kuje Kocaeli Üniversitesi Eğitim Dergisi 2636-8846 Kocaeli Üniversitesi 10.33400/kuje.1059336 Other Fields of Education Alan Eğitimleri Erken Matematik Ölçeği’nin Türkçeye uyarlanması: Geçerlik ve güvenirlik çalışması Adaptation of Early Math Questionnaire to Turkish: A study of validity and reliability https://orcid.org/0000-0002-1439-9468 Karakuş Hilal SİNOP ÜNİVERSİTESİ 05 31 2022 5 1 197 220 01 19 2022 05 30 2022 Copyright © 2018, Kocaeli Üniversitesi Eğitim Dergisi 2018 Kocaeli Üniversitesi Eğitim Dergisi

Matematiksel kavram ve becerilerin gelişiminde erken çocukluk döneminin son derece etkili ve önemli olduğu bilindiği için çocukların matematik becerileri okulda ve evde sistemli matematik programlarıyla desteklenmelidir. Dolayısıyla öğretmenlerin ve ebeveynlerin işbirliği içinde çalışmaları gerekmektedir. Ebeveynlerin matematik etkinliklerine katılımları çocukların matematiksel gelişimlerine katkı sağlamaktadır. Ebeveynlerin matematik etkinliklerine katılımlarının yanı sıra ebeveynlerin matematik inançları da çocukların matematiksel gelişimlerini etkilemektedir. Bu araştırmanın amacı Missall ve diğerleri (2015) tarafından geliştirilen ve orijinal adı “Early Math Questionnaire” olan Erken Matematik Ölçeği’ni Türkçeye uyarlamak ve ölçeğin geçerlik ve güvenirliğini test etmektir. Araştırmanın çalışma grubunu okul öncesi dönemde çocuğu olan ve araştırmaya gönüllü olarak katılan 205 ebeveyn oluşturmuştur. Erken Matematik Ölçeği’nin orijinali, Matematik Etkinlikleri ve Matematik İnançları olmak üzere iki bölümden oluşmaktadır. Yapılan Doğrulayıcı Faktör Analizi (DFA) sonucunda Matematik Etkinlikleri Bölümünün dört alt boyut ve 36 maddeden oluştuğu bulunmuştur. Ölçeğin Matematik Etkinlikleri Bölümünün genel Cronbach Alfa (α) ve McDonald Omega (ω) güvenirlik katsayıları sırasıyla .966 ve .988 olarak bulunmuştur. Matematik İnançları Bölümünün iki alt boyut ve sekiz maddeden sekiz maddeden oluştuğu bulunmuştur. Ölçeğin Matematik İnançları Bölümünün genel Cronbach Alfa (α) ve McDonald Omega (ω) güvenirlik katsayıları sırasıyla .842 ve .883 olarak bulunmuştur. Bu sonuçlar Erken Matematik Ölçeği’nin Türkçe formunun geçerli ve güvenilir bir ölçme aracı olduğunu göstermektedir.

Since it is known that the early childhood period is extremely effective and important in the development of mathematical concepts and skills, children's mathematical skills should be supported by systematic mathematics programs at school and home. Therefore, teachers and parents need to work collaboratively. Parents' participation in mathematical activities contributes to the mathematical development of children. In addition to parents' participation in mathematical activities, parents' mathematical beliefs also affect children's mathematical development. This study aims to adapt the Early Math Questionnaire, which was developed by Missall et al. (2015), into Turkish and test the validity and reliability of the scale. The study group of the research consisted of 205 parents who had preschool children and who participated in the study voluntarily. The original “Early Math Questionnaire” consists of two sections: Math Activities and Math Beliefs. As a result of the Confirmatory Factor Analysis (CFA), it was found that the Math Activities Section consisted of four sub-dimensions and 36 items. The general Cronbach Alpha (α) and McDonald Omega (ω) reliability coefficients of the Math Activities Section of the scale were found as .966 and .988, respectively. It was found that the Math Beliefs Section consisted of two sub-dimensions and eight items. The general Cronbach Alpha (α) and McDonald Omega (ω) reliability coefficients of the Math Beliefs Section of the scale were found as .842 and .883, respectively. These results show that the Turkish form of the Early Math Questionnaire is a valid and reliable measurement tool.

 erken çocukluk dönemi erken matematik ölçeği ebeveynlerin matematik etkinliklerine katılımları ebeveynlerin matematik inançları geçerlik güvenirlik early childhood early math questionnaire participation of parents in math activities parents validity reliability Akıncı-Coşgun, A. (2018). Ev merkezli sayı ve işlem eğitim programının okul öncesi çocukların erken matematik yetenekleri ile anne çocuk ilişkisi üzerine etkisinin incelenmesi (Yayımlanmamış doktora tezi). Gazi Üniversitesi. Akman, B. (2002). Okulöncesi dönemde matematik. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23(23), 244-248. Alpar, R. (2017). Uygulamalı çok değişkenli istatistiksel yöntemler (5.Baskı). Detay Yayıncılık. 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. Anderson, A. (1997). Families and mathematics: A study of parent-child interactions. Journal for Research in Mathematics Education, 28(4), 484-513. Bailey, D. H., Siegler, R. S., & Geary, D. C. (2014). Early Predictors of Middle School Fraction Knowledge. Developmental Science, 17, 775–785. Bartlett, M. S. (1950). Tests of significance in factor analysis. British Journal of Statistical Psychology, 3(2), 77-85. Begum, N. N. (2007). Effect of parent involvement on math and reading achievement of young children: Evidence from the early childhood longitudinal study (Unpublished doctoral dissertation). Indiana University. 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. Blevins-Knabe, B., Austin, A. B., Musun, L., Eddy, A., & Jones, R. M. (2000). Family home care providers’ and parents’ beliefs and practices concerning mathematics with young children. Early Child Development and Care, 165, 41–58. Bronfenbrenner, U. (1979). The ecology of human development. Harvard University Press. Büyüköztürk, Ş. (2002). Faktör analizi: Temel kavramlar ve ölçek geliştirmede kullanımı. Kuram ve uygulamada eğitim yönetimi, 32(32), 470-483. Büyüköztürk, Ş. (2018). Sosyal bilimler için veri analizi el kitabı: İstatistik, araştırma deseni, SPSS uygulamaları ve yorum (24. Baskı). Pegem Akademi Yayıncılık. Cannon, J., & Ginsburg, H. P. (2008). ‘‘Doing the math’’: Maternal beliefs about early mathematics versus language learning. Early Education and Development, 19, 238–260. Castro, M., Expósito-Casas, E., López-Martín, E., Lizasoain, L., Navarro-Asencio, E., & Gaviria, J. (2015). Parental involvement on student academic achievement: A meta-analysis. Educational Research Review, 14(1), 33–46. Charlesworth, R., & Lind, K. K. (2013). Math & science for young children (7. Baskı). Wadsworth Cengage Learning. Charlesworth, R., & Radeloff, J. D. (1991). Experiences in math for young children. Delmar. Cheung, C., & Pomerantz, E. (2011). Parents’ involvement in children’s learning in the United States and China: Implications for children’s academic and emotional adjustment. Child Development, 82(3), 932–950. Claessens, A., & Engel, M. (2013). How important is where you start? Early mathematics knowledge and later school success. Teachers College Record, 115(6), 1-29. Clements, D. H. (2004). Major themes and recommendations. D. H. Clements, J. Sarama & A. M. DiBiase (Ed.) içinde, Engaging young children in mathematics: Standards for early childhood mathematics education (ss. 7–76). Lawrence Erlbaum. Clements, D. H., & Sarama, J. (2009). Learning and teaching early math. The learning trajectories approach. Routledge. Cronbach, L. J. (1951). Coeffıcient alpha and the internal structure of tests. Psychometrika, 16, 297-334. Daucourt, M. C., Napoli, A. R., Quinn, J. M., Wood, S. G., & Hart, S. A. (2021). The home math environment and math achievement: A meta-analysis. Psychological Bulletin, 147(6), 565–596. DeFlorio, L. L. (2011). The influence of the home learning environment on preschool children's informal mathematical development: Variation by age and socioeconomic status (Unpublished doctoral dissertation). The University of California. Denton, K., & West, J. (2002). Children’s reading and mathematics achievement in kindergarten and first grade. https://nces.ed.gov/pubs2002/2002125.pdf Dinçer, Ç., & Ulutaş, İ. (1999). Yaşamımızdaki ilk matematiksel kavramlar ve materyaller. Çağdaş Eğitim, 253, 23-28. Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., ... & Sexton, H. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428-1446. Ergel, A., & Aydoğan., (2021). Erken çocukluk döneminde matematik becerilerini kazandırmaya yönelik ebeveyn görüşlerini kazandırmaya yönelik ebeveyn görüşleri. Uluslararası Sosyal Araştırmalar Dergisi, 14 (77), 761-768. 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. Ertürk Kara, H. G., & Kılıç Çoksoyluer, Ş. (2017). Encouragement of early academic skills at home during early childhood period: Validity and reliability study of the EASYC Scale. Universal Journal of Educational Research, 5(12), 2294 – 2303. Gall, M. D., Gall, J. P., & Borg, W. R. (2007). Educational research: An introduction (8. Baskı). Pearson Education. George, D., & Mallery, M. (2003). Using SPSS for Windows step by step: A simple guide and reference. Allyn & Bacon. Ginsburg, H. P., & Baroody, A. J. (2003). Test of Early Mathematics Ability–Third Edition. PRO-ED. Griffin, S. (2004). Building number sense with Number Worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19, 173-180. Gujarati, D. N. (2004). Basic Econometrics (4. Baskı). McGraw-Hill. Gunderson, E. A., Ramirez, G., Levine, S. C., & Beilock, S. L. (2012). The role of parents and teachers in the development of gender-related math attitudes. Sex Roles, 66, 153-166. Güleç, N., & İvrendi, A. (2017). 5-6 yaş çocuklarının sayı kavramı becerilerinin ebeveyn ve öğretmen değişkenleri açısından yordanması. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 32(1), 81-98. Günay-Bilaloğlu, R. (2014). Okul öncesi eğitimde aile katılımı etkinliklerinin uygulanmasında karşılaşılan sorunlar ve aile katılımı etkinliklerinin dil-matematik becerilerinin geliştirilmesine etkisi (Yayımlanmamış doktora tezi). Çukurova Üniversitesi. Gürgah Oğul İ., Aslan, D., & Aktaş Arnas, Y. (2018, June). A validity and reliability study of parents’ participation in home math activities scale. Paper presented at 70th OMEP World Assembly and Conference, Prague, Czechia. Gürgah Oğul, İ., & Aktaş Arnas, Y. (2021). Role of home mathematics activities and mothers’ maths talk in predicting children’s maths talk and early maths skills. European Early Childhood Education Research Journal, 29(4), 501-518. Gürgah Oğul, İ., & Aktaş Arnas, Y. (2022). Understanding home math environments and math talks of children with low and middle socioeconomic status. Participatory Educational Research, 9(4), 53-70. Haktanır, H. (2021). Okul öncesi dönemde matematik ve okuma yazmaya hazırlık becerilerinin evde desteklenme düzeyinin incelenmesi (Yayımlanmamış doktora tezi). Pamukkale Üniversitesi. Huntsinger, C. S., Jose, P. E., Larson, S. L., Krieg, D. B., & Shaligram, C. (2000). Mathematics, vocabulary, and reading development in Chinese American and European American children over the primary school years. Journal of Educational Psychology, 92, 745–760. Huntsinger, C. S., Jose, P. E., & Luo, Z. (2016). Parental facilitation of early mathematics and reading skills and knowledge through encouragement of home-based activities. Early Childhood Research Quarterly, 37, 1-15. İrkörücü, S. (2006). Okul öncesi eğitim kurumuna devam eden altı yaşındaki çocuklara uygulanan ev odaklı matematiksel destek programının çocukların matematiksel kavram edinimine etkisinin incelenmesi (Yayımlanmamış yüksek lisans tezi). Gazi Üniversitesi. İvrendi, A., & Wakefield, A. (2009). Mothers’ and fathers’ participation in mathematical activities of their young children. The 5th International Balkan Education and Science Congress (ss. 50-54). Edirne: Trakya University. Jacobs, J. E., & Bleeker, M. M. (2004). Girls' and boys' developing interests in math and science: Do parents matter?. New Directions for Child and Adolescent Development, 106, 5-21. Johnson, R. B., & Christensen, L. B. (2019). Educational research: Quantitative, qualitative, and mixed approaches (7. Baskı). Sage Publications. Jöreskog, K., & Sörbom, D. (1993). Lisrel 8: Structural equation modeling with the SİMPLİS command language. Scientific Software International. Kaiser, H. (1974). An index of factorial simplicity. Psychometrika, 39(1), 31–36 Kaiser, H. F., & Rice, J. (1974). Little jiffy, mark IV. Educational and Psychological Measurement, 34(1), 111-117. Kandır, A., & Orçan, M. (2010). Okul öncesi dönemde matematik eğitimi. Morpa Kültür Yayınları. Karakuş, H. (2020). “Okul Öncesi Matematik Programı”nın çocukların matematik becerilerine etkisi (Yayımlanmamış doktora tezi). Hacettepe Üniversitesi. Keilty, B. (2010). The early intervention guidebook for families and professionals: Partnering for success. Teachers College Press. Kleemans, T., Peeters, M., Segers, E., & Verhoeven, L. (2012). Child and home predictors of early numeracy skills in kindergarten. Early Childhood Research Quarterly, 27,471-477. 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. Klein, A., Starkey, P., Deflorio, L., & Brown, E. T. (2011). Scaling up an effective pre-k mathematics intervention: Mediators and child outcomes. Society for Research on Educational Effectiveness 2011 Conference, Washington, DC, 8–11 September. Klein, A., Starkey, P., & Ramirez, A. (2002). Pre-K Mathematics curriculum. Scott Foresman. Klein, A., Starkey, P., & Wakeley, A. (1999). Enhancing pre-kindergarten children’s readiness for school mathematics. Paper presented at the American Educational Research Association, Montreal, Canada. http://files.eric.ed.gov/fulltext/ED431556.pdf Kleinbaum, D. G., Kupper, L. L., Nizam, A., & Rosenberg, E. S. (2014). Applied regression analysis and other multivariable methods (5. Baskı). Cengage Learning. Kline, P. (1994). An easy guide to factor analysis. Routledge. 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. 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), 55-56. Linnell, M., & Fluck, M. (2001). The effect of maternal support for counting and cardinal understanding in pre‐school children. Social Development, 10(2), 202-220. Lucke, J. F. (2005). The α and ω of congeneric test theory: An extension of reliability and internal consistency to heterogeneous tests. Applied Psychological Measurements, 29(1), 65-81. Manolitsis, G., Georgiou, G., & Tziraki, N. (2013). Examining the effects of home literacy and numeracy environment on early reading and math acquisition. Early Childhood Research Quarterly, 28, 692-703. McDonald, R. (1985). Factor analysis and related methods. Lawrence Erlbaum. Melhuish, E. C., Sylva, K., Sammons, P., Siraj-Blatchford, I., Taggart, B., Phan, M. B., & Malin, A. (2008). Preschool influences on mathematics achievement. Science, 321(5893), 1161-1162. Missall, K. N., 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. Missall, K. N., Hojnoski, R. L., & Moreano, G. (2017). Parent-child mathematical interactions: examining self-report and direct observation. Early Child Development and Care, 187(12), 1896-1908. National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. NCTM. National Research Council, (2001). Adding it up: Helping children learn mathematics. The National Academies Press. Niklas, F., & Schneider, W. (2014). Casting the die before the die is cast: The importance of the home numeracy environment for preschool children. European Journal of Psychology of Education, 29, 327-345. Nunnally, J. C., & Bernstein, I. H. (1994). Psychometric theory (3. Baskı). McGraw-Hill. Pallant, J. (2007). SPSS survival manual: A step-by-step guide to data analysis using SPSS for windows. Open University Pres. Perry, B., Gervasoni, A., & Dockett, S. (2012). Let’s Count: Evaluation of a pilot early mathematics program in low socioeconomic locations in Australia. J. Dindyal, L. P. Cheng, & S. F. Ng (Ed.) içinde, Mathematics education: Expanding horizons. Proceedings of the 35th Annual Conference of the Mathematics Education Research Group of Australasia (ss.594–601). MERGA. Pett, M. A., Lackey, N. R., & Sullivan, J. J. (2003). Making sense of factor analysis: The use of factor analysis for instrument development in health care research. Sage Publications. Preschool Curriculum Evaluation Research [PCER] Consortium. (2008). Effects of preschool curriculum programs on school readiness (NCER 2008-2009). National Center for Education Research, Institute of Education Sciences. Purpura, D. J., King, Y.A., Rolan, E., Hornburg, C.B., Schmitt, S.A., Hart, S.A., & Ganley, M. (2020). Examining the factor structure of the home mathematics environment to delineate ıts role in predicting preschool numeracy, mathematical language, and spatial skills. Frontiers in Psychology, 11(1925), 1-14. Ramani, G. B., & Siegler, R. S. (2015). How informal learning activities can promote children’s numerical knowledge. R. C. Kadosh, & A. Dowker (Ed.) içinde, In the Oxford Handbook of numerical cognition (1135–1153). Oxford University Press. Rodriguez, E. T., & 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, 1058-1075 Ross, T. (2016). The differential effects of parental involvement on high school completion and postsecondary attendance. Education Policy Analysis Archives, 24, 30. 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. Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of Psychological Research Online, 8(2), 23–74. Skwarchuk, S. (2009). How do parents support preschoolers’ numeracy learning experiences at home?. Early Childhood Education Journal, 37(3), 189–197. Smith, S. (2015). Playing to engage: Fostering engagement for children and teachers in low socioeconomic regions through science and mathematics play-based learning (Unpublished doctoral dissertation). University of Notre Dame Australia. Starkey, P., & Klein, A. (2000). Fostering parental support for children's mathematical development: An intervention with Head Start families. Early Education and Development, 11(5), 659-680. Starkey, P., & Klein, A. (2008). Sociocultural influences on young children’s mathematical knowledge. O. N. Saracho, & B. Spodek (Ed.) içinde, Contemporary perspectives on mathematics in early childhood education (ss. 253–276). Information Age Publishing. 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. Susperreguy, M. I., Douglas, H., Xu, C., Molina-Rojas, N., & LeFevre, J.-A. (2020). Expanding the Home Numeracy Model to Chilean children: Relations among parental expectations, attitudes, activities, and children’s mathematical outcomes. Early Childhood Research Quarterly, 50(3), 16–28. Sümer, N. (2000). Yapısal eşitlik modelleri: Temel kavramlar ve örnek uygulamalar. Türk Psikoloji Yazılar, 3(6), 49–74. Tabachnick, B. G. & Fidell, L. S.(2019). Using multivariate statistics (7. Baskı). Pearson Education. Ullman, J. B. (2019). Structural Equation Modeling. B. G. Tabachnick & L. S. Fidell (Eds.) içinde, Using Multivariate Statistics (7. Baskı) (ss. 653-771). Pearson Education. Vandermaas-Peeler, M., Nelson, J., Bumpass, C., & Sassine, B. (2009). Numeracy-related exchanges in joint storybook reading and play. International Journal of Early Years Education, 17, 67–84. Van-Voorhis, F. L., Maier, M. F., Epstein, J. L., & Lloyd, C. M. (2013). The impact of family involvement on the education of children ages 3 to 8: A focus on literacy and math achievement outcomes and social-emotional skills. Building Knowledge to Improve Social Policy. http://www.mdrc.org/sites/default/files/The_Impact_of_Family_Involvement_FR.pdf Vukovic, R., Roberts, S., & Green Wright, L. (2013). From parental involvement to children’s mathematical performance: The role of mathematics anxiety. Early Education and Development, 24(4), 446–467. Wakefield, A. P. (1997). Supporting math thinking. The Phi Delta Kappan, 79(3), 233-236. Yan, W., & Lin, Q. (2005). Parent involvement and mathematics achievement: Contrast across racial and ethnic groups. The Journal of Educational Research, 99(2), 116-127. Young-Loveridge, J. M. (2004). Effects on early numeracy of a program using number books and games. Early Childhood Research Quarterly, 19(1), 82-98. Yurdugül, H. (2006). Paralel, eşdeğer ve konjenerik ölçmelerde güvenirlik katsayılarının karşılaştırılması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Dergisi, 39(1), 15- 37. Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s a, Revelle’s, b and Mcdonald's w: Their Relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70(1), 1-11.