Erken Çocuklukta Matematik Becerileri: Çeşitli Değişkenler ve Erken Matematik Müdahale Programları

Yıl 2022, Cilt: 12 Sayı: 2, 665 - 690, 01.07.2022

Binnur Yıldırım Hacıibrahimoğlu

https://doi.org/10.18039/ajesi.929169

Öz

Okul öncesi dönemde edinilen nitelikli matematik kavram ve becerileri, çocukların matematik başarısını artırmasının yanı sıra farklı etkinliklerle bütünleştirilerek diğer öğrenme alanlarını da desteklemektedir. Küçük yaşta matematik becerilerinin desteklenmesi, çocukların akademik başarılarına yansıyan bir etken olarak pek çok araştırma ile tespit edilmiştir. Bu nedenle, çocukların ileriki yıllarda matematik alanındaki yetersizlikleri ile mücadele etmek ve onları başarılı bir okul hayatına hazırlamak için okul öncesi dönemde matematik becerilerinde görülen bireysel farklılıkları anlamak büyük önem taşımaktadır. Sosyoekonomik düzey, etnik köken, özel gereksinim gibi farklı özellikleri göz önünde bulundurarak oluşturulan matematik etkinlikleri ve uygulamaları tüm çocukların gereksinimlerini karşılamada yardımcı olacaktır. Özellikle sosyoekonomik durum ve özel gereksinim, çocukların matematik performanslarında farklılıkların önemli etkenleri olarak karşımıza çıkmakta ve bu gruplarda yer alan çocuklar matematik başarısı açısından dezavantajlı ya da risk grupları olarak değerlendirilmektedir. Son yıllarda ulusal alanyazında okul öncesi dönemde matematik eğitimine yönelik çalışmalar artış göstermektedir. Bu noktada dezavantajlı gruplarda erken matematik becerilerinin gelişimi ve desteklenmesi de önemli görülmektedir. Bu derleme çalışmasında, erken çocukluk döneminde matematik becerilerini etkileyen değişkenler ele alınmıştır. Ayrıca sosyoekonomik durum ve özel gereksinime sahip olma değişkenleri kapsamında dezavantajlı grupta yer alan çocuklar için geliştirilmiş araştırma temelli, sistemli erken matematik müdahale programları incelenmiştir. Çalışma sonucunda, okul öncesi dönemde dezavantajlı grupta yer alan çocukların matematik becerilerini desteklemek için kendi kültürümüze, programımıza yönelik oluşturulacak araştırma temelli matematik müdahale programlarının çocuklar için yararlı olabileceği düşünülmektedir.

Anahtar Kelimeler

dezavantajlı çocuklar, erken çocukluk eğitimi, erken matematik müdahale programı, erken matematik becerileri

Mathematical Skills in Early Childhood: Various Variables and Early Mathematics Intervention Programs

Öz

In addition to increasing the mathematics achievement of children, the qualified mathematical concepts and skills acquired in preschool period support other learning areas by integrating them with different activities. Supporting math skills at a young age has been identified by many studies as a factor that reflects on children's academic success. It is of great importance to understand the individual differences in mathematics skills in the preschool period in order to cope with the inadequacies of children in the field of mathematics and to prepare them for a successful school life. Mathematical activities and practices created by considering different characteristics such as socioeconomic level, ethnicity, special needs will help to meet the needs of all children. In particular, socioeconomic status and special needs appear as important factors of differences in children's mathematics performance, and children in these groups are considered disadvantaged or risk groups in terms of mathemetics achievement. In recent years, studies on mathematics education in preschool education have been increasing in the national literature. At this point, the development of early mathematics skills in disadvantaged groups and how they are supported seems important. In this review study, the variables that affect math skills in early childhood are discussed. At the same time, research-based, systematic early mathematics intervention programs developed for children in the disadvantaged group within the scope of socioeconomic status and having special needs variables are examined. As a result of the study, it is thought that research-based mathematics intervention programs that will be created for our own culture and program in order to support the mathematics skills of children in the disadvantaged group in preschool education may be benefical for children.

Anahtar Kelimeler

disadvantage children, early childhood education, early mathematic intervention program, early mathematic skills

Kaynakça

• Adey, P., Robertson, A. & Venville, G. (2001) Let’s think! A programme for developing thinking in five and six year olds (Windsor, NFER-NELSON).
• Ai, X. (2002). Gender differences in growth in mathematics achievement: Three-level longitudinal and multilevel analyses of individual, home, and school influences. Mathematical Thinking and Learning, 4(1), 1–22. https://doi.org/10.1207/S15327833MTL0401_1 adresinden 05.01.2021 tarihinde erişilmiştir.
• Aldemir, Ö. (2017). Okulöncesi öğretmenlerince sunulan gömülü öğretimin kaynaştırma öğrencilerinin hedef davranışlarını edinmelerindeki etkileri. (Yayın No.463438 ) [Doktora tezi, Anadolu Üniversitesi]. Anadolu Üniversitesi. YÖK Ulusal Tez Merkezi. https://tez.yok.gov.tr/UlusalTezMerkezi/ adresinden 23.11.2021 tarihinde erişilmiştir.
• Al Otaiba, S., Puranik, C. S., Rouby, A., Greulich, L., Sidler, J. F., & Lee, J. (2010). Predicting kindergarteners’ end-of-year spelling ability based on their reading, alphabetic, vocabulary, and phonological awareness skills as well as priorliteracy experiences. Learning Disability Quarterly, 33, 171–183. https://doi.org/10.1177/073194871003300306 adresinden 10.01.2021 tarihinde erişilmiştir.
• Altındağ Kumaş, Ö. (2019). Küçük Çocuklar için Büyük Matematik eğitim programının risk grubu çocukların erken matematik becerileri üzerindeki etkililiği. (Yayın No. 550817) [Doktora tezi, Ankara Üniversitesi]. Ankara Üniversitesi. YÖK Ulusal Tez Merkezi. https://tez.yok.gov.tr/UlusalTezMerkezi/ adresinden 01.03.2021 tarihinde erişilmiştir.
• Altındağ Kumaş, Ö. (2020). Effectiveness of The Big Math for Little Kids program on the early mathematics skills of preschool children with a bilingual group. Participatory Educational Research, 7(2), 33-46. https://doi.org/10.17275/per.20.18.7.2 adresinden 18.03.2021 tarihinde erişilmiştir.
• 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, 231-244. https://doi.org/10.1016/j.ecresq.2011.08.003 adresinden 09.02.2021 tarihinde erişilmiştir.
• Andersson, U. (2008). Working memory as a predictor of written arithmetical skills in children: The importance of central executive functions. British Journal of Educational Psychology, 78, 181–203. https://doi.org/10.1348/000709907X209854 adresinden 10.01.2021 tarihinde erişilmiştir.
• Arnold, D. H., Fisher, P. H., Doctoroff, G. L., & Dobbs, J. (2002). Accelerating math development in Head Start classrooms. Journal of Educational Psychology, 94, 762-770. https://doi.org/10.1037/0022-0663.94.4.762 adresinden 09.01.2021 tarihinde erişilmiştir.
• Aubrey, C., Bottle, G., & Godfrey, G. (2003). Early mathematics in the home and out-of-home contexts. International Journal of Early Years Education, 11, 91-103. https://doi.org/10.1080/09669760304708 adresinden 15.12.2020 tarihinde erişilmiştir.
• Aunio, P. Hautamäki, J. & E. H. Van Luit, J.E.H. (2005). Mathematical thinking intervention programmes for preschool children with normal and low number sense. European Journal of Special Needs Education, 20(2), 131-146. https://doi.org/10.1080/08856250500055578 adresinden 19.01.2021 tarihinde erişilmiştir.
• Avcı, K. (2019). Erken çocukluk döneminde yürütücü işlevler ve matematik. B. Akman (Ed.), Erken çocuklukta matematik eğitimi içinde (9.baskı, ss. 238-247) Ankara: Pegem Akademi.
• Barnes, M.A., Klein, A., Swank, P., Starkey, P., McCandliss, B., Flynn, K., …Roberts, G. (2016). Effects of tutorial interventions in mathematics and attention for low-performing preschool children. Journal of Research on Educational Effectiveness, 9 (4), 577-606, https://doi.org/10.1080/19345747.2016.1191575
• Baroody, A. J., Eiland, M., & Thompson, B. (2009). Fostering at-risk preschoolers’ number sense. Early Education and Development, 20, 80-128. https://doi.org/10.1080/10409280802206619 adresinden 26.01.2021 tarihinde erişilmiştir.
• Benigno, J. P. & Ellis, S. (2008). Do parents count? The socialization of children's numeracy. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics early childhood education (pp. 291-308). Charlotte, NC: Information Age.
• Bevan, R. (2001). Boys, girls and mathematics: Beginning to leam from the gender debate. Mathematics in School, 30 (4), 2.
• Blevins-Knabe, B., & Musun-Miller, L. (1996). Number use at home by children and their parents and its relationship to early mathematical performance. Early Development and Parenting, 5, 35-45. https://doi.org/10.1002/(SICI)1099-0917(199603)5:1%3C35::AID-EDP113%3E3.0.CO;2-0 adresinden 28.12.2021 tarihinde erişilmiştir.
• Blevins-Knabe, B., Whiteside-Mansell, L. & Selig, J. P. (2007). Parenting and mathematical development. Academic Exchange Quarterly, 11, 76-80.
• Carlson, E., Jenkins, F., Bitterman, A., & Keller, B. (2011). A Longitudinal View of Receptive Vocabulary and Math Achievement of Young Children with Disabilities, (NCSER 2011-3006). U.S. Department of Education. Washington, DC: National Center for Special Education Research
• Charitaki, G., Tzivinikou, S., Stefanou, G., & Soulis, S-G. (2021). A meta-analytic synthesis of early numeracy interventions for low-performing young children. SN Social Science, 1, 105 (2021). https://doi.org/10.1007/s43545-021-00094-w adresinden 18.11.2021 tarihinde erişilmiştir.
• Charlesworth, R. ( 2005). Prekindergarten mathematics: Connecting with national standards. Early Childhood Education Journal, 32(4), 229- 236. https://doi.org/10.1007/s10643-004-1423-7 adresinden 09.01.2020 tarihinde erişilmiştir.
• Chu, F. W., vanMarle, K., & Geary, D. C. (2015). Early numerical foundations of young children’s mathematical development. Journal of Experimental Child Psychology, 132, 205-212. https://doi.org/10.1016/j.jecp.2015.01.006 adresinden 05.01.2021 tarihinde erişilmiştir.
• Claessens, A., Duncan, G., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28, 415-427. https://doi.org/10.1016/j.econedurev.2008.09.003 adresinden 21.12.2020 tarihinde erişilmiştir.
• Clark, C. A. C., Pritchard, V. E., & Woodward, L. J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Developmental Psychology, 46, 1176- 1191. https://doi.org/10.1037/a0019672 adresinden 09.02.2021 tarihinde erişilmiştir.
• Clements, D. H., & Sarama, J. (2007). Effects of a preschool mathematics curriculum: Summative research on the Building Blocks project. Journal of Research in Mathematics Education, 38, 136-163. https://doi.org/10.2307/30034954 adresinden 07.02.2021 tarihinde erişilmiştir.
• Clements, D. H., & Sarama, J. (2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal, 45, 443-494. https://doi.org/10.3102%2F0002831207312908 adresinden 05.01.2021 tarihinde erişilmiştir.
• Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.
• Clements, D. & Sarama, J. (2011). Early childhood mathematics intervention. Science, 333 (6045), 968–70. https://psycnet.apa.org/doi/10.1126/science.1204537 adresinden 04.12.2020 tarihinde erişilmiştir.
• Çelik, M. ve Kandır, A. (2013). 61-72 aylık çocukların matematik gelişimine “Küçük Çocuklar İçin Büyük Matematik (Big Math for Little Kids)” eğitim programının etkisi. Kuramsal Eğitimbilim Dergisi, 6(4), 551-567.
• DeFlorio, L. & Beliakoff, A. (2015). Socioeconomic status and preschoolers' mathematical knowledge: the contribution of home activities and parent beliefs. Early Education and Development, 26 (3), 319-341. https://doi.org/10.1080/10409289.2015.968239 adresinden 05.12.2020 tarihinde erişilmiştir.
• DeLoach, D. (2012). Effects of a prekindergarten mathematics intervention on mathematical abilities of preschoolers with low socio-economic status. [Unpublished doctoral dissertation]. Walden University. https://www.proquest.com/docview/1284153517 adresinden 14.12.2020 tarihinde erişilmiştir.
• Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., Pagani, L. S., Feinstein, L., Engel, M., Brooks-Gunn, J., Sexton, H., Duckworth, K., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446. https://doi.org/10.1037/0012-1649.43.6.1428 adresinden 07.12.2020 tarihinde erişilmiştir.
• Dyson, N. I., Jordan, N. C., & Glutting, J. A. (2011). A number sense intervention for low-income kindergarteners at risk for mathematics difficulties. Journal of Learning Disabilities, 46(2), 166–181. https://doi.org/doi:10.1177/0022219411410233 adresinden 23.11.2021 tarihinde erişilmiştir.
• Elliott, L., & Bachman, H. J. (2018). SES disparities in early math abilities: The contributions of parents’ math cognitions, practices to support math, and math talk. Developmental Review, 49, 1–15. https://doi.org/10.1016/j.dr.2018.08.001 adresinden 18.11.2021 tarihinde erişilmiştir.
• Espy, K. A., McDiarmid, M. M., Cwik, M. F., Stalets, M. M., Hamby, A. & Senn, T. E. (2004). The contribution of executive functions to emergent mathematic skills in preschool children, Developmental Neuropsychology, 26 (1), 465-486. https://doi.org/10.1207/s15326942dn2601_6 adresinden 04.02.2021 tarihinde erişilmiştir.
• Fuchs, L. S., Fuchs, D., & Karns, K. (2001). Enhancing kindergartners’ mathematical development: Effects of peer-assisted learning strategies. The Elementary School Journal, 101, 495-510. https://psycnet.apa.org/doi/10.1086/499684 adresinden 20.12.2020 tarihinde erişilmiştir.
• Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15. https://psycnet.apa.org/doi/10.1177/00222194040370010201 adresinden 20.01.2021 tarihinde erişilmiştir.
• Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choice in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88, 121-151. https://doi.org/10.1016/j.jecp.2004.03.002 adresinden 22.02.2021 tarihinde erişilmiştir.
• Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104 (1), 206-223. https://psycnet.apa.org/doi/10.1037/a0025398 adresinden 22.02.2021 tarihinde erişilmiştir.
• Geist, E. (2009). Children are Born Mathematicians. New Jersey: Pearson Education. Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293-304. https://doi.org/10.1177/00222194050380040301 adresinden 17.11.2021 tarihinde erişilmiştir.
• Green, K. B. & Gallagher, P. A. (2014). Mathematics for young children: A review of the literature with implications for children with disabilities. Baskent University Journal of Education, 1 (1), 81-92.
• Green, K. B., Gallagher, P. A., & L. Hart. (2018). Integrating mathematics and children’s literature for young children with disabilities. Journal of Early Intervention, 40(1), 13–19. https://doi.org/10.1177%2F1053815117737339 adresinden 09.02.2021 tarihinde erişilmiştir.
• Greenes, C., Ginsburg, H. P., & Balfanz, R. (2004). Big math for little kids. Early Childhood Research Quarterly, 19, 159–166. https://doi.org/10.1016/j.ecresq.2004.01.010 adresinden 23.02.2021 tarihinde erişilmiştir.
• Griffin, S. (2004). Building number sense with Number Worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173–180. https://psycnet.apa.org/doi/10.1016/j.ecresq.2004.01.012 adresinden 19.02.2021 tarihinde erişilmiştir.
• Harvey, H. A., & Miller, G. E. (2017). Executive function skills, early mathematics, and vocabulary in head start preschool children. Early Education & Development, 28(3), 1–18. https://doi.org/10.1080/10409289.2016.1218728 adresinden 27.02.2021 tarihinde erişilmiştir.
• Hawkins-Lear, S., & Grisham-Brown, J. (2018). Teaching early math skills to young children with disabilities in rural blended early childhood settings. Rural Special Education Quarterly, 38(1), 15–25. https://doi.org/10.1177%2F8756870518792907 adresinden 04.02.2021 tarihinde erişilmiştir.
• 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, 487– 495. https://doi.org/10.1016/j.ecresq.2013.02.002 adresinden 20.12.2020 tarihinde erişilmiştir.
• Isquith, P. K., Crawford, J. S., Espy, K. A., & Gioia, G. A. (2005). Assessment of executive function in preschool-aged children. Mental Retardation and Developmental Disabilities Research Reviews, 11, 209–215. https://doi.org/10.1016/j.ecresq.2013.02.002 adresinden 17.01.2021 tarihinde erişilmiştir.
• 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. https://doi.org/10.1016/1041-6080(94)90003-5 adresinden 21.02.2021 tarihinde erişilmiştir.
• Jordan, N.C., Kaplan, D., Locuniak, M.N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research and Practice, 22(1), 36-46. https://doi.org/10.1111/j.1540-5826.2007.00229.x adresinden 04.02.2021 tarihinde erişilmiştir.
• Jordan, N.C., Kaplan, D., Nabors Olah, L., & Locuniak, M.N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153-175. https://doi.org/10.1111/j.1467-8624.2006.00862.x adresinden 01.03.2021 tarihinde erişilmiştir.
• Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45 (3), 850–867. https://doi.org/10.1037/a0014939 adresinden 16.01.2021 tarihinde erişilmiştir.
• Jordan, N.C., Levine, S.C., & Huttenlocher, J. (1994). Development of calculation abilities in middle- and low-income children after formal instruction in school. Journal of Applied Developmental Psychology, 15, 223-240. https://doi.org/10.1016/0193-3973(94)90014-0 adresinden 20.02.2021 tarihinde erişilmiştir.
• 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. https://doi.org/10.1002/ddrr.46 adresinden 04.01.2021 tarihinde erişilmiştir.
• Kılıçkaya, A. (2017). Küçük Çocuklar için Büyük Matematik eğitim programının okul öncesi dönem çocuklarının sayıları anlama becerilerine etkisi. (Yayın No. 463323) [Doktora tezi, İnönü Üniversitesi.] YÖK Ulusal Tez Merkezi. https://tez.yok.gov.tr/UlusalTezMerkezi/ adresinden 15.02.2021 tarihinde erişilmiştir.
• Kleemans, T., Peeters, M., Segers, E., & Verhoeven, L. (2012). Child and home predictors of early numeracy skills in kindergarten. Early Childhood Research Quarterly, 27(3), 471–477. https://doi.org/10.1016/J.ECRESQ.2011.12.004 adresinden 09.01.2021 tarihinde erişilmiştir.
• Klein, A., Starkey, P., Clements, D., Sarama, J. & Iyer, R. (2008). Effects of a pre-kindergarten mathematics intervention: A randomized experiment. Journal of Research on Educational Effectiveness, 1 (3), 155-178. https://doi.org/10.1080/19345740802114533 adresinden 04.11.2020 tarihinde erişilmiştir.
• Klein, A., Starkey, P., Deflorio, L., & Brown, E. T. (2011). Scaling up an effective pre-k mathematics intervention: Mediators and child (ED518141). ERIC. https://files.eric.ed.gov/fulltext/ED518141.pdf adresinden 10.12.2020 tarihinde erişilmiştir.
• Klibanoff, R. S., Levine, S.C., Huttenlocher, J., Vasilyeva, M. & Hedges, L.V. (2006). Preschool children’s mathematical knowledge. Developmental Psychology, 42(1), 59–69. https://doi.org/10.1037/0012-1649.42.1.59 adresinden 14.11.2020 tarihinde erişilmiştir.
• Kluczniok, K., Lehrl, S., Kuger, S., & Rossbach, H.-G. (2013). Quality of the home learning environment during preschool age-Domains and contextual conditions. European Early Childhood Education Research Journal, 21, 420-438. https://doi.org/10.1080/1350293X.2013.814356 adresinden 01.12.2020 tarihinde erişilmiştir.
• Krajewski, K., & Schneider, W. (2009). Early development of quantity to number-word linkage as a precursor of mathematical school achievement and mathematical difficulties: Findings from a four-year longitudinal study. Learning and Instruction, 19, 513-526. https://doi.org/10.1016/j.learninstruc.2008.10.002 adresinden 12.01.2021 tarihinde erişilmiştir.
• Leedy, M.G., LaLonde, D., & Runk, K. (2003). Gender equity in mathematics: Beliefs of students, parents and teachers. School Science and Mathematics, 103 (6), 285-292. https://doi.org/10.1111/j.1949-8594.2003.tb18151.x adresinden 17.12.2020 tarihinde erişilmiştir.
• 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. https://doi.org/10.1111/j.1467-8624.2010.01508.x. adresinden 20.12.2020 tarihinde erişilmiştir.
• LeFevre, J.-A., Skwarchuk, S.-L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children’s math performance in the early school years. Canadian Journal of Behavioural Science, 41(2), 55-66. https://doi.org/10.1037/a0014532 adresinden 20.12.2020 tarihinde erişilmiştir.
• Lembke, E. & Foegen, A. (2009). Identifying early numeracy indicators for kindergarten and first grade students. Learning Disabilities Research & Practice, 24(1), 12-20. https://doi.org/10.1111/j.1540-5826.2008.01273.x adresinden 17.12.2020 tarihinde erişilmiştir.
• Lewis Presser, E. L., Clements, M., Ginsburg, H. & Ertle, B. (2015). Big math for little kids: The effectiveness of a preschool and kindergarten mathematics curriculum. Early Education and Development, 26 (3), 399-426. https://doi.org/10.1080/10409289.2015.994451 adresinden 23.12.2020 tarihinde erişilmiştir.
• Manolitsis, G., & Tafa, E. (2011). Letter-name letter-sound and phonological awareness: Evidence from Greek-speaking kindergarten children. Reading and Writing: An Interdisciplinary Journal, 24, 27–53. https://doi.org/10.1007/s11145-009-9200-z adresinden 20.12.2020 tarihinde erişilmiştir.
• McGivern, R. F., Hilliard, V. R., Anderson, J., Reilly, J. S., Rodriguez, A., Fielding, B., & Shapiro, L. (2007). Improving preliteracy and premath skills of Head Start children with classroom computer games. Early Childhood Services, 1, 71-81.
• Morgan, P. L., Farkas, G., & Wu, Q. (2011). Kindergarten children’s growth trajectories in reading and mathematics: Who falls increasingly behind? Journal of Learning Disabilities, 44, 472-488. https://doi.org/10.1177%2F0022219411414010 adresinden 08.01.2021 tarihinde erişilmiştir.
• Morgenlander, M., & Manlapig, L. (2006). Big Math for Little Kids workshops: Background and content. Paper presented at the annual meeting of the American Educational Research, San Francisco.
• Murphy, M. M., Mazzocco, M. M. M., Hanich, L. B., & Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cut off criterion used to define MLD. Journal of Learning Disabilities, 40, 458-478. https://doi.org/10.1177%2F00222194070400050901 adresinden 08.01.2021 tarihinde erişilmiştir.
• NAEYC & NCTM (2010). Early childhood mathematics education: Promoting good beginnings. https://www.naeyc.org/sites/default/files/globally-shared/downloads/PDFs/resources/position-statements/psmath.pdf adresinden 15.11.2020 tarihinde erişilmiştir.
• Naslund-Hadley, E., Parker, S. W., & Hernandez-Agramonte, J. M. (2014). Fostering early math comprehension: Experimental evidence from Paraguay. Global Education Review, 1(4), 123-135.
• OECD (2018). PISA 2018 results: Where all students can succed (Volume II). PISA, OECD Publishing, Paris. https://www.oecd-ilibrary.org/sites/f7986824-en/index.html?itemId=/content/component/f7986824-en adresinden 20.11.2021 tarihinde erişilmiştir.
• Opel, A., Zaman, S. S., Khanom, F., & Aboud, F. E. (2012). Evaluation of a mathematics program for preprimary children in rural Bangladesh. International Journal of Educational Development, 32, 104-110. https://doi.org/10.1016/j.ijedudev.2011.01.013 adresinden 15.11.2020 tarihinde erişilmiştir.
• Öztürk, H. Z. ve Yıkmış, A. (2020). Tablet üzerinde eş zamanlı ipucuyla sunulan nokta belirleme tekniği kullanarak rakam-nesne eşleme öğretiminde dokunarak rakamları öğrenelim yazılımının etkililiği. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 21(4), 639-662 . https://doi.org/10.21565/ozelegitimdergisi.518651 adresinden 19.11.2021 tarihinde erişilmiştir.
• Pasnak, R., Greene, M. S., Ferguson, E. O., & Levit, K. (2006). Applying principles of development to help at-risk preschoolers develop numeracy. The Journal of Psychology, 140, 155-173. https://doi.org/10.3200/JRLP.140.2.155-173 adresinden 09.01.2021 tarihinde erişilmiştir.
• Passolunghi, M. C., & Lanfranchi, S. (2012). Domain-specific and domain-general pre-cursors 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 adresinden 14.01.2021 tarihinde erişilmiştir.
• Purpura, D. J., Baroody, A. J., & Lonigan, C. J. (2013). The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge. Journal of Educational Psychology, 105 (2), 453-464. http://dx.doi.org/10.1037/a0031753 adresinden 10.01.2021 tarihinde erişilmiştir.
• Rakap, S. (2017). Impact of coaching on preservice teachers’ use of embedded ınstruction in ınclusive preschool classrooms. Journal of Teacher Education, 68(2), 125–139. https://doi.org/10.1177/0022487116685753 adresinden 23.11.2021 tarihinde erişilmiştir.
• Ramani, G.B., & Siegler, R.S. (2008). Promoting broad and stable improvements in low income children’s numerical knowledge through playing number board games. Child Development, 79, 375-394. http://dx.doi.org/10.1037/a0031753 adresinden 08.02.2021 tarihinde erişilmiştir.
• Rasmussen, C., & Bisanz, J. (2011). The relation between mathematics and working memory in young children with fetal alcohol spectrum disorders. The Journal of Special Education, 45, 184-191. https://doi.org/10.1177%2F0022466909356110 adresinden 25.02.2021 tarihinde erişilmiştir.
• Rittle-Johnson, B., Fyfe, E.R., Loehr, A.M., & Miller, M.R. (2017). Beyond numeracy in preschool: Adding patterns to the equation. Early Childhood Research Quarterly, 31,101-112. https://doi.org/10.1016/j.ecresq.2015.01.005 adresinden 17.11.2020 tarihinde erişilmiştir.
• Rodriguez, E. L., & Tamis-Lemonda, C. S. (2011). Trajectories of the home learning environment across the first 5 years: Associations with children’s vocabulary and literacy skills at prekindergarten. Child Development, 82 (4), 1058-1075. https://doi.org/10.1111/j.1467-8624.2011.01614.x adresinden 14.11.2020 tarihinde erişilmiştir.
• Sarama, J., & Clements, D. H. (2002). Building Blocks for young children’s mathematical development. Journal of Educational Computing Research, 27 (1/2), 93–110. https://doi.org/10.2190%2FF85E-QQXB-UAX4-BMBJ adresinden 26.01.2021 tarihinde erişilmiştir.
• Sarama, J., & Clements, D. H. (2004). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19(1), 181. https://doi.org/10.1016/j.ecresq.2004.01.014 adresinden 26.01.2021 tarihinde erişilmiştir.
• Sarama, J. & Clements, D. H. (2008). Mathematics in early childhood. In Spodek, B. & Saracho, O. N., Contemporary Perspectives on Mathematics in Early Childhood Education (pp. 67-89). Charlotte, N.C: Information Age Publishing.
• Sarama, J., Clements, D.H., Starkey, P., Klein, A. & Wakeley, A. (2008). Scaling up the implementation of a pre-kindergarten mathematics curriculum: Teaching for understanding with trajectories and technologies. Journal of Research on Educational Effectiveness, 1(2), 89-119. https://doi.org/10.1080/19345740801941332 adresinden 10.11.2020 tarihinde erişilmiştir.
• Sarama, J., Lange, A., Clements, D. H., & Wolfe, C. B. (2012). The impacts of an early mathematics curriculum on emerging literacy and language. Early Childhood Research Quarterly, 27, 489-502. https://doi.org/10.1016/j.ecresq.2011.12.002 adresinden 24.12.2020 tarihinde erişilmiştir.
• Schopman, E.A.M. & Van Luit, J.E.H. (1999). Counting strategies among kindergartners with special educational needs: An exploratory study. European Journal of Special Needs Education, 14 (1), 61-69. https://doi.org/10.1080/0885625990140106 adresinden 27.01.2021 tarihinde erişilmiştir.
• Schweingruber, H., Woods, T. A., Cross, C. T., & National Research Council. (2009). Mathematics learning in early childhood: Paths towards excellence and equality. Washington, D.C.: National Academies Press.
• Seefeldt, C., & Galper, A. (2008). Active experiences for active children: Mathematics (2nd ed.). Upper Saddle River, NJ: Pearson.
• Siegler, R. S., & Ramani, G. B. (2008). Playing linear numerical board games promotes low-income children’s numerical development. Developmental Science, 11, 655-661. https://doi.org/10.1111/j.1467-7687.2008.00714.x adresinden 06.03.2021 tarihinde erişilmiştir.
• Skoumpourdi, C., & Mpakopoulou, I. (2011). The prints: A picture book for pre-formal geometry. Journal of Early Childhood Education, 39, 197-206. https://doi.org/10.1007/s10643-011-0454-0 adresinden 13.12.2020 tarihinde erişilmiştir.
• Skwarchuk, S.-L., Sowinski, C., & LeFevre, J.-A. (2014). Formal and informal home learning activities in relation to children’s early numeracy and literacy skills: The development of a home numeracy model. Journal of Experimental Child Psychology, 121, 63–84. https://doi.org/10.1016/j.jecp.2013.11.006 adresinden 19.02.2021 tarihinde erişilmiştir.
• Starkey, P., & Klein, A. (2008). Sociocultural influences on young children’s mathematical knowledge. In O. N. Saracho, & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education, (pp. 253–276). Greenwich, CT: Information Age.
• Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children’s mathematical knowledge through a pre-kindergarten mathematics intervention. Early Childhood Research Quarterly, 19, 99–120. https://doi.org/10.1016/j.ecresq.2004.01.002 adresinden 05.01.2021 tarihinde erişilmiştir.
• Sterner, G., Wolff, U., & Helenius, O. (2020). Reasoning about representations: Effects of an early math intervention. Scandinavian Journal of Educational Research, 64(5), 782–800. https://doi.org/10.1080/00313831.2019.1600579
• Swanson, H., & Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76, 249-274. https://doi.org/10.3102%2F00346543076002249 adresinden 15.01.2021 tarihinde erişilmiştir.
• Toll, S.W.M, Van der Ven, S.H.G., Kroesbergen, E.H. , & Van Luit, J.E.H. (2011). Executive functions as predictors of math learning disabilities. Journal of Learning Disabilities, 44, 521-532. https://doi.org/10.1177%2F0022219410387302 adresinden 17.01.2021 tarihinde erişilmiştir.
• Wei, X., Lenz, K. B., & Blackorby, J. (2012). Math growth trajectories of students with disabilities: Disability category, gender, racial, and socioeconomic status differences from ages 7 to 17. Remedial and Special Education, 34(3), 154–165. https://doi.org/10.1177%2F0741932512448253 adresinden 17.01.2021 tarihinde erişilmiştir.
• Welsh, J. A., Nix, R. L., Blair, C., Bierman, K. L., & Nelson, K. E. (2010). The development of cognitive skills and gains in academic school readiness for children from low-income families. Journal of Educational Psychology, 102, 43–53. https://doi.org/10.1037/a0016738 adresinden 20.11.2021 tarihinde erişilmiştir.
• Wilson, A. J., Dehaene, S., Dubois, O., & Fayol, M. (2009). Effects of an adaptive game intervention on accessing number sense in low‐socioeconomic‐status kindergarten children. Mind, Brain, and Education, 3 (4), 224-234. https://doi.org/10.1111/j.1751-228X.2009.01075.x adresinden 19.01.2021 tarihinde erişilmiştir.
• Wortham, C. S. (2006). Early childhood curriculum, developmental bases for learning and teaching (Fourth edition). New Jersey: Pearson/ Merrill/Prentice Hall.
• Van den Heuvel-Panhuizen, M., & Iliada, E. (2011). Kindergartener’s performance in length measurement and the effect of picture book reading. ZDM Mathematics Education, 43, 621-635. https://doi.org/10.1007/s11858-011-0331-8 adresinden 12.01.2021 tarihinde erişilmiştir.
• VanDerHeyden, A. M. (2010). Determining early mathematical risk: Ideas for extending the research. School Psychology Review, 39 (7), 196-202. https://doi.org/10.1080/02796015.2010.12087773 adresinden 24.12.2020 tarihinde erişilmiştir.
• Van der Sluis, S., De Jong, P. F., & Van der Leij, A. (2007). Executive functioning in children, and its relations with reasoning, reading, and arithmetic. Intelligence, 35, 427–449. https://doi.org/10.1016/j.intell.2006.09.001 adresinden 20.11.2021 tarihinde erişilmiştir.
• Van Luit, E. H. J. (2011.) Difficulties with preparatory skills in kindergartners. International Journal of Disability, Development and Education, 58(1), 89-95. https://doi.org/10.1080/1034912X.2011.547355 adresinden 19.01.2021 tarihinde erişilmiştir.
• Van Luit, J. E. H., & Schopman, E. A. M. (2000). Improving early numeracy of young children with special educational needs. Remedial and Special Education, 21(1), 27–40. https://doi.org/10.1177%2F074193250002100105 adresinden 05.01.2021 tarihinde erişilmiştir.
• Vukovic, R. K. (2012). Mathematics difficulty with and without reading difficulty: Findings and implications from a four-year longitudinal study. Exceptional Children, 78, 280-300. https://doi.org/10.1177%2F001440291207800302 adresinden 24.02.2021 tarihinde erişilmiştir.
• Yüzbaşıoğlu, Y. (2019). Küçük Çocuklar için Büyük Matematik (Big Math for Little Kids) eğitim programının 36-48 aylık çocukların matematik becerilerine etkisinin incelenmesi. (Yayın No. 594303) [Doktora tezi, Selçuk Üniversitesi]. YÖK Ulusal Tez Merkezi. https://tez.yok.gov.tr/UlusalTezMerkezi/ adresinden 06.03.2021 tarihinde erişilmiştir.