Differences and Associations in Symbolic and Non-Symbolic Early Numeracy Competencies of Chilean Kinder Grade Children, considering Socioeconomic Status of Schools

References

• Alloway, T. P., Alloway, R. G., & Wootan, S. (2014). Journal of experimental child home sweet home : Does where you live matter to working memory and other cognitive skills? Journal of Experimental Child Psychology, 124, 124–131. doi:10.1016/j.jecp.2013.11.012
   PubMed Web of Science ®Google Scholar
• Anders, Y., Grosse, C., Rossbach, H.-G., Ebert, S., & Weinert, S. (2013). Preschool and primary school influences on the development of children’s early numeracy skills between the ages of 3 and 7 years in Germany. School Effectiveness and School Improvement, 24(2), 195–211. doi:10.1080/09243453.2012.749794
   Web of Science ®Google Scholar
• Anders, Y., Rossbach, H.-G., Weinert, S., Ebert, S., Kuger, S., Lehrl, S., & von Maurice, J. (2012). Home and preschool learning environments and their relations to the development of early numeracy skills. Early Childhood Research Quarterly, 27(2), 231–244. doi:10.1016/j.ecresq.2011.08.003
   Web of Science ®Google Scholar
• Ansari, D. (2008). Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience, 9, 278–291. doi:10.1038/nrn2334
   PubMed Web of Science ®Google Scholar
• Aunio, P., Mononen, R., Ragpot, L., & Tormanen, M. (2015). Early numeracy performance of South African school beginners. South African Journal of Childhood Education, 6(1), 1–8. doi:10.4102/sajce.v6i1.496
   Google Scholar
• Aunio, P., & 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. doi:10.1080/1350293X.2014.996424
   Web of Science ®Google Scholar
• Banerjee, P. A. (2016). A systematic review of factors linked to poor academic performance of disadvantaged students in science and maths in schools. Cogent Education, 3(1), 1–17. doi:10.1080/2331186X.2016.1178441
   Web of Science ®Google Scholar
• Blevins-Knabe, B. (2016). Early mathematical development: How the home environment matters. In B. Blevins-Knabe & A. M. Austin (Eds.), Early childhood mathematics skill development in the home environment (pp. 7–28). Switzerland: Springer International. doi:10.1007/978-3-319-43974-7
   Google Scholar
• Brandt, N. (2010). Chile: Climbing on Giants’ shoulders: Better schools for all Chilean children. OECD Economics Department Working Papers, (784), 1–44. doi:10.1787/5kmd41g7x9g0-en
   Google Scholar
• Bravo Sanzana, M., Salvo Garrido, S., & Muñoz Poblete, C. (2015). Profiles of Chilean students according to academic performance in mathematics: An exploratory study using classification trees and random forests. Studies in Educational Evaluation, 44, 50–59. doi:10.1016/j.stueduc.2015.01.002
   Web of Science ®Google Scholar
• Castro, D., Estévez, N., Gómez, D., & Dartnell, P. R. (2017). Reliability and validity of nonsymbolic and symbolic comparison tasks in school-aged children. Spanish Journal of Psychology, 1–14. doi:10.1017/sjp.2017.68
   Web of Science ®Google Scholar
• Cerda, G. A., & Pérez, C. (2014). Relationship between early mathematical competence, gender and social background in Chilean elementary school population. [Relacion entre los niveles de competencia matematica temprana, genero y extraccion social en la poblacion escolar primaria en Chile]. Anales de Psicología, 30(3), 1006–1013. doi:10.1016/j.cedpsych.2006.09.002\rhttp://dx.doi.org/10.6018/analesps.30.3.152891
   Web of Science ®Google Scholar
• 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
   PubMed Web of Science ®Google Scholar
• Clarke, B., Baker, S., Smolkowski, K., & Chard, D. J. (2008). An analysis of early numeracy curriculum-based measurement: Examining the role of growth in student outcomes. Remedial and Special Education, 29(1), 46–57. doi:10.1177/0741932507309694
   Web of Science ®Google Scholar
• Clarke, B., & Shinn, M. R. (2004). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review, 33(2), 234–248. Article
   Web of Science ®Google Scholar
• Claro, M., Cabello, T., San Martín, E., & Nussbaum, M. (2015). Comparing marginal effects of Chilean students’ economic, social and cultural status on digital versus reading and mathematics performance. Computers & Education, 82, 1–10. doi:10.1016/j.compedu.2014.10.018
   Web of Science ®Google Scholar
• Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York, NY: Routledge.
   Google Scholar
• CONADI. (2017). VIII Región Biobío. Estadisticas Sociales. Biobío, Chile: Ministerio de Desarrollo Social y Familia.
   Google Scholar
• Cordoba, C. A., Farris, M., & Rojas, K. (2017). Discussing school socioeconomic segregation in territorial terms: The differentiated influence of urban fragmentation and daily mobility. Investigaciones Geográficas, 92, 34–50. doi:10.14350/rig.54766
   Google Scholar
• Crosnoe, R., & Schneider, B. (2010). Social capital, information, and socioeconomic disparities in math course work. American Journal of Education, 117(1), 79–107. doi:10.1086/656347
   PubMed Web of Science ®Google Scholar
• Dehaene, S. (2011). The number sense. How the mind creates mathematics (2nd ed.). New York, NY: Oxford.
   Google Scholar
• Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., … Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. doi:10.1037/0012-1649.43.6.1428.supp
   PubMed Web of Science ®Google Scholar
• Elacqua, G., Martinez, M., Santos, H., & Urbina, D. (2012). School closures in Chile : Access to quality alternatives in a school choice system. Estudios de Economia, 39, 179–202. doi:10.4067/S0718-52862012000200005
   Web of Science ®Google Scholar
• Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Journal of experimental child relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53–72. doi:10.1016/j.jecp.2014.01.013
   PubMed Web of Science ®Google Scholar
• Field, A. (2013). Discovering statistics using SPSS (4th ed.). London: Sage. doi:10.1111/j.1365-2648.2007.04270_1.x
   Google Scholar
• Friso-van den Bos, I., Kroesbergen, E. H., Van Luit, J. E. H., Xenidou-Dervou, I., Jonkman, L. M., Van der Schoot, M., & Van Lieshout, E. C. D. M. (2015). Longitudinal development of number line estimation and mathematics performance in primary school children. Journal of Experimental Child Psychology, 134, 12–29. doi:10.1016/j.jecp.2015.02.002
   PubMed Web of Science ®Google Scholar
• Friso-van den Bos, I., Kroesbergen, E, & Van Luit, J. E. H. (2014). Number sense in kindergarten children: Factor structure and working memory predictors. Learning and Individual Differences, 33, 23–29. doi:10.1016/j.lindif.2014.05.003
   Web of Science ®Google Scholar
• Galindo, C., & Sonnenschein, S. (2015). Decreasing the SES math achievement gap: Initial math proficiency and home learning environments. Contemporary Educational Psychology, 43, 25–38. doi:10.1016/j.cedpsych.2015.08.003
   Web of Science ®Google Scholar
• Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. doi:10.1037/a0025510
   PubMed Web of Science ®Google Scholar
• Gelman, R., & Gallister, C. (1978). The child’s understanding of number. Cambridge, MA: Harvard University.
   Google Scholar
• Göbel, S. M., Watson, S. E., Lervåg, A., & Hulme, C. (2014). Children’s arithmetic development: It is number knowledge, not the approximate number sense, that counts. Psychological Science, 25(3), 789–798. doi:10.1177/0956797613516471
   PubMed Web of Science ®Google Scholar
• Guzmán, B., Rodriguez, C., Sepúlveda, F., & Ferreira, R. (2019). Number sense abilities, working memory and RAN : A longitudinal approximation of typical and atypical development in chilean children. Revista De Psicodidáctica, 24(1), 62–70. doi:10.1016/j.psicod.2018.11.002
   Web of Science ®Google Scholar
• Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457–1465. doi:10.1037/a0012682
   PubMed Web of Science ®Google Scholar
• 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
   PubMed Web of Science ®Google Scholar
• Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668. doi:10.1038/nature07246
   PubMed Web of Science ®Google Scholar
• Hannula-Sormunen, M. M., Lehtinen, E., & Räsänen, P. (2015). Preschool children’s spontaneous focusing on numerosity, subitizing, and counting skills as predictors of their mathematical performance seven years later at school. Mathematical Thinking and Learning, 17(2–3), 155–177. doi:10.1080/10986065.2015.1016814
   Web of Science ®Google Scholar
• Hofer, K. G., Farran, D. C., & Cummings, T. P. (2013). Preschool children’s math-related behaviors mediate curriculum effects on math achievement gains. Early Childhood Research Quarterly, 28(3), 487–495. doi:10.1016/j.ecresq.2013.02.002
   Web of Science ®Google Scholar
• 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
   PubMed Web of Science ®Google Scholar
• Ivanovic, R., Sparosvich, H., Durán, M. C., Hazbún, J., Castro, C., & 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.
   Google Scholar
• Jacobi-Vessels, J. L., Todd Brown, E., Molfese, V. J., & Do, A. (2016). Teaching preschoolers to count: Effective strategies for achieving early mathematics milestones. Early Childhood Education Journal, 44(1), 1–9. doi:10.1007/s10643-014-0671-4
   Web of Science ®Google Scholar
• Jordan, N. C. (2010). Early predictors of mathematics achievement and mathematics learning difficulties. Retrieved from  http://www.child-encyclopedia.com/numeracy/
   Google Scholar
• 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
   PubMed Web of Science ®Google Scholar
• Jordan, N. C., Huttenlocher, J., & Levine, S. C. (1994). Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle-and low-income children. Learning and Individual Differences, 6(4), 413–432. doi:10.1016/1041-6080(94)90003-5
   Web of Science ®Google Scholar
• Jordan, N. C., Kaplan, D., Nabors Oláh, L., & Locuniak, M. N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153–175. doi:10.1111/j.1467-8624.2006.00862.x
   PubMed Web of Science ®Google Scholar
• Jordan, N. C., & Levine, S. C. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews, 15(1), 60–68. doi:10.1002/ddrr.v15:1
   PubMed Web of Science ®Google Scholar
• Lefevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., & Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 1753–1767. doi:10.1111/j.1467-8624.2010.01508.x
   PubMed Web of Science ®Google Scholar
• Libertus, M. E. (2015). The role of intuitive approximation skills for school math abilities. Mind, Brain, and Education, 9(2), 112–120. doi:10.1111/mbe.12072
   Web of Science ®Google Scholar
• Liu, X., & Hannum, E. (2017). Early poverty exposure predicts young adult educational outcomes in China. China Economic Review, 44, 79–97. doi:10.1016/j.chieco.2017.03.006
   Web of Science ®Google Scholar
• Martin, R. B., Cirino, P. T., Sharp, C., & Barnes, M. (2014). Number and counting skills in kindergarten as predictors of grade 1 mathematical skills. Learning and Individual Differences, 34, 12–23. doi:10.1016/j.lindif.2014.05.006
   PubMed Web of Science ®Google Scholar
• Melhuish, E., Sylva, K., Sammons, P., Siraj-Blatchford, I., Taggart, B., Phan, M. B., & Malin, A. (2008). Preschool influences on mathematics achievement. Science, 321(August), 1161–1162. doi:10.1126/science.1158808
   PubMedGoogle Scholar
• Merkley, R., & Ansari, D. (2016). Why numerical symbols count in the development of mathematical skills: Evidence from brain and behavior. Current Opinion in Behavioral Sciences, 10, 14–20. doi:10.1016/j.cobeha.2016.04.006
   Web of Science ®Google Scholar
• MINEDUC. (2010). Metodología de Construcción Grupos Socioeconomicos en SIMCE. Santiago de Chile, Chile: Agencia de la Calidad de la Educación.
   Google Scholar
• Missall, K., Hojnoski, R. L., Caskie, G. I. L., & Repasky, P. (2015). Home numeracy environments of preschoolers: Examining relations among mathematical activities, parent mathematical beliefs, and early mathematical skills. Early Education and Development, 26(3), 356–376. doi:10.1080/10409289.2015.968243
   Web of Science ®Google Scholar
• Mizala, A., & Torche, F. (2012). Bringing the schools back in: The stratification of educational achievement in the Chilean voucher system. International Journal of Educational Development, 32(1), 132–144. doi:10.1016/j.ijedudev.2010.09.004
   Web of Science ®Google Scholar
• Muñoz-Chereau, B., & Thomas, S. M. (2016). Educational effectiveness in Chilean secondary education: Comparing different ‘value added’ approaches to evaluate schools. Assessment in Education: Principles, Policy and Practice, 23(1), 26–52. doi:10.1080/0969594X.2015.1066307
   Web of Science ®Google Scholar
• Nguyen, T., Watts, T. W., Duncan, G. J., Clements, D. H., Sarama, J. S., Wolfe, C., & Spitler, M. E. (2016). Which preschool mathematics competencies are most predictive of fifth grade achievement? Early Childhood Research Quarterly, 36, 550–560. doi:10.1016/j.ecresq.2016.02.003
   PubMed Web of Science ®Google Scholar
• Nys, J., Ventura, P., Fernandes, T., Querido, L., Leybaert, J., & Content, A. (2013). Does math education modify the approximate number system? A comparison of schooled and unschooled adults. Trends in Neuroscience and Education, 2(1), 13–22. doi:10.1016/j.tine.2013.01.001
   Google Scholar
• OECD. (2010). PISA 2009 results: Overcoming social background - equity in learning opportunities and outcomes (Vol. II). Paris: Author. doi:10.1787/9789264091504-en
   Google Scholar
• OECD. (2016). Equations and inequalities: Making mathematics accessible to all. Paris. doi:10.1787/9789264258495-en
   Google Scholar
• OREALC/UNESCO. (2016). TERCE. factores asociados. Retrieved from https://unesdoc.unesco.org/ark:/48223/pf0000243533.locale=en
   Google Scholar
• Pappas, S., Ginsburg, H. P., & Jiang, M. (2003). SES differences in young children’s metacognition in the context of mathematical problem solving. Cognitive Development, 18(3), 431–450. doi:10.1016/S0885-2014(03)00043-1
   Web of Science ®Google Scholar
• Piazza, M., Pica, P., Izard, V., Spelke, E. S., & Dehaene, S. (2013). Education enhances the acuity of the nonverbal approximate number system. Psychological Science, 24(6), 1037–1043. doi:10.1177/0956797612464057
   PubMed Web of Science ®Google Scholar
• Platas, L. M., Ketterlin-Geller, L. R., & Sitabkhan, Y. (2016). Using an assessment of early mathematical knowledge and skills to inform policy and practice: Examples from the early grade mathematics assessment. International Journal of Education in Mathematics, Science and Technology, 4(3), 163–173. doi:10.18404/ijemst.20881
   Web of Science ®Google Scholar
• Purpura, D. J., & Lonigan, C. J. (2013). Informal numeracy skills: The structure and relations among numbering, relations, and arithmetic operations in preschool. American Educational Research Journal, 50(1), 178–209. doi:10.3102/0002831212465332
   Web of Science ®Google Scholar
• Ramírez, M. J. (2006). Understanding the low mathematics achievement of Chilean students: A cross-national analysis using TIMSS data. International Journal of Educational Research, 45(3), 102–116. doi:10.1016/j.ijer.2006.11.005
   Google Scholar
• Raven, J., Raven, J., & Court, J. H. (1993). Test de Matrices Progresivas (Manual). Buenos Aires, Argentina: Paidós.
   Google Scholar
• Schneider, M., Beeres, K., Coban, L., Merz, S., Susan Schmidt, S., Stricker, J., & De Smedt, B. (2017). Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: A meta-analysis. Developmental Science, 20(3), e12372. doi:10.1111/desc.2017.20.issue-3
   Web of Science ®Google Scholar
• Siegler, R. S., & Braithwaite, D. W. (2017). Numerical Development. Annual Review of Psychology, 68(1), 187–213. doi:10.1146/annurev-psych-010416-044101
   PubMedGoogle Scholar
• Spaull, N., & Kotze, J. (2015). Starting behind and staying behind in South Africa. The case of insurmountable learning deficits in mathematics. International Journal of Educational Development, 41, 13–24. doi:10.1016/j.ijedudev.2015.01.002
   Web of Science ®Google Scholar
• Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99–120. doi:10.1016/j.ecresq.2004.01.002
   Web of Science ®Google Scholar
• Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Psycological and Cognitive Sciences, 110(45), 18116–18120. doi: http://doi.org/10.1073/pnas.1302751110
   Google Scholar
• Szkudlarek, E., & Brannon, E. M. (2017). Language learning and development does the approximate number system serve as a foundation for symbolic mathematics? Does the approximate number system serve as a foundation for symbolic mathematics? Language Learning and Development, 00(00), 1–20. doi:10.1080/15475441.2016.1263573
   Google Scholar
• Thieme, C., Prior, D., Tortosa-Ausina, E., & Gempp, R. (2013). Value added, educational accountability approaches and their effects on schools’ rankings: Evidence from Chile. European Journal of Operational Research, 253, 456–471. doi:10.1016/j.ejor.2016.01.023
   Google Scholar
• Toll, S. W. M., Van Viersen, S., Kroesbergen, E. H., & Van Luit, J. E. H. (2015). The development of (non-) symbolic comparison skills throughout kindergarten and their relations with basic mathematical skills. Learning and Individual Differences, 38, 10–17. http://doi.org/10.1016/j.lindif.2014.12.006
   Web of Science ®Google Scholar
• Valle-Lisboa, J., Cabana, Á., Eisinger, R., Mailhos, Á., Luzardo, M., Halberda, J., & Maiche, A. (2016). Cognitive abilities that mediate SES’s effect on elementary mathematics learning: The Uruguayan tablet-based intervention. Prospects, 46(2), 301–315. doi:10.1007/s11125-017-9392-y
   Google Scholar
• Vanbinst, K., Ansari, D., Ghesquière, P., & Smedt, B. D. (2016). Symbolic numerical magnitude proceing is as important to arithmetic as phonological awarene is to reading. PLoS ONE, 11(3), 1–11. doi:10.1371/journal.pone.0151045
   Web of Science ®Google Scholar
• Vanbinst, K., Ghesquière, P., & De Smedt, B. (2015). Does numerical processing uniquely predict first graders’ future development of single-digit arithmetic? Learning and Individual Differences, 37, 153–160. doi:10.1016/j.lindif.2014.12.004
   Web of Science ®Google Scholar
• Xenidou-Dervou, I., Molenaar, D., Ansari, D., van der Schoot, M., & van Lieshout, E. C. D. M. (2017). Nonsymbolic and symbolic magnitude comparison skills as longitudinal predictors of mathematical achievement. Learning and Instruction, 50, 1–13. doi:10.1016/j.learninstruc.2016.11.001
   Web of Science ®Google Scholar
• Yang, D. C., & Li, M. N. F. (2008). An investigation of 3rd-grade Taiwanese students’ performance in number sense. Educational Studies, 34(5), 443–455. doi:10.1080/03055690802288494
   Web of Science ®Google Scholar