Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities

Este estudio siguió un enfoque basado en procesos, en el que la variabilidad describe los cambios que ocurren momento a momento. El objetivo de este estudio es explorar las trayectorias intraindividuales del uso conjunto del cardinal numérico y la notación de cantidades. Veintitrés niños en edad pre...

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Autores:: Martínez Mora, Brehinert Alfredo
Guevara, Marlenny

Tipo de recurso:: Article of journal

Fecha de publicación:: 2023

Institución:: Universidad Cooperativa de Colombia

Repositorio:: Repositorio UCC

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repository_id_str
dc.title.none.fl_str_mv	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
title	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
spellingShingle	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities Cardinalidad Variabilidad intra-individual Niños preescolares Diseño microgenético Notaciones Cardinaly Intra-individual variability Preschool children Microgenetic design Notations
title_short	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
title_full	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
title_fullStr	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
title_full_unstemmed	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
title_sort	Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities
dc.creator.fl_str_mv	Martínez Mora, Brehinert Alfredo Guevara, Marlenny
dc.contributor.author.none.fl_str_mv	Martínez Mora, Brehinert Alfredo Guevara, Marlenny
dc.subject.none.fl_str_mv	Cardinalidad Variabilidad intra-individual Niños preescolares Diseño microgenético Notaciones
topic	Cardinalidad Variabilidad intra-individual Niños preescolares Diseño microgenético Notaciones Cardinaly Intra-individual variability Preschool children Microgenetic design Notations
dc.subject.other.none.fl_str_mv	Cardinaly Intra-individual variability Preschool children Microgenetic design Notations
description	Este estudio siguió un enfoque basado en procesos, en el que la variabilidad describe los cambios que ocurren momento a momento. El objetivo de este estudio es explorar las trayectorias intraindividuales del uso conjunto del cardinal numérico y la notación de cantidades. Veintitrés niños en edad preescolar de 4-5 años participaron en el estudio. Los niños asistían a la escuela pública en Cali-Colombia. En cuanto al método, se utilizó un diseño microgenético y una tarea denominada “Dar y anotar un número” para capturar la variabilidad. De la actuación de los niños. La tarea fue una adaptación de la tarea “Dar un número” de LeCorre y Carey (2007). Para el análisis de datos se implementó la técnica de análisis de conglomerados. Los resultados revelaron algunos patrones de las trayectorias intraindividuales del desempeño de los niños: (1) cinco patrones de cardinalidad, (2) cinco patrones de notaciones y (3) varios perfiles conjuntos para “dar” y “anotar” cantidades. En conclusión, nuestros hallazgos sugieren un proceso dinámico de uso conjunto de la cardinalidad y las notaciones, mostrando la coexistencia de diferentes niveles de complejidad.
publishDate	2023
dc.date.accessioned.none.fl_str_mv	2023-08-09T14:49:47Z
dc.date.available.none.fl_str_mv	2023-08-09T14:49:47Z
dc.date.issued.none.fl_str_mv	2023-08-08
dc.type.none.fl_str_mv	Artículo
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dc.identifier.issn.none.fl_str_mv	25870130
dc.identifier.uri.none.fl_str_mv	https://hdl.handle.net/20.500.12494/52374
dc.identifier.bibliographicCitation.none.fl_str_mv	Martínez, B. y Guevara, M. (2022). Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities. Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities, 6 (2), 2070 – 2089
identifier_str_mv	25870130 Martínez, B. y Guevara, M. (2022). Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities. Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities, 6 (2), 2070 – 2089
url	https://hdl.handle.net/20.500.12494/52374
dc.relation.isversionof.none.fl_str_mv	https://www.journalppw.com/index.php/jppw/article/view/13875
dc.relation.ispartofjournal.none.fl_str_mv	Journal of Positive Psychology & Wellbeing
dc.relation.references.none.fl_str_mv	Bassano, D., & van Geert, P. (2007). Modeling continuity and discontinuity in utterance length: a quantitative approach to changes, transitions, and intra-individual variability in early grammatical development. Developmental Science, 10, (5),588-612. https://doi.org/10.1111/j.1467- 7687.2007.00629.x. Bafalluy, M, & Pascale Noël, M. (2008). Does finger training increase young children’s numerical performance. Cortex 44, 368 – 375. Baroody, A. & Wilkins, L. (1999). The development of informal counting, number and arithmetic skills and concepts. Mathematics in the Early Years, 48–65. Bermejo, V. (2005). Microgénesis y cambio cognitivo: Adquisición del cardinal numérico [Microgenesis and cognitive change: Acquisition of the numerical cardinal]. Psicothema Vol. 17, (4) 559 – 562. Bermejo, V, Morales, S, & de Osuna, J. (2004). Supporting children’s development of cardinality understanding. Learning and Instruction, 14, 381-394. Blote, A., Van Otterloo, S., Stevenson, C, & Veenman, M. (2004) Discovery and maintenance of the many-to-one counting strategy in 4-year-olds: A microgenetic study British Journal of developmental psychology, 22, 83 – 102 Brizuela, B., & Cayton, G. (2010). Anotar números desde preescolar hasta segundo grado: el impacto del uso de dos sistemas de representación en la presentación [Writing Numbers from Preschool to Second Grade: The Impact of Using Two Representation Systems on Presentation]. Cultura y Educación, 22 (2), 149 – 167. Cañellas, A. & Rassetto, M. (2013). Representaciones infantiles sobre las notaciones numéricas [Children's representations about numerical notations]. Artículo de la Revista: Tecné, Episteme y Didaxis (TED). N° 33. Universidad Pedagógica Nacional. Bogotá. Colombia Costa, A, Silva, B, Chagas, P, Krinzinger, H, Lonnemaan, J, Willmes, K, Wood, G, & Haase, V. (2011). A hand full of number: a role for offloading in arithmetics learning? Frontiers in psychology, 13 -24 Chentland, E. & Fluck, M. (2007) Children’s Performance on the ‘Give x’ Task: A Microgenetic Analysis of ‘Counting’ and ‘Grabbing’ Behaviour. Infant and child development, 16, 35–51. Chu, F, VanMarle, K, & Geary, D. (2015). Early numerical foundations of young children mathematical development. Journal of Experimental Child Psychology, 132, 205– 212. Crollen,V, Seron, X, & Pascale Noël, M. (2011). Is finger –counting necessary for the development of arithmetic abilities? Frontiers in Psychology, 25 -27 Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42. Dowker. A, (2008). Individual differences in numerical abilities in preschoolers. Developmental Science 11, (5) 650–654. Escudero, A., Rodríguez, P., Lago, O., & Enesco, I. (2015). A 3-year longitudinal study of children’s comprehension of counting: ¿Do they recognize the optional nature of nonessential counting features? Cognitive Development, 33, 73-83. Fischer, K., & Bidell, T. (1998) Developmental of psychological structures in action and thought. In W. Damon and R.M. Lerner (Eds.). Handbook of Child Psychology. Vol.1: Theorical Models of Human Development (467 -561). New York: john Wiley and Sons. Fleiss, J. (1981). Statistical Methods for Rates and Proportions. London, Estados Unidos: John Wiley& Sons. Geary, D. (2006) Development of mathematical understanding. InD. Kuhl& R. S. Siegler (Vol. Eds.), Cognition, perception,and language, Vol 2. 777-810. W. Damon (Gen. Ed.), Handbook of child psychology (6th Ed.). New York: John Wiley & Sons. Geary, D &Moore, A. (2016). Cognitive and brain systems underlying early mathematicaldevelopment. Brain research, 1 – 29. Geary, D,& VanMarle, K.(2018). Growth of symbolic number knowledge accelerates after children understand cardinality. Cognition, 1- 10. Geary, D, VanMarle, K, Chu, F, & Hoard, M. (2019). Predicting age of becoming a cardinal principle knower. Journal of educational psychologic 111, 2), 256- 267. Gelman, R. & Gallistel, C. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43 – 74. Gelman, R. (1978). Counting in the preschooler: What does and does not develop. In R. S. Siegler (Ed.). Children's thinking: What develops? (pp. 213-240). Hillsdale, N. J: Erlbaum. Gibson, D. J., Gunderson, E. A., & Levine, S.C. (2020). Causal effects of parent number talk on preschoolers’ number knowledged. Child development, 91 (6) e1162-e1177. Gillian, M. & Lewis, B. (1993). An analysis of the relation between sequence counting and knowledge of place value in the early years of school. Mathematics Education Journal, 5, (2), 94 – 106. Hayes, A. M., Laurenceau, J.-P., Feldman, G., Strauss, J. L., & Cardaciotto, L. (2007). Change is Not Always Linear: The Study of Nonlinear and Discontinuous Patterns of Change in Psychotherapy. Clinical Psychology Review, 27, (6), 715–723. http://doi.org/10.1016/j.cpr.2007.01.008. 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. Lafay, A, Thevenot, C, Castel, C & Fayol, M. (2013). The role of fingers in number processing in young children. Frontiers in Psycholgy, 1 – 8. LeCorre, M. & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual source of the verbal counting principles. Cognition, 105, 395 - 438.0 LeCorre, M. & Carey, S. (2008). Why the verbal counting principles are constructedout of representations of small sets of individuals: A reply to Gallistel. Cognition, 107, 650-662. Lee, K., Karmiloff-Smith, A., Cameron, C., & Dodsworth, P. (1998). Notational adaptation in children. Canadian Journal of Behavioural Science,30, (3),159-171 Lerner, D. & Sadovsky, P. (1994). El sistema de numeración: un problema didáctico [The numbering system: a didactic problem]. in C. Parra and J. Saiz (Eds.), Didáctica de las matemáticas, 95-84. Paidós. Libertus, M, Feigenson, L, & Halberda, J. (2013). Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities. Journal of Experimental Child Psychology, 116, 829- 838. Martinez, B, (2018). Informe de investigación del proyecto cambio cognitivo en habilidades numéricas tempranas [Project research report cognitive change in early numerical skills] (Report N° 1799). Universidad Cooperativa de Colombia Sede – Cali. Morra, S., Gobbo, C., Zopito, M., & Sheese,R. (2008). Cognitive Development: Neo- Piagetian Perspectives. New York, Estados Unidos: Psychology Press. Munn, P. (2001). Symbolic function in presscholers. Editado por Chris Donlan, The development of Mathematical skills, 47–71. University College London, UK. Psychology Press. Nesselroade, J. R., & Salthouse, T. A. (2004). Methodological and theoretical implications of intraindividual variability in perceptual-motor performance. The Journals of Gerontology Series B: Psychological Sciences and Social Sciences, 59, (2), 49-55. O’Rear, C & McNeil, N.(2019).Improved set-size labeling mediates the effect of a counting intervention on children’s understanding of cardinality . Developmental Science, 22 (6), 1-13. Paliwal, V , & Baroody, A. J. (2018). How best to teach the cardinality principle? Early Childhood Research Quarterly, 44, 152-160. Piazza, M, Mechelli, A, Butterworth, B, & Price, C. (2002). Are subitizing and counting implemented as separate or functionally overlapping processes? Neuroimagen, 15, 435-446. Posid, T, & Cordes, S. (2015). Verbal counting moderates perceptual biases found in children’s cardinality judgments. Journal of Cognition & Development, 16, (4), 621- 637. Rabbitt P, Osman P, Moore B, & Stollery B. (2001). There are stable individual differences in performance variability, both from moment to moment and from day to day. Quarterly Journal of Experimental Psychology: 54, 981–1003 Rakotomalala, R. (2005). TANAGRA: a free software for research and academic purposes. In proceedings of EGC (Vol. 2, pp.697-702). Rodríguez, J., Martí, E., & Salsa, A. (2018). Symbolic representations and cardinal knowledge in 3- and 4-year-old children. Cognitive Development, 48, 235-243. Sarnecka, B, & Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition,108, 662-674. Sarnecka, B, & Lee, M. (2009). Levels of number knowledge during early childhood. Journal of experimental child psychology, 103, 325 -337. Saxton, M, & Cakir, K. (2006). Counting – on, trading and partitioning: Effects of training and prior knowledge on performance on base – 10 tasks. Child Development, 77, (3), 767–785. Scheuer, N, Santamaria, F, & Echenique, M.(2016). Exploring children’s thinking with and about numbers from a resource – based approach. Early child Development and Care. 1-15. DOI:10.1080/03004430.2016. Scheuer, N, De la Cruz, M, & Iparraguirre, M. (2010). El aprendizaje de distintos dominios notacionales según niños de preescolar y primer grado [The learning of different notational domains according to children of preschool and first grade]. Revista latinoamericana de ciencias sociales, niñez y juventud. Vol 8 (2). 1083 – 1097. Scheuer, N, Sinclair, A, Merlo de Rivas, S, & Tièche, C. (2000). Cuando ciento setenta y uno se escribe10071: niños de 5 a 8 años produciendo numerales [When one hundred seventy-one is written 10071: children from 5 to 8 years old producing numerals]. Infancia y Aprendizaje, 90, 31–50. Siegler, R.S. (1994). Cognitive variability: A key to understanding cognitive development. Current Directions in Psychological Science,3, 1-5 Siegler, R.S. (2000). The rebirth of children`s learning. Child development 71 (1), 26-35. Siegler, R. S. (2006). Microgenetic analysesof learning. En Handbook of child psychologic (pp. 464-504). Siegler, R.S. (2007). Cognitive variability. Developmental Science, 10, (1), 104 -109. Siegler, R.S. & Crowley, K. (1991). The microgenetic method: a direct means for studying cognitive development. American Psychologist, 46, 606-620. Sinclair, A., & Scheuer, N. (1993). Understanding the Written Number System: 6 Year- Olds in Argentina and Switzerland. Educational Studies in Mathematics, 24, 2, 199-221. Thelen, E & Smith, L. (1994). A Dynamic Systems Approach to the Development of Cognition and Action. Cambridge, MA, US: The MIT Press. Tolchinsky, L. & Karmiloff – Smith, A. (1993). Las restricciones del conocimiento notacional [The restrictions of notational knowledge]. Infancia y Aprendizaje, 62, 19 – 51. Vallacher R, Read S & Nowak, A. (2002). The dynamical perspective in personality and social psychology. Personality & Social Psychology Review, 6, 264–273. van Dijk, M., & van Geert, P. (2014). The nature and meaning of intraindividual variability in development in the early life span. En Handbook of intraindividual variability across the life span (pp. 57-78). Routledge. Van Geert, P., & van Dijk, M. (2002). Focus on variability: New tools to study intraindividual variability in developmental data. Infant Behavior and Development 25, 340–374. DOI: 10.1016/ S0163-638300140- 6. Wynn, K. (1990). Children’s understanding of counting. Cognition, 36, 155–193. Wynn, K. (1992). Children’s acquisition of number words and the counting system. Cognitive Psychologic, 24, 220–251.
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spelling	Martínez Mora, Brehinert AlfredoGuevara, Marlenny6 (2)2023-08-09T14:49:47Z2023-08-09T14:49:47Z2023-08-0825870130https://hdl.handle.net/20.500.12494/52374Martínez, B. y Guevara, M. (2022). Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities. Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities, 6 (2), 2070 – 2089Este estudio siguió un enfoque basado en procesos, en el que la variabilidad describe los cambios que ocurren momento a momento. El objetivo de este estudio es explorar las trayectorias intraindividuales del uso conjunto del cardinal numérico y la notación de cantidades. Veintitrés niños en edad preescolar de 4-5 años participaron en el estudio. Los niños asistían a la escuela pública en Cali-Colombia. En cuanto al método, se utilizó un diseño microgenético y una tarea denominada “Dar y anotar un número” para capturar la variabilidad. De la actuación de los niños. La tarea fue una adaptación de la tarea “Dar un número” de LeCorre y Carey (2007). Para el análisis de datos se implementó la técnica de análisis de conglomerados. Los resultados revelaron algunos patrones de las trayectorias intraindividuales del desempeño de los niños: (1) cinco patrones de cardinalidad, (2) cinco patrones de notaciones y (3) varios perfiles conjuntos para “dar” y “anotar” cantidades. En conclusión, nuestros hallazgos sugieren un proceso dinámico de uso conjunto de la cardinalidad y las notaciones, mostrando la coexistencia de diferentes niveles de complejidad.This study followed a process-based approach, in which variability describe the changes that occurs moment-to-moment. The aim of this study is to explore the intra-individual trajectories of the joint use of the numerical cardinal and the notation of quantities. Twenty-three preschool children of 4-5 years old participated on the study. The children were attending public school in Cali-Colombia. Regarding the method, a microgenetic design and a task called “Give and Note a Number” was used to capture the variability of the children’s performance. The task was an adaptation of the task “Give a Number” by LeCorre and Carey (2007). The technique of cluster analysis was implemented for data analysis. The results revealed some patterns of the intra-individual trajectories of the children’s performance: (1) five patterns of cardinality, (2) five patterns of notations, and (3) several joint profiles to“give” and “note” quantities. In conclusion, our findings suggest a dynamic process of the joint use of the cardinality and notations,showing the co-existence of different levels of complexity.brehmert.martinez@campusucc.edu.co2070-2089Universidad Cooperativa de Colombia, Facultad de Ciencias Sociales, Psicología, CaliPsicologíaCalihttps://www.journalppw.com/index.php/jppw/article/view/13875Journal of Positive Psychology & WellbeingBassano, D., & van Geert, P. (2007). Modeling continuity and discontinuity in utterance length: a quantitative approach to changes, transitions, and intra-individual variability in early grammatical development. Developmental Science, 10, (5),588-612. https://doi.org/10.1111/j.1467- 7687.2007.00629.x.Bafalluy, M, & Pascale Noël, M. (2008). Does finger training increase young children’s numerical performance. Cortex 44, 368 – 375.Baroody, A. & Wilkins, L. (1999). The development of informal counting, number and arithmetic skills and concepts. Mathematics in the Early Years, 48–65.Bermejo, V. (2005). Microgénesis y cambio cognitivo: Adquisición del cardinal numérico [Microgenesis and cognitive change: Acquisition of the numerical cardinal]. Psicothema Vol. 17, (4) 559 – 562.Bermejo, V, Morales, S, & de Osuna, J. (2004). Supporting children’s development of cardinality understanding. Learning and Instruction, 14, 381-394.Blote, A., Van Otterloo, S., Stevenson, C, & Veenman, M. (2004) Discovery and maintenance of the many-to-one counting strategy in 4-year-olds: A microgenetic study British Journal of developmental psychology, 22, 83 – 102Brizuela, B., & Cayton, G. (2010). Anotar números desde preescolar hasta segundo grado: el impacto del uso de dos sistemas de representación en la presentación [Writing Numbers from Preschool to Second Grade: The Impact of Using Two Representation Systems on Presentation]. Cultura y Educación, 22 (2), 149 – 167.Cañellas, A. & Rassetto, M. (2013). Representaciones infantiles sobre las notaciones numéricas [Children's representations about numerical notations]. Artículo de la Revista: Tecné, Episteme y Didaxis (TED). N° 33. Universidad Pedagógica Nacional. Bogotá. ColombiaCosta, A, Silva, B, Chagas, P, Krinzinger, H, Lonnemaan, J, Willmes, K, Wood, G, & Haase, V. (2011). A hand full of number: a role for offloading in arithmetics learning? Frontiers in psychology, 13 -24Chentland, E. & Fluck, M. (2007) Children’s Performance on the ‘Give x’ Task: A Microgenetic Analysis of ‘Counting’ and ‘Grabbing’ Behaviour. Infant and child development, 16, 35–51.Chu, F, VanMarle, K, & Geary, D. (2015). Early numerical foundations of young children mathematical development. Journal of Experimental Child Psychology, 132, 205– 212.Crollen,V, Seron, X, & Pascale Noël, M. (2011). Is finger –counting necessary for the development of arithmetic abilities? Frontiers in Psychology, 25 -27Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.Dowker. A, (2008). Individual differences in numerical abilities in preschoolers. Developmental Science 11, (5) 650–654.Escudero, A., Rodríguez, P., Lago, O., & Enesco, I. (2015). A 3-year longitudinal study of children’s comprehension of counting: ¿Do they recognize the optional nature of nonessential counting features? Cognitive Development, 33, 73-83.Fischer, K., & Bidell, T. (1998) Developmental of psychological structures in action and thought. In W. Damon and R.M. Lerner (Eds.). Handbook of Child Psychology. Vol.1: Theorical Models of Human Development (467 -561). New York: john Wiley and Sons.Fleiss, J. (1981). Statistical Methods for Rates and Proportions. London, Estados Unidos: John Wiley& Sons.Geary, D. (2006) Development of mathematical understanding. InD. Kuhl& R. S. Siegler (Vol. Eds.), Cognition, perception,and language, Vol 2. 777-810. W. Damon (Gen. Ed.), Handbook of child psychology (6th Ed.). New York: John Wiley & Sons.Geary, D &Moore, A. (2016). Cognitive and brain systems underlying early mathematicaldevelopment. Brain research, 1 – 29.Geary, D,& VanMarle, K.(2018). Growth of symbolic number knowledge accelerates after children understand cardinality. Cognition, 1- 10.Geary, D, VanMarle, K, Chu, F, & Hoard, M. (2019). Predicting age of becoming a cardinal principle knower. Journal of educational psychologic 111, 2), 256- 267.Gelman, R. & Gallistel, C. (1992). Preverbal and verbal counting and computation. Cognition, 44, 43 – 74.Gelman, R. (1978). Counting in the preschooler: What does and does not develop. In R. S. Siegler (Ed.). Children's thinking: What develops? (pp. 213-240). Hillsdale, N. J: Erlbaum.Gibson, D. J., Gunderson, E. A., & Levine, S.C. (2020). Causal effects of parent number talk on preschoolers’ number knowledged. Child development, 91 (6) e1162-e1177.Gillian, M. & Lewis, B. (1993). An analysis of the relation between sequence counting and knowledge of place value in the early years of school. Mathematics Education Journal, 5, (2), 94 – 106.Hayes, A. M., Laurenceau, J.-P., Feldman, G., Strauss, J. L., & Cardaciotto, L. (2007). Change is Not Always Linear: The Study of Nonlinear and Discontinuous Patterns of Change in Psychotherapy. Clinical Psychology Review, 27, (6), 715–723. http://doi.org/10.1016/j.cpr.2007.01.008.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.Lafay, A, Thevenot, C, Castel, C & Fayol, M. (2013). The role of fingers in number processing in young children. Frontiers in Psycholgy, 1 – 8.LeCorre, M. & Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual source of the verbal counting principles. Cognition, 105, 395 - 438.0LeCorre, M. & Carey, S. (2008). Why the verbal counting principles are constructedout of representations of small sets of individuals: A reply to Gallistel. 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Variability in the acquisition of number in preschool children: an approach from the cardinal number and the notation of quantities

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