American Medical Informatics Association, 14(6), 713-721.
Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9(4), 278-291. doi: 10.1038/nrn2334
Ashcraft, M. H. (1987). Children’s knowledge of simple arithmetic: A developmental model and simulation. In C. J. Brainerd, R. Kail, & J. Bisanz (Eds.), Formal methods in developmental research (pp. 302-338). New York: Springer-Verlag.
Bailey, D. H., Littlefield, A., & Geary, D. C. (2012). The co-development of skill at and preference of use of retrieval-based processes for solving addition problems: individual and sex differences from first to sixth grades. Journal of Experimental Child Psychology, 113, 78-92. doi: 10.1016/j.jecp.2012.04.014
Banfield, J. D., & Raftery, A. E. (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics, 49(3), 803-821.
Barrouillet, P., & Lépine, R. (2005). Working memory and children’s use of retrieval to solve addition problems. Journal of Experimental Child Psychology, 91, 183-204. doi: 10.1016/j.jecp.2005.03.002
Barrouillet, P., Fayol, M., & Lathulière, E. (1997). Selecting between competitors in multiplication tasks: An explanation of the errors produced by adolescents with learning disabilities. International Journal of Behavioural Development, 21(2), 253-275.
Barrouillet, P., Mignon, M., & Thevenot, C. (2008). Strategies in subtraction problem solving in children. Journal of Experimental Child Psychology, 99(4), 233-251. doi: 10.1016/j.jecp.2007.12.001
Bayliss, D. M., & Roodenrys, S. (2000). Executive processing and ADHD: An application of the supervisory attentional system. Developmental Neuropsychology, 17(2), 161-180. doi: 10.1207/S15326942DN1702_02
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(2), 647-663.
Brock, L. L., Rimm-Kaufman, S. E., Nathanson, L., & Grimm, K. J. (2009). The contribution of ‘hot’ and ‘cool’ executive function to children’s academic achievement, learning-related behaviors, and engagement in kindergarten. Early Childhood Research Quarterly, 24(3), 337-349. doi: 10.1016/j.ecresq.2009.06.001
Brus, B. T., & Voeten, B. J. (1995). Eén minuut test vorm A en B. Verantwoording en handleiding [One Minute Test version A and B. Justification and manual]. Nijmegen, The Netherlands: Berkhout.
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. doi: 10.1207/S15326942DN1903_3
Byrnes, J. P., & Wasik, B. A. (2009). Factors predictive of mathematics achievement in kindergarten, first and third grades: An opportunity-propensity analysis. Contemporary Educational Psychology, 34(2), 167-183. doi: 10.1016/j.cedpsych.2009.01.002
Campbell, J. I. D. (1995). Mechanisms of simple addition and multiplication: A modified network-interference theory and simulation. Mathematical Cognition, 1(2), 121-164.
Campbell, J. I. D., & Xue, Q. L. (2001). Cognitive arithmetic across cultures. Journal of Experimental Psychology: General, 130, 299-315. doi: 10.1037/0096-3445.130.2.299
Censabella, S., & Noël, M. P. (2007). The inhibition capacities of children with mathematical disabilities. Child Neuropsychology, 14(1), 1-20. doi: 10.1080/09297040601052318
Cho, S., Metcalfe, A. W. S., Young, C. B., Ryali, S., Geary, D. C., & Menon, V. (2012). Hippocampal-prefrontal engagement and dynamic causal interactions in the maturation of children’s fact retrieval. Journal of Cognitive Neuroscience, 24(9), 1849-1866. doi: 10.1162/jocn_a_00246
Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 63-68. doi: 10.1016/j.tine.2013.12.001
De Smedt, B., & Boets, B. (2010). Phonological processing and arithmetic fact retrieval: Evidence form developmental dyslexia. Neuropsychologia, 48(14), 3973-3981. doi: 10.1016/j.neuropsychologia.2010.10.018
De Smedt, B., & Gilmore, C. K. (2011). Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties. Journal of Experimental Child Psychology, 108(2), 278-292. doi: 10.1016/j.jecp.2010.09.003
De Smedt, B., Ansari, D., Grabner, R. H., Hannula, M. M., Schneider, M., & Verschaffel, L. (2010). Cognitive neuroscience meets mathematics education. Educational Research Review, 5, 97-105. doi: 10.1016/j.edurev.2009.11.001
De Smedt, B., Noël, M. P., Gilmore, C., & Ansari, D. (2013). The relationship between symbolic and non-symbolic numerical magnitude processing skills and the typical and atypical development of mathematics: 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
De Smedt, B., Reynvoet, B., Swillen, A., Verschaffel, L., Boets, B., & Ghesquière, P. (2009). Basic number processing and difficulties in single-digit arithmetic: Evidence from velo-cardio-facial syndrome. Cortex, 45(2), 177-188. doi: 10.1016/j.cortex.2007.06.003
De Smedt, B., Verschaffel, L., & Ghesquière, P. (2009). The predictive value of numerical magnitude comparison for individual differences in mathematics achievement. Journal of Experimental Child Psychology, 103(4), 469-479. doi: 10.1016/j.jecp.2009.01.010
De Visscher, A., & Noël, M. P. (2013). A case study of arithmetic facts dyscalculia caused by a hypersensitivity-to-interference in memory. Cortex, 49(1), 50-70. doi: 10.1016/j.cortex.2012.01.003
De Visscher, A., & Noël, M.P. (2014a). Arithmetic facts storage deficit: the hypersensitivity-to-interference in memory hypothesis. Developmental Science, 17(3), 434-442. doi: 10.1111/desc.12135
De Visscher, A., & Noël, M.P. (2014b). The detrimental effect of interference in multiplication facts storing: typical development and individual differences. Journal of Experimental Psychology: General, 143(6), 2380-2400. doi: 10.1037/xge0000029
de Vos, T. (1992). Tempo-Test-Rekenen. Handleiding [Tempo Test Arithmetic. Manual]. Nijmegen, The Netherlands: Berkhout.
Dempster, F. N., & Corkill, A. J. (1999). Individual differences in susceptibility to interference and general cognitive ability. Acta Psychologica, 101, 395-416. doi: 10.1016/S0001-6918(99)00013-X
Diamond, A. (2013). Executive Functions. Annual Review of Psychology, 64, 135-168. doi: 10.1146/annurev-psych-113011-143750
Dilwordth-Bart, J.E. (2012). Does executive function mediate SES and home quality associations with academic readiness? Early Childhood Research Quarterly, 27(3), 416-425. doi: 10.1016/j.ecresq.2012.02.002
Donlan, C., Cowan, R., Newton, E., & Lloyd, D. (2007). The role of language in mathematical development: Evidence from children with specific language impairments. Cognition, 103(1), 23-33. doi: 10.1016/j.cognition.2006.02.007
Dowker, A. (2005). Individual differences in arithmetic. Implications for psychology, neuroscience and education. Hove: Psychology Press.
Dudal, P. (2000). Leerlingvolgsysteem: Wiskunde-Toetsen 1-2-3 Basisboek [Student monitoring system: Mathematics-Tests 1-2-3 manual]. Leuven, Belgium: Garant.
Durand, M., Hulme, C., Larkin, R., & Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7- to 10-year-olds. Journal of Experimental Child Psychology, 91(2), 113-136. doi: 10.1016/j.jecp.2005.01.003
Espy, K. A., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A., & Senn, T. E. (2004). The contribution of executive functions to emergent mathematic skills in preschool children. Developmental Neuropsychology, 26(1), 465-486. doi: 10.1207/s15326942dn2601_6
Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of development dyscalculia. Trends in Neuroscience and Education, 2(2), 43-47. doi: 10.1016/j.tine.2013.06.006
Finnie, R., & Meng, R. (2001). Cognitive skills and the youth labour market. Applied Economics Letters, 8, 675-679.
Friso-van den Bos, I., van der Ven, S. H. G., Kroesbergen, E. H., & van Luit, J. E. H. (2013). Working memory and mathematics in primary school children: A meta-analysis. Educational Research Review, 10, 29-44. doi: 10.1016/j.edurev.2013.05.003
Fuhs, M., & McNeil, N. (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.
Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345-362. doi: 10.1037/0033-2909.114.2.345
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15. doi: 10.1177/00222194040370010201
Geary, D. C. (2010). Mathematical disabilities: Reflections on cognitive, neuropsychological, and genetic components. Learning and Individual Differences, 20, 130-133. doi: 10.1016/j.lindif.2009.10.008
Geary, D. C. (2013). Early foundations for mathematics learning and their relation to learning disabilities. Current Directions in Psychological Science, 22(1), 23-27. doi: 10.1177/0963721412469398
Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77(3), 236-263. doi: 10.1006/jecp.2000.2561
Geary, D. C., Hoard, M. K., & Bailey, D. H. (2012). Fact retrieval deficits in low achieving children and children with mathematical learning disability. Journal of Learning Disabilities, 45(4), 291-307. doi: 10.1177/0022219410392046
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
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
Harnishfeger, K. K. (1995). The development of cognitive inhibition: Theories, definitions, and research evidence. In F. N. Dempster & C.J. Brainerd (Eds.), Interference and inhibition in cognition (pp. 175-204). San Diego, CA: Academic Press.
Hasher, L., Zacks, R. T., & May, C. P. (1999). Inhibitory control, circadian arousal, and age. In D. Gopher & A. Koriat (Eds.), Attention and performance xvii. Cognitive regulation of performance: Interaction of theory and application (pp. 653-675). Cambridge, MA: The MIT Press.
Hecht, S. A., Torgesen, J. K., Wagner, R. K. & Rashotte, C. A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79(2), 192-227. doi: 10.1006/jecp.2000.2586
Holloway, I. D., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17-29. doi: 10.1016/j.jecp.2008.04.001
Jackson, N., & Coney, J. (2007). Simple arithmetic processing: Individual differences in automaticity. European Journal of Cognitive Psychology, 19, 141-160. doi: 10.1080/09541440600612712
Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82-88. doi: 10.1016/j.lindif.2009.07.004
Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). Arithmetic fact mastery in young children: A longitudinal investigation. Journal of Experimental Child Psychology, 85(2), 103-119. doi: 10.1016/S0022-0965(03)00032-8
Kaufmann, L., & Nuerk, H. C. (2006). Interference effects in a numerical stroop paradigm in 9- to 12-year-old children with ADHD-C. Child Neuropsychology, 12(3), 223-243. doi: 10.1080/09297040500477483
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
Konopen, T., Salmi, P., Eklund, K., & Aro, T. (2013). Counting and RAN: Predictors of arithmetic calculation and reading fluency. Journal of Educational Psychology, 105, 162-175. doi: 10.1037/a0029285
Koontz, K. L., & Berch, D. B. (1996). Identifying simple numerical stimuli: Processing inefficiencies exhibited by arithmetic learning disabled children. Mathematical Cognition, 2, 1-23. doi: 10.1080/135467996387525
Kroesbergen, E., Van Luit, J., Van Lieshout, E., Van Loosbroek, E., & Van der Rijt, B. (2009). Individual differences in early numeracy: The role of executive functions and subitizing. Journal of Psychoeducational Assessment, 27(3), 226-236. doi: 10.1177/0734282908330586
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8-9-year-old students. Cognition, 93(2), 99-125. doi: 10.1016/j.cognition.2003.11.004
Lee, K., Ng, S. F., Pe, M. L., Ang, S. Y., Hasshim, M. N. A. M., & Bull, R. (2010). The cognitive underpinnings of emerging mathematical skills: executive functioning, patterns, numeracy, and arithmetic. British Journal of Educational Psychology, 82(1), 82-99. doi: 10.1111/j.2044-8279.2010.02016.x
LeFevre, J. A., Berrigan, L., Vendetti, C., Kamawar, D., Bisanz, J., Skwarchuk, S. L., & Smith-Chant, B. L. (2013). The role of executive attention in the acquisition of mathematical skills for children in Grades 2 through 4. Journal of Experimental Child Psychology, 114(2), 243-261. doi: 10.1016/j.jecp.2012.10.005
LeFevre, J. A., Sadesky, G. S., & Bisanz, J. (1996). Selection of procedures in mental addition: Reassessing the problem size effect in adults. Journal of Experimental Psychology: Learning, Memory, and Cognition, 22, 216-230.
Luna, B. (2009). Developmental changes in cognitive control through adolescence. Advances in Child Development and Behavior, 37, 233-278.
Luna, B., Garver, K. E., Urban, T. A., Lazar, N. A., & Sweeney, J. A. (2004). Maturation of cognitive processes from late childhood to adulthood. Child Development, 75(5), 1357-1372. doi: 10.1111/j.1467-8624.2004.00745.x
Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5), 520-540.
MacLeod, C. (1991). Half a century of research on the Stroop effect: an integrative review. Psychological Bulletin, 109(2), 163-203. doi: 10.1037/0033-2909.109.2.163
Mahone, E. M., Cirino, P. T., Cutting, L. E., Cerrone, P. M., Hagelthorn, K. M., Hiemenz, J. R., Singer, H. S., & Denckla, M. B. (2002). Validity of the behaviour rating inventory of executive function in children with ADHD and/or Tourette syndrome. Archives of Clinical Neuropsychology, 17(7), 643-662. doi: 10.1016/S0887-6177(01)00168-8
Mayes, S. D., Calhoun, S. L., Bixler, E. O., & Zimmerman, D. N. (2009). IQ and neuropsychological predictors of academic achievement. Learning and Individual differences, 19(2), 238-241. doi: 10.1016/j.lindif.2008.09.001
McAuley, T., Chen, S., Goos, L., Schachar, R., & Crosbie, J. (2010). Is behavior rating inventory of executive function more strongly associated with measures of impairment or executive function? Journal of the International Neuropsychological Society, 16(3), 495-505. doi: 10.1017/S1355617710000093
McCloskey, M., & Lindemann, A. M. (1992). Mathnet: Preliminary results from a distributed model of arithmetic fact retrieval. In J. I. D. Campbell (Ed.), The nature and origins of mathematical skills (pp. 365-409). Amsterdam: Elsevier.
Menon, V. (2015). Arithmetic in the Child and Adult Brain. In R. Cohen-Kadosh, & A. Dowker (Eds.) The Oxford Handbook of Mathematical Cognition (pp. 502-530). Oxford: Oxford University Press.
Moffitt, T. E., Arseneault, L., Belsky, D., Dickson, N., Hancox, R. J., Harrington, H., … Caspi, A. (2011). A gradient of childhood self-control predicts health, wealth, and public safety. Proceedings of the National Academy of Sciences of the United States of America, 108(7), 2693-2698. doi: 10.1073/pnas.1010076108
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
Nigg, J. T. (2000). On inhibition/disinhibition in developmental psychopathology: Views from cognitive and personality psychology and a working inhibition taxonomy. Psychological Bulletin, 126(2), 220-246. doi: 10.1037/0033-2909.126.2.220
Opdenakker, M. C., & Van Damme, J. (2007). Do school context, student composition and school leadership affect school practice and outcomes in secondary education? British Educational Research Journal, 33(2), 179-206. doi: 10.1080/01411920701208233
Parsons, S., & Bynner, J. (2005). Does numeracy matter more? London: National Research and Development Centre for Adult Literacy.
Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348-367. doi: 10.1016/j.jecp.2004.04.002
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: 10.16/j.neuron.2004.10.014
Raghubar, K., Barnes, F., & Hecht, S. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20(2), 110-122. doi: 10.1016/j.lindif.2009.10.005
Raven, J. C., Court, J. H. & Raven, J. (1992). Standard progressive matrices. Oxford, United Kingdom: Oxford Psychologists Press.
Ritchie, S. J., & Bates, T. C. (2013). Enduring links form childhood mathematics and reading achievement to adult socioeconomic status. Psychological science, 24, 1301-1308. doi : 10.1177/0956797612466268
Robinson, C. S., Menchetti, B. M. & Torgesen, J. K. (2002). Toward a two-factor theory of one type of mathematics disabilities. Learning Disabilities Research & Practice, 17(2), 81-89. doi: 10.1111/1540-5826.00035
Sarsour, K., Sheridan, M., Jutte, D., Nuru-Jeter, A., Hinshaw, S., & Boyce, W.T. (2011). Family socioeconomic status and child executive functions: The roles of language, home environment, and single parenthood. Journal of the International Neuropsychological Society, 17(1), 120-132. doi: 10.1017/S1355617710001335
Sasanguie, D., Gobel, S. M., Moll, K., Smets, K., & Reynvoet, B. (2013). Approximate number sense, symbolic number processing, or number-space mappings: What underlies mathematics achievement? Journal of Experimental Child Psychology, 114(3), 418-431. doi: 10.1016/j.jecp.2012.10.012
Schneider W., Eschmann, A., & Zuccolotto, A. (2002). E-prime reference guide. Pittsburgh, PA: Psychology Software Tools.
Shilling, V. M., Chetwynd, A., & Rabbitt, P. M. A. (2002). Individual inconsistency across measures of inhibition: An investigation of the construct validity of inhibition in older adults. Neuropsychologia, 40(6), 605-619. doi: 10.1016/S0028-3932(01)00157-9
Siegler, R. S. (1987). The perils of averaging data over strategies: An example from children’s addition. Journal of Experimental Psychology: General, 116(3), 250-264. doi: 10.1037/0096-3445.116.3.250
Siegler, R. S. (1996). Emerging minds: The process of change in children’s thinking. New York: Oxford University Press.
Smidts, D. P. & Huizinga, M. (2009). BRIEF Executieve Functies Gedragsvragenlijst: Handleiding [BRIEF Executive Functions Behavior Inventory]. Amsterdam: Hogrefe Uitgevers.
St Clair-Thomson, H., & Gathercole, S. (2006). Executive functions and achievement in school: Shifting, updating, inhibition, and working memory. The Quarterly Journal of Experimental Psychology, 59(4), 745-759. doi: 10.1080/17470210500162854
Stazyk, E. H., Ashcraft, M. H., & Hamann, M. S. (1982). A network approach to mental multiplication. Journal of Experimental Psychology: Learning, Memory, & Cognition, 8(4), 320-335. doi: 10.1037/0278-7393.8.4.320
Steinmayr, R., & Spinath, B. (2009). The importance of motivation as a predictor of school achievement. Learning and Individual Differences, 19(1), 80-90. doi: 10.1016/j.lindif.2008.05.004
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment. Cortex, 49(10), 2674-2688. doi: 10.1016/j.cortex.2013/06.007
Thorell, L. B. (2007). Do delay aversion and executive function deficits make distinct contributions to the functional impact of ADHD symptoms? A study of early academic skill deficits. Journal of Child Psychology and Psychiatry, 48(11), 1061-1070. doi: 10.1111/j.1469-7610.2007.01777.x
Toplak, M. E., West, R. F., & Stanovich, K. E. (2013). Practioner Review: Do performance-based measures and ratings of executive function assess the same construct? Journal of Child Psychology and Psychiatry, 54(2), 131-143. doi: 10.1111/jcpp.12001
Valiente, C., Lemery-Chalfant, K., & Swanson, J. (2010). Prediction of kindergartners’ academic achievement from their effortful control and emotionality: Evidence for direct and moderate relations. Journal of Educational Psychology, 102(3), 550-560. doi: 10.1037/a0018992
van den Bos, K. P., Spelberg, H. C. L., Scheepstra, A. J. M., & De Vries, J. R. (1994). De Klepel. Vorm A en B. Een test voor de leesvaardigheid van pseudowoorden [Standardized test of reading ability Form A and B]. Nijmegen: Berkhout.
van der Sluis, S., de Jong, P.F., & van der Leij, A. (2004). Inhibition and shifting in children with learning deficits in arithmetic and reading. Journal of Experimental Child Psychology, 87(3), 239-266. doi: 10.1016/j.jecp.2003.12.002
Vanbinst, K., Ceulemans, E., Ghesquière, P., & De Smedt, B. (2015). Profiles of children’s arithmetic fact development: A model-based clustering approach. Journal of Experimental Child Psychology, 133, 29-46. doi: 10.1016/j.jecp.2015.01.003
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
Vanbinst, K., Ghesquière, P., De Smedt, B. (2015). Does numerical processing uniquely predict first graders’ future development of single-digit arithmetic? Learning & Individual Differences, 37, 153-160. doi: 10.1016/j.lindif.2014.12.004
Verguts, T., & Fias, W. (2005). Interacting neighbors: a connectionist model of retrieval in single-digit multiplication. Memory and Cognition, 33(1), 1-16.
Willoughby, M. T., Kupersmidt, J. B., & Voegler-Lee, M. E. (2012). Is preschool executive function causally related to academic achievement? Child Neuropsychology, 18(1), 79-91. doi: 10.1080/09297049.2011.578572
Winkelman, J. H., & Schmidt, J. (1974). Associative confusions in mental arithmetic. Journal of Experimental Psychology, 102, 734-736.
Wu, J. (2012). Advances in K-means clustering. A data mining thinking. Berlin Heidelberg: Springer-Verlag.