Brankaer C, Ghesquière P, De Smedt B. Symbolic magnitude processing in elementary school children: a group administered paper-and-pencil measure (SYMP Test). Behav Res Methods. 2017;49(4):1361–73.

Article
PubMed
Google Scholar

Landerl K. Neurocognitive perspective on numerical development. In: Fritz A, Haase VG, Räsänen P, editors. International handbook of mathematical learning difficulties: from the laboratory to the classroom. Cham: Springer; 2019. p. 9–24.

Chapter
Google Scholar

Reyna VF, Brainerd CJ. The importance of mathematics in health and human judgment: numeracy, risk communication, and medical decision making. Learn Individ Differ. 2007;17(2):147–59.

Article
Google Scholar

Butterworth B. Forward. In: Fritz A, Haase VG, Räsänen P, editors. International handbook of mathematical learning difficulties: from the laboratory to the classroom. Cham: Springer; 2019.

Google Scholar

Ritchie SJ, Bates TC. Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychol Sci. 2013;24(7):1301–8.

Article
PubMed
Google Scholar

Butterworth B, Varma S, Laurillard D. Dyscalculia: from brain to education. Science. 2011;332(6033):1049–53.

Article
PubMed
Google Scholar

Cantlon JF, Brannon EM, Carter EJ, Pelphrey KA. Functional imaging of numerical processing in adults and 4-y-old children. PLOS Biol. 2006;4(5): e125.

Article
PubMed
PubMed Central
Google Scholar

Carvalho MRS, Haase VG. Genetics of Dyscalculia 2. In search of endophenotypes. In: Fritz A, Haase VG, Räsänen P, editors. International handbook of mathematical learning difficulties: from the laboratory to the classroom. Cham: Springer; 2019. p. 345–65.

Chapter
Google Scholar

Cohen Kadosh R, Dowker A. The Oxford handbook of numerical cognition. New York: Oxford University Press; 2014.

Book
Google Scholar

De Smedt B, Noël M-P, Gilmore C, Ansari D. 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 Neurosci Educ. 2013;2(2):48–55.

Article
Google Scholar

Rinaldi L, Girelli L. A place for zero in the brain. Trends Cogn Sci. 2016;20(8):563–4.

Article
PubMed
Google Scholar

Feigenson L, Dehaene S, Spelke E. Core systems of number. Trends Cogn Sci. 2004;8(7):307–14.

Article
PubMed
Google Scholar

Starr A, Libertus ME, Brannon EM. Number sense in infancy predicts mathematical abilities in childhood. Proc Natl Acad Sci. 2013;110:18116–181120.

Article
PubMed
PubMed Central
Google Scholar

Libertus ME, Odic D, Feigenson L, Halberda J. The precision of mapping between number words and the approximate number system predicts children’s formal math abilities. J Exp Child Psychol. 2016;150:207–26.

Article
PubMed
PubMed Central
Google Scholar

Odic D, Le Corre M, Halberda J. Children’s mappings between number words and the approximate number system. Cognition. 2015;138:102–21.

Article
PubMed
Google Scholar

Siegler RS, Lortie-Forgues H. An integrative theory of numerical development. Child Dev Perspect. 2014;8(3):144–50.

Article
Google Scholar

Fias W, Verguts T. The mental number line: exact and approximate. Trends Cogn Sci. 2004;8(10):447–8 (**author reply 8–9**).

Article
PubMed
Google Scholar

von Aster MG, Shalev RS. Number development and developmental dyscalculia. Dev Med Child Neurol. 2007;49(11):868–73.

Article
Google Scholar

Wolf S, McCoy DC. The role of executive function and social-emotional skills in the development of literacy and numeracy during preschool: a cross-lagged longitudinal study. Dev Sci. 2019;22(4): e12800.

Article
PubMed
Google Scholar

Berteletti I, Lucangeli D, Piazza M, Dehaene S, Zorzi M. Numerical estimation in preschoolers. Dev Psychol. 2010;46(2):545–51.

Article
PubMed
Google Scholar

Siegler RS, Booth JL. Development of numerical estimation in young children. Child Dev. 2004;75(2):428–44.

Article
PubMed
Google Scholar

Soltész F, Goswami U, White S, Szűcs D. Executive function effects and numerical development in children: behavioural and ERP evidence from a numerical Stroop paradigm. Learn Individ Differ. 2011;21(6):662–71.

Article
Google Scholar

Best JR, Miller PH. A developmental perspective on executive function. Child Dev. 2010;81(6):1641–60.

Article
PubMed
PubMed Central
Google Scholar

Best JR, Miller PH, Jones LL. Executive functions after age 5: changes and correlates. Dev Rev. 2009;29(3):180–200.

Article
PubMed
PubMed Central
Google Scholar

Miyake A, Friedman NP. The nature and organization of individual differences in executive functions: four general conclusions. Curr Dir Psychol Sci. 2012;21(1):8–14.

Article
PubMed
PubMed Central
Google Scholar

Röthlisberger M, Neuenschwander R, Cimeli P, Michel E, Roebers CM. Improving executive functions in 5- and 6-year-olds: Evaluation of a small group intervention in prekindergarten and kindergarten children. Infant Child Dev. 2012;21(4):411–29.

Article
Google Scholar

Kolkman ME, Hoijtink HJA, Kroesbergen EH, Leseman PPM. The role of executive functions in numerical magnitude skills. Learn Individ Differ. 2013;24:145–51.

Article
Google Scholar

Schmitt SA, Geldhof GJ, Purpura DJ, Duncan R, McClelland MM. Examining the relations between executive function, math, and literacy during the transition to kindergarten: a multi-analytic approach. J Educ Psychol. 2017;109(8):1120–40.

Article
Google Scholar

Geary DC, van Marle K. Young children’s core symbolic and nonsymbolic quantitative knowledge in the prediction of later mathematics achievement. Dev Psychol. 2016;52(12):2130–44.

Article
PubMed
Google Scholar

Prager EO, Sera MD, Carlson SM. Executive function and magnitude skills in preschool children. J Exp Child Psychol. 2016;147:126–39.

Article
PubMed
PubMed Central
Google Scholar

Verdine BN, Irwin CM, Golinkoff RM, Hirsh-Pasek K. Contributions of executive function and spatial skills to preschool mathematics achievement. J Exp Child Psychol. 2014;126:37–51.

Article
PubMed
PubMed Central
Google Scholar

Gashaj V, Oberer N, Mast FW, Roebers CM. The relation between executive functions, fine motor skills, and basic numerical skills and their relevance for later mathematics achievement. Early Educ Dev. 2019;30(7):913–26.

Article
Google Scholar

Hawes Z, Moss J, Caswell B, Seo J, Ansari D. Relations between numerical, spatial, and executive function skills and mathematics achievement: a latent-variable approach. Cogn Psychol. 2019;109:68–90.

Article
PubMed
Google Scholar

Wilkey ED, Pollack C, Price GR. Dyscalculia and typical math achievement are associated with individual differences in number-specific executive function. Child Dev. 2020;91(2):596–619.

Article
PubMed
Google Scholar

Bull R, Scerif G. Executive functioning as a predictor of children’s mathematics ability: inhibition, switching, and working memory. Dev Neuropsychol. 2001;19(3):273–93.

Article
PubMed
Google Scholar

Garon N, Bryson SE, Smith IM. Executive function in preschoolers: a review using an integrative framework. Psychol Bull. 2008;134(1):31–60.

Article
PubMed
Google Scholar

Davidson MC, Amso D, Anderson LC, Diamond A. Development of cognitive control and executive functions from 4 to 13 years: evidence from manipulations of memory, inhibition, and task switching. Neuropsychologia. 2006;44(11):2037–78.

Article
PubMed
PubMed Central
Google Scholar

McKenna R, Rushe T, Woodcock KA. Informing the structure of executive function in children: a meta-analysis of functional neuroimaging data. Front Hum Neurosci. 2017;11:154.

Article
PubMed
PubMed Central
Google Scholar

Anderson P. Assessment and development of executive function (EF) during childhood. Child Neuropsychol. 2002;8(2):71–82.

Article
PubMed
Google Scholar

Fuhs MW, Tavassolie N, Wang Y, Bartek V, Sheeks NA, Gunderson EA. Children’s flexible attention to numerical and spatial magnitudes in early childhood. J Cogn Dev. 2021;22(1):22–47.

Article
Google Scholar

Schmitt SA, McClelland MM, Tominey SL, Acock AC. Strengthening school readiness for Head Start children: evaluation of a self-regulation intervention. Early Child Res Q. 2015;30:20–31.

Article
Google Scholar

Spiegel JA, Goodrich JM, Morris BM, Osborne CM, Lonigan CJ. Relations between executive functions and academic outcomes in elementary school children: a meta-analysis. Psychol Bull. 2021;147(4):329–51.

Article
PubMed
Google Scholar

Miyake A, Friedman NP, Emerson MJ, Witzki AH, Howerter A, Wager TD. The unity and diversity of executive functions and their contributions to complex “frontal lobe” tasks: a latent variable analysis. Cogn Psychol. 2000;41(1):49–100.

Article
Google Scholar

Ribner A, Moeller K, Willoughby M, Blair C. Cognitive abilities and mathematical competencies at school entry. Mind Brain Educ. 2018;12(4):175–85.

Article
PubMed
Google Scholar

Harvey HA, Miller GE. Executive function skills, early mathematics, and vocabulary in head start preschool children. Early Educ Dev. 2017;28(3):290–307.

Article
Google Scholar

Schmerold K, Bock A, Peterson M, Leaf B, Vennergrund K, Pasnak R. The relations between patterning, executive function, and mathematics. J Psychol. 2017;151(2):207–28.

Article
PubMed
Google Scholar

Magalhães S, Carneiro L, Limpo T, Filipe M. Executive functions predict literacy and mathematics achievements: the unique contribution of cognitive flexibility in grades 2, 4, and 6. Child Neuropsychol. 2020;26(7):934–52.

Article
PubMed
Google Scholar

Espy KA, McDiarmid MM, Cwik MF, Stalets MM, Hamby A, Senn TE. The contribution of executive functions to emergent mathematic skills in preschool children. Dev Neuropsychol. 2004;26(1):465–86.

Article
PubMed
Google Scholar

Pellizzoni S, Apuzzo GM, De Vita C, Agostini T, Ambrosini M, Passolunghi MC. Exploring EFs and math abilities in highly deprived contexts. Front Psychol. 2020;11:383.

Article
PubMed
PubMed Central
Google Scholar

Melby-Lervåg M, Hulme C. Is working memory training effective? A meta-analytic review. Dev Psychol. 2013;49(2):270–91.

Article
PubMed
Google Scholar

Viterbori P, Usai MC, Traverso L, De Franchis V. How preschool executive functioning predicts several aspects of math achievement in Grades 1 and 3: a longitudinal study. J Exp Child Psychol. 2015;140:38–55.

Article
PubMed
Google Scholar

Traverso L, Viterbori P, Usai MC. Effectiveness of an executive function training in italian preschool educational services and far transfer effects to pre-academic skills. Front Psychol. 2019;10:2053.

Article
PubMed
PubMed Central
Google Scholar

Scionti N, Cavallero M, Zogmaister C, Marzocchi GM. Is cognitive training effective for improving executive functions in preschoolers? A systematic review and meta-analysis. Front Psychol. 2020;10:2812.

Article
PubMed
PubMed Central
Google Scholar

Diamond A, Ling DS. Conclusions about interventions, programs, and approaches for improving executive functions that appear justified and those that, despite much hype, do not. Dev Cogn Neurosci. 2016;18:34–48.

Article
PubMed
Google Scholar

Gilmore C, Cragg L. Chapter 14—the role of executive function skills in the development of children’s mathematical competencies. In: Henik A, Fias W, editors. Heterogeneity of function in numerical cognition. Cambridge: Academic Press; 2018. p. 263–86.

Chapter
Google Scholar

Coolen I, Merkley R, Ansari D, Dove E, Dowker A, Mills A, et al. Domain-general and domain-specific influences on emerging numerical cognition: contrasting uni-and bidirectional prediction models. Cognition. 2021;215: 104816.

Article
PubMed
Google Scholar

Fuhs MW, Nesbitt KT, O’Rear CD. Approximate number system task performance: associations with domain-general and domain-specific cognitive skills in young children. J Numer Cognit. 2018;4(3):590–612.

Article
Google Scholar

Gilmore C, Keeble S, Richardson S, Cragg L. The role of cognitive inhibition in different components of arithmetic. ZDM Math Educ. 2015;47(5):771–82.

Article
Google Scholar

Braeuning D, Hornung C, Hoffmann D, Lambert K, Ugen S, Fischbach A, et al. Long-term relevance and interrelation of symbolic and non-symbolic abilities in mathematical-numerical development: evidence from large-scale assessment data. Cognit Dev. 2021;58: 101008.

Article
Google Scholar

Scalise NR, Ramani GB. Symbolic magnitude understanding predicts preschoolers’ later addition skills. J Cognit Dev. 2021;22:185–202.

Article
Google Scholar

Geary DC, Bailey DH, Hoard MK. Predicting mathematical achievement and mathematical learning disability with a simple screening tool: the number sets test. J Psychoeduc Assess. 2009;27(3):265–79.

Article
PubMed
PubMed Central
Google Scholar

Arán Filippetti V, Richaud MC. A structural equation modeling of executive functions, IQ and mathematical skills in primary students: differential effects on number production, mental calculus and arithmetical problems. Child Neuropsychol. 2017;23(7):864–88.

PubMed
Google Scholar

Wei W, Guo L, Georgiou GK, Tavouktsoglou A, Deng C. Different subcomponents of executive functioning predict different growth parameters in mathematics: evidence from a 4-year longitudinal study with Chinese children. Front Psychol. 2018;9:1037.

Article
PubMed
PubMed Central
Google Scholar

Geary DC. Cognitive predictors of achievement growth in mathematics: a 5-year longitudinal study. Dev Psychol. 2011;47(6):1539–52.

Article
PubMed
PubMed Central
Google Scholar

Hellstrand H, Korhonen J, Räsänen P, Linnanmäki K, Aunio P. Reliability and validity evidence of the early numeracy test for identifying children at risk for mathematical learning difficulties. Int J Educ Res. 2020;102: 101580.

Article
Google Scholar

Gray SA, Reeve RA. Preschoolers’ Dot Enumeration Abilities Are Markers of Their Arithmetic Competence. PLoS ONE. 2014;9(4): e94428.

Article
PubMed
PubMed Central
Google Scholar

Huber S, Klein E, Moeller K, Willmes K. Spatial-numerical and ordinal positional associations coexist in parallel. Front Psychol. 2016;7:438.

Article
PubMed
PubMed Central
Google Scholar

Schneider M, Merz S, Stricker J, De Smedt B, Torbeyns J, Verschaffel L, et al. Associations of number line estimation with mathematical competence: a meta-analysis. Child Dev. 2018;89(5):1467–84.

Article
PubMed
Google Scholar

Cohen Kadosh R, Henik A, Rubinsten O. Are Arabic and verbal numbers processed in different ways? J Exp Psychol Learn Mem Cogn. 2008;34(6):1377–91.

Article
PubMed
Google Scholar

Dadon G, Henik A. Adjustment of control in the numerical Stroop task. Mem Cognit. 2017;45(6):891–902.

Article
PubMed
PubMed Central
Google Scholar

Henik A, Tzelgov J. Is three greater than five: the relation between physical and semantic size in comparison tasks. Mem Cognit. 1982;10(4):389–95.

Article
PubMed
Google Scholar

Buttelmann F, Karbach J. Development and plasticity of cognitive flexibility in early and middle childhood. Front Psychol. 2017;8:1040.

Article
PubMed
PubMed Central
Google Scholar

Wongupparaj P, Kumari V, Morris RG. The relation between a multicomponent working memory and intelligence: the roles of central executive and short-term storage functions. Intelligence. 2015;53:166–80.

Article
Google Scholar

Sauseng P, Klimesch W, Freunberger R, Pecherstorfer T, Hanslmayr S, Doppelmayr M. Relevance of EEG alpha and theta oscillations during task switching. Exp Brain Res. 2006;170(3):295–301.

Article
PubMed
Google Scholar

Bjork IM, Bowyer-Crane C. Cognitive skills used to solve mathematical word problems and numerical operations: a study of 6- to 7-year-old children. Eur J Psychol Educ. 2013;28(4):1345–60.

Article
Google Scholar

Passolunghi MC, Costa HM. Working memory and mathematical learning. In: Fritz A, Hase V, Räsänen P, editors. International handbook of mathematical learning difficulties: from the laboratory to the classroom. Cham: Springer; 2019. p. 407–21.

Chapter
Google Scholar

Kelley K, Preacher KJ. On effect size. Psychol Methods. 2012;17(2):137–52.

Article
PubMed
Google Scholar

Lakens D. Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Front Psychol. 2013;4:863.

Article
PubMed
PubMed Central
Google Scholar

Arbuckle JL. SPSS Amos. 26.0 ed. Chicago: IBM SPSS; 2019.

Fan Y, Chen J, Shirkey G, John R, Wu SR, Park H, et al. Applications of structural equation modeling (SEM) in ecological studies: an updated review. Ecol Process. 2016;5(1):19.

Article
Google Scholar

Schermelleh-Engel K, Moosbrugger H, Müller H. Evaluating the fit of structural equation models: tests of significance and descriptive goodness-of-fit measures. Methods Psychol Res. 2003;8(2):23–74.

Google Scholar

Gao S, Mokhtarian PL, Johnston RA. Nonnormality of data in structural equation models. Transp Res Rec. 2008;2082(1):116–24.

Article
Google Scholar

Montgomery DC, Peck EA, Vining GG. Introduction to linear regression analysis. 3rd ed. New York: Wiley; 2001.

Google Scholar

Göbel SM, Watson SE, Lervåg A, Hulme C. Children’s arithmetic development: it is number knowledge, not the approximate number sense, that counts. Psychol Sci. 2014;25(3):789–98.

Article
PubMed
Google Scholar

van Marle K, Chu FW, Li Y, Geary DC. Acuity of the approximate number system and preschoolers’ quantitative development. Dev Sci. 2014;17(4):492–505.

Article
PubMed
Google Scholar

Gimbert F, Camos V, Gentaz E, Mazens K. What predicts mathematics achievement? Developmental change in 5- and 7-year-old children. J Exp Child Psychol. 2019;178:104–20.

Article
PubMed
Google Scholar

Fuson KC. Relating math words, visual images, and math symbols for understanding and competence. Int J Disabil Dev Educ. 2019;66(2):119–32.

Article
Google Scholar

Daucourt MC, Schatschneider C, Connor CM, Al Otaiba S, Hart SA. Inhibition, updating working memory, and shifting predict reading disability symptoms in a hybrid model: project KIDS. Front Psychol. 2018;9:238.

Article
PubMed
PubMed Central
Google Scholar

Park J, Li R, Brannon EM. Neural connectivity patterns underlying symbolic number processing indicate mathematical achievement in children. Dev Sci. 2014;17(2):187–202.

Article
PubMed
Google Scholar

Shrager J, Siegler RS. SCADS: a model of children’s strategy choices and strategy discoveries. Psychol Sci. 1998;9(5):405–10.

Article
Google Scholar

Siegler RS, Crowley K. The microgenetic method. A direct means for studying cognitive development. Am Psychol. 1991;46(6):606–20.

Article
PubMed
Google Scholar

Ecker UK, Lewandowsky S, Oberauer K, Chee AE. The components of working memory updating: an experimental decomposition and individual differences. J Exp Psychol Learn Mem Cogn. 2010;36(1):170–89.

Article
PubMed
Google Scholar

Passolunghi MC, Pazzaglia F. Individual differences in memory updating in relation to arithmetic problem solving. Learn Individ Differ. 2004;14(4):219–30.

Article
Google Scholar

Passolunghi MC, Siegel LS. Working memory and access to numerical information in children with disability in mathematics. J Exp Child Psychol. 2004;88(4):348–67.

Article
PubMed
Google Scholar

Gebuis T, Reynvoet B. The interplay between nonsymbolic number and its continuous visual properties. J Exp Psychol Gen. 2012;141(4):642–8.

Article
PubMed
Google Scholar

Gevers W, Kadosh RC, Gebuis T. Chapter 18—sensory integration theory: an alternative to the approximate number system. In: Henik A, editor. Continuous issues in numerical cognition. San Diego: Academic Press; 2016. p. 405–18.

Chapter
Google Scholar

Hassler Hallstedt M, Ghaderi A. Tablets instead of paper-based tests for young children? Comparability between paper and tablet versions of the mathematical Heidelberger Rechen Test 1–4. Educ Assess. 2018;23(3):195–210.

Article
Google Scholar

Blumenthal S, Blumenthal Y. Tablet or paper and pen? Examining mode effects on german elementary school students’ computation skills with curriculum-based measurements. Int J Educ Methodol. 2020;6(4):669–80.

Article
Google Scholar

Landerl K. Development of numerical processing in children with typical and dyscalculic arithmetic skills-a longitudinal study. Front Psychol. 2013;4:459.

Article
PubMed
PubMed Central
Google Scholar

Balzer C. Computer-Based Assessments. Office of Assessment, Research, and Data Analysis; 2010.