Domain-specific and domain-general precursors of informal mathematical thinking in Chilean preschoolers
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In this study, informal mathematical thinking was explored by assessing domain-specific and domain-general precursors of mathematical achievement. Specifically, the study focused on these precursors in a sample of Chilean boys and girls around the age of four, from public schools that serve populations with high social vulnerability (N= 137). Our findings indicate that both domain-specific and domain-general precursors are important in the development of informal mathematical thinking. Our general multiple regression model explains 48.4% of the variability of the scores obtained in the TEMA 3 instrument. The main precursor of the model, in order of importance, are non-symbolic comparison, symbolic comparison, short-term verbal memory, processing speed and visuospatial working memory. Likewise, except for the doubletask and the knowledge of concepts, no significant differences were observed the explanatory models when comparing boys and girls. These findings support the need for systematic support and monitoring practices in these areas in initial educational cycles, in order to reduce and avoid possible difficulties in school mathematics.
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Cerda , G., Pérez , C., & Chandía , E. (2021). Domain-specific and domain-general precursors of informal mathematical thinking in Chilean preschoolers. Psychology, Society & Education, 13(3), 93–105. Retrieved from https://journals.uco.es/psye/article/view/14009
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References
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Aunio, P., Heiskari, P., van Luit, J., y Vuorio, J. (2015). The development of early numeracy skills in kindergarten in low-, average- and high-performance groups. Journal of Early Childhood Research, 13, 3-16. https://doi.org/10.1177/1476718
Bleses, D., Makransky, G., Dale, P.S., Højen, A., y Ari, B.A. (2016). Early productive vocabulary predicts academic achievement 10 years later. Applied Psycholinguistics, 37(6), 1461-1476. https://doi.org/10.1017/S0142716416000060
Bull, R., y Lee, K. (2014). Executive functioning and mathematics achievement. Child Development Perspectives, 8(1), 36-41.
Cai, D., Zhang, L., Li Y., Wei, W., y Georgiou, G. (2018) The role of approximate number system in different mathematics skills across grades. Frontiers in Psychology, 9 (1733), 1-10. https://doi.org/10.3389/fpsyg.2018.01733
Cerda, G.A., Pérez, C., y Ortega, R. (2014). Relationship between early mathematical competence, gender and social background in chilean elementary school population. Anales de Psicología, 30(3), 1006-1013. https://doi.org/10.6018/analesps.30.3.152891
Cerda, G., Aragón, E., Pérez, C., Navarro, J.I., y Aguilar, M. (2018). The open algorithm based on numbers (ABN) method: an effective instructional approach to domain-specific precursors of arithmetic development. Frontiers in Psychology, 9 (1811), 1-12. https://doi.org/10.3389/fpsyg.2018.01811
Cerda, G., Pérez, C., Navarro, J., Aguilar, M., Casas, J., y Aragón, E. (2015) Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school. Frontiers in Psychology, 6 (1363), 1-10. https://doi.org/10.3389/fpsyg.2015.01363
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Geary, D.C., Nicholas, A., Li, Y., y Sun, J. (2017). Developmental change in the influence of domain-general abilities and domain-specific knowledge on mathematics achievement: An eight-year longitudinal study. Journal of Educational Psychology, 109(5), 680-693. https://doi.org/10.1037/edu0000159
Ginsburg, H., Baroody, A.J., del Río, M.C.N., y Guerra, I.L. (2007). TEMA-3: Test de competencia matemática básica. [Test of early mathematics ability]. TEA.
Guzmán, B., Rodríguez, C., y Ferreira, R. (2021). Longitudinal performance in basic numerical skills mediates the relationship between socio-economic status and mathematics anxiety: evidence from Chile. Frontiers in Psychology, 11(3983), 1-11. https://doi.org/10.3389/fpsyg.2020.611395
Harvey, H.A., y Miller, G.E. (2017). Executive function skills, early mathematics, and vocabulary in head start preschool children. Early Education and Development, 28(3), 290-307. https://doi.org/10.1080/10409289.2016.1218728
Ivanovic, R., Forno, H., Durán, M., Hazbún, J., Castro, C., y Ivanovic, D. (2000). Estudio de la capacidad intelectual (test de matrices progresivas de Raven) en escolares chilenos de 5 a 18 años. I. antecedentes generales, normas y recomendaciones. Revista de Psicología General y Aplicada, 53(1) 5-30.
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Kersey, A., Braham, E., Csumitta, K., Libertus, M., y Cantlon, J. (2018). No intrinsic gender differences in children’s earliest numerical abilities. Npj Science Learn, 3(12), 1-10. https://doi.org/10.1038/s41539-018-0028-7
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Lyons, I.M., Price, G.R., Vaessen, A., Blomert, L., y Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714-726. https://doi.org/10.1111/desc.12152
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Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., y De Smedt, B. (2017). Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis. Developmental Science, 20(3), e12372https://doi.org/10.1111/desc.12372
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Aunio, P., y Räsänen, P. (2016). Core numerical skills for learning mathematics in children aged five to eight years–A working model for educators. European Early Childhood Education Research Journal, 24(5), 684-704. https://doi.org/10.1080/1350293X.2014.996424
Aunio, P., Heiskari, P., van Luit, J., y Vuorio, J. (2015). The development of early numeracy skills in kindergarten in low-, average- and high-performance groups. Journal of Early Childhood Research, 13, 3-16. https://doi.org/10.1177/1476718
Bleses, D., Makransky, G., Dale, P.S., Højen, A., y Ari, B.A. (2016). Early productive vocabulary predicts academic achievement 10 years later. Applied Psycholinguistics, 37(6), 1461-1476. https://doi.org/10.1017/S0142716416000060
Bull, R., y Lee, K. (2014). Executive functioning and mathematics achievement. Child Development Perspectives, 8(1), 36-41.
Cai, D., Zhang, L., Li Y., Wei, W., y Georgiou, G. (2018) The role of approximate number system in different mathematics skills across grades. Frontiers in Psychology, 9 (1733), 1-10. https://doi.org/10.3389/fpsyg.2018.01733
Cerda, G.A., Pérez, C., y Ortega, R. (2014). Relationship between early mathematical competence, gender and social background in chilean elementary school population. Anales de Psicología, 30(3), 1006-1013. https://doi.org/10.6018/analesps.30.3.152891
Cerda, G., Aragón, E., Pérez, C., Navarro, J.I., y Aguilar, M. (2018). The open algorithm based on numbers (ABN) method: an effective instructional approach to domain-specific precursors of arithmetic development. Frontiers in Psychology, 9 (1811), 1-12. https://doi.org/10.3389/fpsyg.2018.01811
Cerda, G., Pérez, C., Navarro, J., Aguilar, M., Casas, J., y Aragón, E. (2015) Explanatory model of emotional-cognitive variables in school mathematics performance: a longitudinal study in primary school. Frontiers in Psychology, 6 (1363), 1-10. https://doi.org/10.3389/fpsyg.2015.01363
Clearman, J., Klinger, V., y Szűcs, D. (2017). Visuospatial and verbal memory in mental arithmetic. The Quarterly Journal of Experimental Psychology, 70(9), 1837-1855. https://doi.org/10.1080/17470218.2016.1209534
Costa, H.M., Nicholson, B., Donlan, C., y Van Herwegen, J. (2018). Low performance on mathematical tasks in preschoolers: the importance of domain‐general and domain‐specific abilities. Journal of Intellectual Disability Research, 62(4), 292-302. https://doi.org/10.1111/jir.12465
Cragg, L., Richardson, S., Hubber, P.J., Keeble, S., y Gilmore, C. (2017). When is working memory important for arithmetic? The impact of strategy and age. PloS one, 12(12), e0188693. https://doi.org/10.1371/journal.pone.0188693
Decker, S.L., y Roberts, A.M. (2015). Specific cognitive predictors of early math problem solving. Psychology in the Schools, 52(5), 477-488. https://doi.org/10.1002/pits.21837
del Río, M.F., y Strasser, K. (2013). Preschool children’s beliefs about gender differences in academic skills. Sex Roles, 68, 231-238. https://doi.org/10.1007/s11199-012-0195-6
Fawcett, A.J., y Nicholson, R. (2013). DST-J. Test para la detección de la dislexia en niños. [DST-J. The dyslexia screening test – Junior]. TEA.
Formoso, J., Injoque-Ricle, I., Barreyro, J., Calero, A., Jacubovich, S., y Burín, D. (2018). Mathematical cognition, working memory, and processing speed in children. Cognition, Brain, Behavior. An Interdisciplinary Journal, 22(2), 59-86. https://doi.org/10.24193/cbb.2018.22.05
Garon-Carrier, G., Boivin, M., Lemelin, J.P., Kovas, Y., Parent, S., Séguin, J., y Dionne, G. (2018). Early developmental trajectories of number knowledge and math achievement from 4 to 10 years: Low-persistent profile and early-life predictors. Journal of School Psychology, 68, 84-98. https://doi.org/10.1016/j.jsp.2018.02.004
Geary, D.C., Nicholas, A., Li, Y., y Sun, J. (2017). Developmental change in the influence of domain-general abilities and domain-specific knowledge on mathematics achievement: An eight-year longitudinal study. Journal of Educational Psychology, 109(5), 680-693. https://doi.org/10.1037/edu0000159
Ginsburg, H., Baroody, A.J., del Río, M.C.N., y Guerra, I.L. (2007). TEMA-3: Test de competencia matemática básica. [Test of early mathematics ability]. TEA.
Guzmán, B., Rodríguez, C., y Ferreira, R. (2021). Longitudinal performance in basic numerical skills mediates the relationship between socio-economic status and mathematics anxiety: evidence from Chile. Frontiers in Psychology, 11(3983), 1-11. https://doi.org/10.3389/fpsyg.2020.611395
Harvey, H.A., y Miller, G.E. (2017). Executive function skills, early mathematics, and vocabulary in head start preschool children. Early Education and Development, 28(3), 290-307. https://doi.org/10.1080/10409289.2016.1218728
Ivanovic, R., Forno, H., Durán, M., Hazbún, J., Castro, C., y Ivanovic, D. (2000). Estudio de la capacidad intelectual (test de matrices progresivas de Raven) en escolares chilenos de 5 a 18 años. I. antecedentes generales, normas y recomendaciones. Revista de Psicología General y Aplicada, 53(1) 5-30.
Jara, N., y Troncoso, J. (2014). Validación test de matrices progresivas de Raven escala coloreada, en escolares de la ciudad de Chillán. Tesis para optar al grado de Psicólogo. Universidad del Bío Bío. http://repobib.ubiobio.cl/jspui/handle/123456789/204
Jordan, N.C., y Dyson, N. (2016). Catching math problems early: findings from the number sense intervention project. En A. Henik, (Ed), Continuous Issues in Numerical Cognition (pp. 59-79). Elsevier Academic Press. https://doi.org/10.1016/B978-0-12-801637-4.00003-2
Kersey, A., Braham, E., Csumitta, K., Libertus, M., y Cantlon, J. (2018). No intrinsic gender differences in children’s earliest numerical abilities. Npj Science Learn, 3(12), 1-10. https://doi.org/10.1038/s41539-018-0028-7
Lanfranchi, S., Cornoldi, C., y Vianello, R. (2004). Verbal and visuo-spatial working memory deficits in children with Down syndrome. American Journal on Mental Retardation, 109(6), 456-466.
Lyons, I.M., Price, G.R., Vaessen, A., Blomert, L., y Ansari, D. (2014). Numerical predictors of arithmetic success in grades 1-6. Developmental Science, 17(5), 714-726. https://doi.org/10.1111/desc.12152
Montoya, M., Susperreguy, M., Dinarte, L., Morrison, F., San Martín, E., Rojas-Barahona, C., y Förster, C. (2019). Executive function in chilean preschool children: do short-term memory, working memory, and response inhibition contribute differentially to early academic skills? Early Childhood Research Quarterly, 46, 187-200. https://doi.org/10.1016/j.ecresq.2018.02.009.
Nguyen, T., Watts, T.W., Duncan, G.J., Clements, D.H., Sarama, J.S., Wolfe, C., y Spitler, M.E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement? Early Childhood Research Quarterly, 36, 550-560. https://doi.org/10.1016/J.ECRESQ.2016.02.003
Nosworthy, N., Bugden, S., Archibald, L., Evans, B., y Ansari, D. (2013). A two-minute paper-and-pencil test of symbolic and non-symbolic numerical magnitude processing explains variability in primary school children's arithmetic competence. PloS one, 8(7), e67918. https://doi.org/10.1371/journal.pone.0067918
Paliwal, V., y Baroody, A.J. (2018). How best to teach the cardinality principle? Early Childhood Research Quarterly, 44, 152-160. https://doi.org/10.1016/j.ecresq.2018.03.012
Passolunghi, M.C., y Lanfranchi, S. (2012). Domain-specific and domain-general precursors of mathematical achievement: a longitudinal study from kindergarten to first grade. British Journal of Educational Psychology, 82, 42-63. https://doi.org/10.1111/j.2044-8279.2011.02039.x
Passolunghi, M.C., Lanfranchi, S., Altoè, G., y Sollazzo, N. (2015). Early numerical abilities and cognitive skills in kindergarten children. Journal of Experimental Child Psychology, 135, 25-42. https://doi.org/10.1016/j.jecp.2015.02.001
Price, G., y Wilkey, E. (2017). Cognitive mechanisms underlying the relation between nonsymbolic and symbolic magnitude processing and their relation to math. Cognitive Development, 44, 139-149. https://doi.org/10.1016/j.cogdev.2017.09.003
Purpura, D.J., Day, E., Napoli, A.R., y Hart, S.A. (2017). Identifying domain-general and domain-specific predictors of low mathematics performance: a classification and regression tree analysis. Journal of Numerical Cognition, 3(2), 365-399. https://doi.org/10.5964/jnc.v3i2.53
Raghubar, K., y Barnes, M. (2017). Early numeracy skills in preschool-aged children: a review of neurocognitive findings and implications for assessment and intervention. Clinical Neuropsychological, 31(2), 329-351. https://doi.org/10.1080/13854046.2016.1259387
Raven, J., Court, H., y Raven, J. (1996) Test de matrices progresivas: escalas coloreada, general y avanzada (2ª ed.). Paidós.
Rodríguez, C., González, S., Peake, C., Sepúlveda, F., y Hernández-Cabrera, J. (2020). Number processing skill trajectories in children with specific language impairment. Psicothema, 32 (1), 92-99. https://doi.org/10.7334/psicothema2019.104
Salminen, J., Koponen, T., y Tolvanen, A. (2018) Individuality in the early number skill components underlying basic arithmetic skills. Frontiers in Psychology, 9(1056), 1-11. https://doi.org/10.3389/fpsyg.2018.01056
Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., y De Smedt, B. (2017). Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: a meta‐analysis. Developmental Science, 20(3), e12372https://doi.org/10.1111/desc.12372
Sepúlveda, F., Rodríguez, C., y Peake, C. (2019). Differences and associations in symbolic and non-symbolic early numeracy competencies of chilean kinder grade children, considering socioeconomic status of schools. Early Education and Development, 31(1), 1-15. https://doi.org/10.1080/10409289.2019.1609819
Siegenthaler, R., Miranda, A., Mercader, J., y Presentación, Mª.J. (2017). Habilidades matemáticas iniciales y dificultades matemáticas persistentes. International Journal of Developmental and Educational Psychology 3(1), 233-241, https://doi.org/10.17060/ijodaep.2017.n1.v3.992
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