NUMBER DEVELOPMENT FROM INFANCY TO SCHOOL AGE

Yıl 2024, Cilt: 64 Sayı: 1, 762 - 788, 25.06.2024

Hüseyin Yalçıner , Tuğçe Yalçınkaya , Dilay Z. Karadöller

https://doi.org/10.33171/dtcfjournal.2024.64.1.30

Öz

Number development from infancy to school age is reported to be affected by many factors that are related to the child and the environment. These factors can be examined based on age, language skills, spatial abilities, and parental input. This review starts with synthesizing the theories on number development and the empirical findings supporting these theories, and then examines the child- and environment-related factors such as spatial abilities, language skills and parental input, which are closely related to number development. Core Knowledge Theory states that humans are innately endowed with basic knowledge of numeracy and geometry. Many studies agree on several principles in the context of innate understanding of numeracy. Number development in the preschool years is an important predictor of children's mathematics achievement in the school years. Various studies have stated that age is one of the dimensions of number learning. In addition to age, the spatial abilities and language skills of the child are also important factors that are related to their mathematical performance in the future. In addition to these factors that are related to the child, it has been shown that the environmental factors that preschool children are exposed to also have important effects on number development. Exposure to conversations about numbers in book reading or play activities in home environment or encountering numbers and mathematical concepts in daily activities such as during shopping is highly related to children's number development in current and future years.

Anahtar Kelimeler

Number Development, Spatial Abilities, Language Skills, Parental Input

BEBEKLİKTEN OKUL ÇAĞINA SAYI GELİŞİMİ

Öz

Bebeklikten okul çağına sayı gelişiminin, çocuğa dair ve çevresel birçok faktörden etkilendiği öne sürülmektedir. Bu faktörler, yaş, dil becerisi, uzamsal beceriler ve ebeveyn girdisi gibi başlıklarda incelenebilir. Bu derlemede öncelikle sayı gelişimi üzerine öne sürülmüş teorilerin ve bu teorileri destekleyen ampirik bulguların bir sentezi yapılıp devamında sayı gelişimi ile yakından ilişkisi olduğu bulunan uzamsal beceriler, dil becerileri ve ebeveyn girdisi gibi çocuğa dair ve çevresel faktörlerin incelemesi yapılmıştır. Temel Bilgi Teorisi (İng. Core Knowledge Theory), insanların sayısallık ve geometri konusunda temel bilgilere doğuştan sahip olduğunu belirtir. Birçok çalışma doğuştan gelen sayısallık bilgisi bağlamında çeşitli ilkelerde hemfikirdir. Okul öncesi dönemdeki sayı gelişimi, çocukların okul dönemindeki matematik başarılarının önemli bir yordayıcısıdır. Çeşitli çalışmalar yaşın sayı öğrenimindeki boyutlardan biri olduğunu ifade etmiştir. Yaşa ek olarak çocuğun uzamsal becerileri ve dil yetenekleri de ilerleyen dönemlerdeki matematik performansları ile ilişkisi olan önemli faktörlerdendir. Çocuğa dair bu faktörlerin yanı sıra okul öncesi dönemdeki çocukların maruz kaldığı çevresel faktörlerin de sayı gelişimi konusunda önemli etkileri olduğu gösterilmektedir. Ev ortamında yapılan aktivitelerde (örn., kitap okuma, oyun oynama) sayılarla ilgili konuşmalara maruz kalmanın veya günlük aktivitelerde (örn., alışveriş) sayılar ve matematiksel kavramlar ile tanışmanın, çocukların güncel ve gelecek yıllardaki sayı gelişimi ile yüksek derecede ilişkili olduğu bulunmuştur.

Anahtar Kelimeler

Sayı Gelişimi, Uzamsal Beceriler, Dil Becerisi, Ebeveyn Girdisi

Kaynakça

• Anderson, A., Anderson, J. ve Shapiro, J. (2005). Supporting multiple literacies: Parents’ and children’s mathematical talk within storybook reading. Mathematics Education Research Journal, 16(3), 5-26. doi: 10.1007/BF03217399
• Andres, M., Davare, M., Pesenti, M., Olivier, E. ve Seron, X. (2004). Number magnitude and grip aperture interaction. Neuroreport, 15(18), 2773-2777.
• Andres, M., Ostry, D. J., Nicol, F. ve Paus, T. (2008). Time course of number magnitude interference during grasping. Cortex, 44(4), 414-419. doi: 10.1016/j.cortex.2007.08.007
• Assel, M. A., Landry, S. H., Swank, P., Smith, K. E. ve Steelman, L. M. (2003). Precursors to mathematical skills: Examining the roles of visual-spatial skills, executive processes, and parenting factors. Applied Developmental Science, 7(1), 27-38. doi: 10.1207/S1532480XADS0701_3
• Aunola, K., Leskinen, E., Lerkkanen, M. K. ve Nurmi, J. E. (2004). Developmental dynamics of math performance from preschool to grade 2. Journal of Educational Psychology, 96(4), 699-713. doi: 10.1037/0022-0663.96.4.699
• Bandura, A. (1982). Self-efficacy mechanism in human agency. American Psychologist, 37, 122-147. doi: 10.1037/0003-066X.37.2.122
• Beydoğan, B. E. (2023). Çocuklarda matematik öğrenmeye karşı olumsuz direnci etkileyen değişkenler. Uluslararası Bilim ve Eğitim Dergisi, 6(2), 121-140. doi: 10.47477/ubed.1282195
• Byrnes, J. P. ve 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
• Carey, S. ve Sarnecka, B. W. (2006). The development of human conceptual representations: A case study. Processes of Change in Brain and Cognitive Development.
• Casey, B. M., Pezaris, E., Fineman, B., Pollock, A., Demers, L. ve Dearing, E. (2015). A longitudinal analysis of early spatial skills compared to arithmetic and verbal skills as predictors of fifth-grade girls’ math reasoning. Learning and Individual Differences, 40, 90-100. doi: 10.1016/j.lindif.2015.03.028
• Chang, A., Sandhofer, C. M. ve Brown, C. S. (2011). Gender biases in early number exposure to preschool-aged children. Journal of Language and Social Psychology, 30(4), 440-450. doi: 10.1177/0261927X11416207
• Ceylan, M. ve Aslan, D. (2018). Cardinal number acquisition of Turkish children. Journal of Education and e-Learning Research, 5(4), 217-224. doi: 10.20448/journal.509.2018.54.217.224
• Çekirdekçi, S., Şengül, S. ve Cihangir Doğan, M. (2016). 4. Sınıf öğrencilerinin sayı hissi ile matematik başarıları arasındaki ilişkinin incelenmesi. Qualitative Studies, 11(4), 48-66. doi: 10.12739/NWSA.2016.11.4.E0028
• Çelik, M. (2015). Anasınıfına Devam Eden 60-72 Aylık Çocukların Matematik Gelişimlerinin Bazı Değişkenler Açısından İncelenmesi. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, (24), 1-18. doi: 10.14582/DUZGEF/401
• Dehaene, S., Bossini, S. ve Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122(3), 371-396. doi: 10.1037/0096-3445.122.3.371
• Demir-Lira, Ö. E. (2016). Okul öncesi dönemde ve okul çağında okuma yazma ve matematik gelişimi. Aklın çocuk hali: Zihin gelişimi araştırmaları (Der. Aydın, Ç., Aydin, C., Göksun, T., Goksun, T., Kuntay, AC, Tahiroğlu, D. ve Tahiroglu, D.).(ss. 319-342). İstanbul: Koç Üniversitesi Yayınları.
• Duncan, G. J., Claessens, A., Huston, A. C., Pagani, L. S., Engel, M., Sexton, H., … ve Duckworth, K. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. doi: 10.1037/0012-1649.43.6.1428
• Durkin, K., Shire, B., Riem, R., Crowther, R. D. ve Rutter, D. R. (1986). The social and linguistic context of early number word use. British Journal of Developmental Psychology, 4(3), 269-288. doi: 10.1111/j.2044-835X.1986.tb01018.x
• Eccles, J. S., Barber, B. ve Jozefowicz, D. (1999). Linking gender to educational, occupational, and recreational choices: Applying the Eccles et al. model of achievement-related choices. In W. B. Swann, Jr., J. H. Langlois, & L. A. Gilbert (Eds.), Sexism and stereotypes in modern society: The gender science of Janet Taylor Spence (pp. 153–192). American Psychological Association. doi: 10.1037/10277-007
• Ertürk Kara, H. G. (2019). Okul öncesi dönemde çocuğa evde sunulan desteğin okuma yazmaya hazırlık ve matematik becerileri bağlamında incelenmesi. Bayburt Eğitim Fakültesi Dergisi, 14(27), 87-105. doi: 10.35675/befdergi.422261
• Foster-Cohen, S., Edgin, J. O., Champion, P. R. ve Woodward, L. J. (2007). Early delayed language development in very preterm infants: evidence from the MacArthur-Bates CDI. Journal of Child Language, 34(3), 655-675. doi: 10.1017/S0305000907008070
• Fuson, K. C., Richards, J. ve Briars, D. J. (1982). The acquisition and elaboration of the number word sequence. Children’s Logical and Mathematical Cognition, 33-92. doi: 10.1007/978-1-4613-9466-2
• Gallistel, C. R. ve Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition, 44(1-2), 43-74. doi: 10.1016/0010-0277(92)90050-R
• Geary, D. C. (2018). Growth of symbolic number knowledge accelerates after children understand cardinality. Cognition, 177, 69-78. doi: 10.1016/j.cognition.2018.04.002
• Geer, E. A., Quinn, J. M. ve Ganley, C. M. (2019). Relations between spatial skills and math performance in elementary school children: A longitudinal investigation. Developmental Psychology, 55(3), 637-652. doi: 10.1037/dev0000649
• Gelman, R. ve Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.
• Glenn, D. E., Demir-Lira, Ö. E., Gibson, D. J., Congdon, E. L. ve Levine, S. C. (2018). Resilience in mathematics after early brain injury: The roles of parental input and early plasticity. Developmental Cognitive Neuroscience, 30, 304-313. doi: 10.1016/j.dcn.2017.07.005
• Goldstein, A., Cole, T. ve Cordes, S. (2016). How parents read counting books and non-numerical books to their preverbal infants: An observational study. Frontiers in Psychology, 7, 1100. doi: 10.3389/fpsyg.2016.01100
• Gunderson, E. A. ve Levine, S. C. (2011). Some types of parent number talk count more than others: Relations between parents’ input and children’s cardinal‐number knowledge. Developmental Science, 14(5), 1021-1032. doi: 10.1111/j.1467-7687.2011.01050.x
• Günay Bilaloğlu, R. (2014). Okul öncesi eğitimde aile katılımı etkinliklerinin uygulanmasında karşılaşılan sorunlar ve aile katılımı etkinliklerinin dil-matematik becerilerinin geliştirilmesine etkisi. (Doktora tezi). Erişim adresi https://acikbilim.yok.gov.tr/handle/20.500.12812/130956
• Hargrave, A. C. ve Sėnėchal, M. (2000). A book reading intervention with preschool children who have limited vocabularies: the benefits of regular reading and dialogic reading. Early Childhood Research Quarterly, 15(1), 75-90. doi: 10.1016/S0885-2006(99)00038-1
• Hanner, E., Braham, E. J., Elliott, L. ve Libertus, M. E. (2019). Promoting math talk in adult–child interactions through grocery store signs. Mind, Brain, and Education, 13(2), 110-118. doi: 10.1111/mbe.12195
• Izard, V. ve Dehaene, S. (2008). Calibrating the mental number line. Cognition, 106(3), 1221-1247. doi: 10.1016/j.cognition.2007.06.004
• Izard, V., Sann, C., Spelke, E. S. ve Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences, 106(25), 10382-10385. doi: 10.1073/pnas.0812142106
• Jordan, G. E., Snow, C. E. ve Porche, M. V. (2000). Project EASE: The effect of a family literacy project on kindergarten students' early literacy skills. Reading Research Quarterly, 35(4), 524-546. doi: 10.1598/RRQ.35.4.5
• Karadöller, D. Z., Demir-Lira, Ö. E. ve Göksun, T. (2023, değerlendirme aşamasında). Relationship between multimodal math input, gestational status, and children’s expressive vocabulary.
• Karakuzu, E. ve Koçyiğit, S. (2016). Ebeveyn Destekli İlkokula Hazırlık Programı’nın (EDİHP) okul öncesi dönem çocuklarının ilkokula hazır bulunuşluğuna etkisi. Uluslararası Erken Çocukluk Eğitimi Çalışmaları Dergisi, 1(1), 84-102.
• Keçeli-Kaysılı, B. (2008). Akademik başarının arttırılmasında aile katılımı. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 9(01), 69-83. doi: 10.1501/Ozlegt_0000000115
• Koponen, T., Aunola, K. ve Nurmi, J. E. (2019). Verbal counting skill predicts later math performance and difficulties in middle school. Contemporary Educational Psychology, 59. doi: 10.1016/j.cedpsych.2019.101803
• Kyttälä, M., Aunio, P., Lepola, J. ve Hautamäki, J. (2014). The role of the working memory and language skills in the prediction of word problem-solving in 4-to 7-year-old children. Educational Psychology: An International Journal of Experimental Educational Psychology, 34(6), 674-696. doi: 10.1080/01443410.2013.814192
• Lakoff, G. ve Johnson, M. (1980). The metaphorical structure of the human conceptual system. Cognitive Science, 4(2), 195-208.
• Lakoff, G. ve Núñez, R. (2000). Where mathematics comes from (Vol. 6, p. 489). New York: Basic Books.
• LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith‐Chant, B. L., Bisanz, J., Kamawar, D. ve 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
• LeFevre, J. A., Skwarchuk, S. L., Smith-Chant, B. L., Fast, L., Kamawar, D. ve Bisanz, J. (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science/Revue Canadienne des Sciences du Comportement, 41(2), 55. doi: 10.1037/a0014532
• Lehrl, S., Kluczniok, K. ve Rossbach, H. G. (2016). Longer-term associations of preschool education: The predictive role of preschool quality for the development of mathematical skills through elementary school. Early Childhood Research Quarterly, 36, 475-488. doi: 10.1016/j.ecresq.2016.01.013
• Linn, M. C. ve Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development, 56(6), 1479-1498. doi: 10.2307/1130467
• MacDonald, A. ve Murphy, S. (2021). Mathematics education for children under four years of age: A systematic review of the literature. Early Years, 41(5), 522-539. doi: 10.1080/09575146.2019.1624507
• Markey, S. M. (2009). The relationship between visual-spatial reasoning ability and math and geometry problem-solving. American International College.
• Markson, L. ve Bloom, P. (1997). Evidence against a dedicated system for word learning in children. Nature, 385(6619), 813-815. doi: 10.1038/385813a0
• Maxwell, J. R., Yellowhair, T. R., Oppong, A. Y., Camacho, J. E., Lowe, J. R., Jantzie, L. L. ve Ohls, R. K. (2017). Cognitive development in preterm infants: multifaceted deficits reflect vulnerability of rigorous neurodevelopmental pathways. Minerva Pediatrica, 69(4), 298-313. doi: 10.23736/s0026-4946.17.04905-2
• Mix, K. S. ve Cheng, Y. L. (2012). The relation between space and math: Developmental and educational implications. Advances in Child Development and Behavior, 42, 197-243. doi: 10.1016/B978-0-12-394388-0.00006-X
• Mix, K. S., Cheng, Y. L., Hambrick, D. Z., Levine, S. C., Young, C., Ping, R. ve Konstantopoulos, S. (2016). Separate but correlated: The latent structure of space and mathematics across development. Journal of Experimental Psychology: General, 145(9), 1206-1227. doi: 10.1037/xge0000182
• Mix, K. S., Sandhofer, C. M., Moore, J. A. ve Russell, C. (2012). Acquisition of the cardinal word principle: The role of input. Early Childhood Research Quarterly, 27(2), 274-283. doi: 10.1016/j.ecresq.2011.10.003
• Oğul, İ. G. ve Arnas, Y. A. (2020). Erken dönemde matematik konuşmaları. Yaşadıkça Eğitim, 34(1), 186-199. doi: 10.33308/26674874.2020341171
• Olkun, S., Fidan, E. ve Babacan Özer, A. (2013). The development of number concept and the use of counting in problem solving of 5-7 year olds’. Education and Science, 38(169).
• Peng, P., Lin, X., Ünal, Z. E., Lee, K., Namkung, J., Chow, J. ve Sales, A. (2020). Examining the mutual relations between language and mathematics: A meta-analysis. Psychological Bulletin, 146(7), 595. doi: 10.1037/bul0000231
• Pica, P., Lemer, C., Izard, V. ve Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian Indigene group. Science, 306, 499. doi: 10.1126/science.1102085
• Purpura, D. J. ve Reid, E. E. (2016). Mathematics and language: Individual and group differences in mathematical language skills in young children. Early Childhood Research Quarterly, 36, 259-268. doi: 10.1016/j.ecresq.2015.12.020
• Ramani, G. B., Rowe, M. L., Eason, S. H. ve Leech, K. A. (2015). Math talk during informal learning activities in Head Start families. Cognitive Development, 35, 15-33. doi: 10.1016/j.cogdev.2014.11.002
• Rittle-Johnson, B., Hofer, K.G., Fyfe, E. R. ve Farran, D. C. (2017). Early math trajectories: Low-income children’s mathematics knowledge from ages 4 to 11. Child Development, 88(5), 1727-1742. doi: 10.1111/cdev.12662
• Salsa, A., Gariboldi, M. B. ve Rodríguez, J. (2022). Multimodal numerical interactions during mother-child picture book reading. Early Education and Development, 33(6), 997-1012. doi: 10.1080/10409289.2021.1936375
• Sarnecka, B. W., Kamenskaya, V. G., Yamana, Y., Ogura, T. ve Yudovina, Y. B. (2007). From grammatical number to exact numbers: Early meanings of ‘one,’ ‘two,’ and ‘three’ in English, Russian and Japanese. Cognitive Psychology, 55, 136-168. doi: 10.1016/j.cogpsych.2006.09.001
• Sarnecka, B. W. ve Lee, M. D. (2009). Levels of number knowledge during early childhood. Journal of Experimental Child Psychology, 103, 325-337. doi: 10.1016/j.jecp.2009.02.007
• Satlow, E. ve Newcombe, N. (1998). When is a triangle not a triangle? Young children's developing concepts of geometric shape. Cognitive Development, 13(4), 547-559. doi: 10.1016/S0885-2014(98)90006-5
• Siegler, R. S. (1988). Strategy choice procedures and the development of multiplication skill. Journal of Experimental Psychology: General, 117(3), 258-275. doi: 10.1037/0096-3445.117.3.258
• Spelke E. S. ve Kinzler, K. D. (2007). Core knowledge. Developmental Science, 10(1), 88-96. doi: 10.1111/j.1467-7687.2007.00569.x
• Starkey, P., Klein, A. ve 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
• Şengül, S. ve Gülbağcı Dede, H. (2013). Sayı hissi bileşenlerine ait sınıflandırmaların incelenmesi. The Journal of Academic Social Science Studies, 6(8), 645-664. doi: 10.9761/JASSS1000
• Toll, S. W. ve Van Luit, J. E. (2014a). Explaining numeracy development in weak performing kindergartners. Journal of Experimental Child Psychology, 124, 97-111. doi: 10.1016/j.jecp.2014.02.001
• Toll, S. W. ve Van Luit, J. E. (2014b). The developmental relationship between language and low early numeracy skills throughout kindergarten. Exceptional Children, 81(1), 64-78. doi: 10.1177/0014402914532233
• Turan, E. ve De Smedt, B. (2022). Mathematical language and mathematical abilities in preschool: A systematic literature review. Educational Research Review, 36, 100457. doi: 10.1016/j.edurev.2022.100457
• Unutkan, Ö. P. (2007). Okul öncesi dönem çocuklarının matematik becerileri açısından ilköğretime hazır bulunuşluğunun incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 32(32), 243-254.
• Uscianowski, C., Almeda, M. V. ve Ginsburg, H. P. (2020). Differences in the complexity of math and literacy questions parents pose during storybook reading. Early Childhood Research Quarterly, 50, 40-50. doi: 10.1016/j.ecresq.2018.07.003
• Uyanık, Ö. ve Kandır, A. (2010). Okul öncesi dönemde erken akademik beceriler. Kuramsal Eğitimbilim Dergisi, 3(2), 118-134.
• Ünlütabak, B., Aktan-Erciyes, A., Yılmaz, D., Kandemir, S. ve Göksun, T. (2022). Parental input during book reading and toddlers' elicited and spontaneous communicative interactions. Journal of Applied Developmental Psychology, 81, 101436. doi: 10.1016/j.appdev.2022.101436
• Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., Newcombe, N. S. ve Bailey, D. H. (2017). Links between spatial and mathematical skills across the preschool year. Monographs of the Society for Research in Child Development, 82(1), 7-149. Retrieved from https://www.jstor.org/stable/45106900
• Wai, J., Lubinsk, D. ve Benbow, C. P. (2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835. doi: 10.1037/a0016127
• Walsh, V. (2003). A theory of magnitude: Common cortical metrics of time, space and quantity. Trends in Cognitive Sciences, 7(11), 483-488. doi: 10.1016/j.tics.2003.09.002
• Winter, B., Marghetis, T. ve Matlock, T. (2015). Of magnitudes and metaphors: Explaining cognitive interactions between space, time, and number. Cortex, 64, 209-224. doi: 10.1016/j.cortex.2014.10.015
• Wynn, K. (1992). Children's acquisition of the number words and the counting system. Cognitive Psychology, 24(2), 220-251. doi: 10.1016/0010-0285(92)90008-P
• Xu, F., Spelke, E. S. ve Goddard, S. (2005). Number sense in human infants. Developmental Science, 8(1), 88-101. doi: 10.1111/j.1467-7687.2005.00395.x
• Zhang, X., Koponen, T., Räsänen, P., Aunola, K., Lerkkanen, M. K. ve Nurmi, J. E. (2014). Linguistic and spatial skills predict early arithmetic development via counting sequence knowledge. Child Development, 85(3), 1091-1107. doi: 10.1111/cdev.12173