Erken Matematik Becerilerinin Geliştirilmesinde Erken Müdahale Programlarının Etkililiği: Bir Meta-analiz Çalışması

Yıl 2025, Cilt: 18 Sayı: 1, 54 - 80, 29.01.2025

Ensar Yıldız , Özge Koca , Şenel Elaldı

https://doi.org/10.30831/akukeg.1462376

Öz

Erken müdahale, planlanan hizmetlerden fayda sağlayabilecek küçük çocukları desteklemeye yönelik yaklaşımları içerir. Bu çalışma, okul öncesi ve anaokulu çocuklarına yönelik Big Math for Little Kids, Building Blocks ve Prekindergarten Mathematics Müdahale programlarını sentezleyerek son 15 yılda deneysel çalışmaları içeren erken müdahale programlarının erken matematik becerilerini geliştirmedeki etkililiğini belirlemeyi amaçlamaktadır. 146 çalışma arasından deneysel çalışma, yayın yanlılığı, etki büyüklüğü, heterojenlik, müdahale programının aracı değişkeni, müdahale süresi ve katılımcı yaşları gibi dâhil edilme kriterlerini karşılayan 10 çalışma değerlendirilmiştir. Sonuç olarak, rastgele etkiler modeline göre ve Cohen’in sınıflandırmasına dayalı olarak müdahale programlarının etkililiğine ilişkin büyük bir etki büyüklüğü (Hedges’g=1.217) bulunmuştur. Moderatör analizleri sonuçları uygulama süreleri arasında istatistiksel olarak anlamlı bir farklılık ortaya koyarken, müdahale programı türü ve yaş değişkenleri açısından anlamlı bir farklılık gözlenmemiştir. Matematik becerilerine yönelik müdahalelerin ilkokul öğrencileri üzerindeki etkilerine ilişkin meta-analizler mevcut olmasına rağmen, okul öncesi ve anaokulu çocuklarının matematik becerilerini geliştirmeye yönelik erken müdahale programlarını ele alan meta-analizler neredeyse yoktur. Bu çalışmanın sonuçları, erken müdahale programlarının matematik becerileri üzerindeki etkililiğine dair bir kanıt sağlamıştır.

Anahtar Kelimeler

erken müdahale, matematik becerileri, meta-analiz

Effectiveness of Early Intervention Programs in Developing Early Mathematical Skills: A meta-Analysis

Öz

Early intervention includes approaches to responding to young children may profit from targeted services. This study aims to synthesize recent evaluations of intervention programs of Big Math for Little Kids, Building Blocks, and Prekindergarten Mathematics Intervention Program in preschool and kindergarten children to determine the effectiveness of early intervention programs including experimental studies in last 15 years in developing early mathematical skills. Among 146 studies, 10 studies that met the inclusion criteria, which included experimental studies, publication bias, effect size, heterogeneity, moderator type of intervention program, the duration of the intervention, and the participants’ age. The results indicated a large effect size (Hedges’g=1.217) for the effectiveness of intervention programs according to random effects model and Cohen’s classification. While the results of moderator analyses highlighted a statistically meaningful difference in implementation periods, no significant differences were observed in terms of type of intervention program and age variables. Although meta-analyses regarding the effects of math interventions on school age students are available, there are hardly any meta-analyses addressing early intervention programs for enhancing preschool and kindergarten children’s math skills. The outcomes of the current study provided an evidence of the effectiveness of early intervention programs on math skills.

Anahtar Kelimeler

early intervention, mathematical skills, meta-analysis

Kaynakça

• Aleknaviciute, V., Lehtinen E., Sodervik I.(2023). Thirty years of conceptual change research in biology – A review and meta-analysis of intervention studies. Educational Research Review, 41, 1-25.
• Altındag Kumas, O. (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 (PER), 7(2), 33-46. http://dx.doi.org/10.17275/per.20.18.7.2.
• Altındag Kumas, O., & Ergul, C. (2021). Effectiveness of the Big Math for Little Kids Program on the early mathematics skills of children with risk group. Athens Journal of Education, 8(4), 385-400. http://dx.doi.org/10.30958/aje.8-4-3.
• Arteaga, I., Thornburg, K., Darolia, R., & Hawks, J. (2019). Improving teacher practices with children under five: Experimental evidence from the Mississippi Buildings Blocks. Evaluation Review, 43(1-2), 41-76. http://dx.doi.org/10.1177/0193841X19865070.
• Baker, S., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-73.
• Bax, L., Yu, L. M., Ikeda, N., & Moons, K. G. (2007). A systematic comparison of software dedicated to meta-analysis of causal studies. BMC Medical Research Methodology, 7, 40. http://dx.doi.org/10.1186/1471-2288-7-40.
• Begg, C. B., & Mazumdar, M. (1994). Operating characteristics of a rank correlation test for publication bias. Biometrics, 50(4), 1088-1101. http://dx.doi.org/10.2307/2533446.
• Björklund, C., van den Heuvel-Panhuizen, M., & Kullberg, A. (2020). Research on early childhood mathematics teaching and learning. ZDM Mathematics Education, 52, 607-619. https://doi.org/10.1007/s11858-020-01177-3.
• Bloch, M. H. (2014). Meta-analysis and moderator analysis: Can the field develop further? Journal of the American Academy of Child and Adolescent Psychiatry, 53(2),135-7. http://dx.doi.org/10.1016/j.jaac.2013.12.001.
• Bojorquea, G., Torbeyns, J., Van Hoof, J., Van Nijlenb, D., & Verschaffel, L. (2018). Effectiveness of the Building Blocks program for enhancing Ecuadorian kindergartners’ numerical competencies. Early Childhood Research Quarterly, 44(3), 231-241. https://doi.org/10.1016/j.ecresq.2017.12.009.
• Borenstein, M., & Rothstein, H. (1999). Comprehensive meta-analysis. A computer program for research synthesis. Biostat.
• Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein, H. R. (2009). Introduction to meta-analysis. John Wiley & Sons, Ltd.
• Braak, D., Lenes, R., Purpura, D. J., Schmitt, S. A., & Størksen, I. (2022). Why do early mathematics skills predict later mathematics and reading achievement? The role of executive function. Journal of Experimental Child Psychology, 214, 1-18. https://doi.org/10.1016/j.jecp.2021.105306.
• Brown, N., Afflerbach, P., & Croninger, R. (2014). Assessment of critical-analytic thinking. Educational Psychology Review, 26, 543-560. https://doi.org/10.1007/s10648-014-9280-4.
• Carson, K. P., Schriesheim, C. A., & Kinicki, A. J. (1990). The usefulness of the "fail-safe" statistic in meta-analysis. Educational and Psychological Measurement, 50, 233-243.
• Celik, M., & Kandir, A. (2013). The effect of “Big Maths for Little Kids” curriculum on mathematical development of 61-72 month-old children. Journal of Theoretical Educational Science, 6(4), 551-567. http://dx.doi.org/10.5578/keg.6712.
• Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In F.K. Lester Jr. (Ed.). Second handbook of research on mathematics teaching and learning. Information Age Publishing, 461-555.
• 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.
• Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. Routledge.
• Coban, A., Yildiz, E., Aslan, H. S., Ögütcen, A., Koca, O., & Kaynar, F. (2023). Effectiveness of School Readiness Programs for Preschool Children: A Meta-Analysis Study. Educational Policy Analysis and Strategic Research, 18(3), 50-77.
• Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155-159. https://doi.org/10.1037/0033-2909.112.1.155.
• Codding, R. S., Hilt-Panahon, A., Panahon, C. J., & Benson, J. L. (2009). Addressing mathematics computation problems: A review of simple and moderate intensity interventions. Education and Treatment of Children, 32(2), 279-312.
• Codding, R. S., Burns, M. K., & Lukito, G. (2011). Meta-analysis of math basic-fact fluency interventions: A component analysis. Learning Disabilities Research & Practice, 26, 36-47.
• Cumming, G. (2012). Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. Routledge/Taylor & Francis Group.
• Deeks, J. J., Higgins, J. P. T., & Altman, D. G. (2021). Analysing data and undertaking meta-analyses. In Higgins J. P. T., Thomas, J., Chandler, J., Cumpston, M., Li T., Page, M.J., Welch, V. A. (editors). Cochrane handbook for systematic reviews of interventions (pp. 241-284). www.training.cochrane.org/handbook.
• Dettori, J. R., Norvell, D. C., & Chapman, J. R. (2021). Seeing the forest by looking at the trees: How to interpret a meta-analysis forest plot. Global spine journal, 11(4), 614-616.
• Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6),1428-1446. https://doi.org/10.1037/0012-1649.43.6.1428.
• Duval, S., & Tweedie, R. (2000). Trim and fill: A simple funnel-plot based method of testing and adjusting for publication bias in meta-analysis. Biometrics, 56(2), 455-463.
• Egger, M., Smith, G. D., Schneider, M., & Minder, C. (1997). Bias in meta-analysis detected by a simple, graphical test. British Medical Journal, 315, 629-634. https://doi.org/10.1136/bmj.315.7109.629.
• Field, A. P., & Gillett, R. (2010). How to do meta-analysis. British Journal of Mathematical and Statistical Psychology, 63, 665-694. https://doi.org/10.1348/000711010X502733.
• Gavaghan, D. J., Moore, A. R., & McQuay, H. J. (2000). An evaluation of homogeneity tests in meta-analyses in pain using simulations of individual patient data. Pain, 85(3), 415–424. https://doi.org/10.1016/S0304-3959(99)00302-4.
• Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242.
• Ginsburg, H. P., Greenes, C. E., & Balfanz, R. (2003). Big Math for Little Kids: Prekindergarten. Pearson Learning Group.
• Ginsburg, J. L., & Audley, S. (2020). You don’t wanna teach little kids about climate change: Beliefs and barriers to sustainability education in early childhood. International Journal of Early Childhood Environmental Education, 7(3), 42-61.
• Greenes, C., Ginsburg, H. P., & Balfanz, R. (2004). Big Math for Little Kids. Early Childhood Research Quarterly, 19(1), 159–166. https://doi.org/10.1016/j.ecresq.2004.01.010.
• Guddat, C., Grouven, U., Bender, R., & Skipka, G. (2012). A note on the graphical presentation of prediction intervals in random-effects meta-analyses. Systematic Reviews, 1(1), 34. https://doi.org/10.1186/2046-4053-1-34.
• Hamilton, M., & Liu, T. (2018). The effects of an intervention on the gross and fine motor skills of Hispanic Pre-K children from low ses backgrounds. Early Childhood Education Journal, 46, 1-8. https://doi.org/10.1007/s10643-017-0845-y.
• Harris, B., & Petersen, D. (2019). Developing math skills in early childhood. Mathematica, 1-6. https://files.eric.ed.gov/fulltext/ED594025.pdf.
• Hedges, L. V. (1992). Meta-Analysis. Journal of Educational Statistics, 17(4), 279-296. https://doi.org/10.3102/10769986017004279
• Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Academic Press.
• Higgins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003). Measuring inconsistency in meta-analyses. British Medical Journal, 327, 557–560.
• Higgins, J. P. T., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21, 1539-1558.
• Huedo Medina, T. B., Sánchez Meca, J., Marín Martínez, F., & Botella, J. (2006). Assessing heterogeneity in meta-analysis: Q statistic or 𝐼2 index?. Psychological Methods, 11(2), 193-206. https://doi.org/10.1037/1082-989X.11.2.193.
• Kandir, A., & Orcan, M. (2011). A comparative study into early learning skills of five six-year old children and their social adaptation and skills. Elementary Education Online, 10(1), 40-50.
• Kandir, A., Uyanık, O., & Celik, M. (2017). The effect of Big Math for Little Kids Program on children’s early academic and language skills. Gazi University Journal of Gazi Education Faculty (GEFAD), 37(1), 193–217.
• Karakus, H. (2020). The effect of pre-k mathematics curriculum on children's mathematics skills (Unpublished doctoral dissertation). Hacettepe University, Ankara, Turkey.
• Kermani, H., & Aldemir, J. (2015). Preparing children for success: integrating science, math, and technology in early childhood classroom. Early Child Development and Care, 185(9), 1504-1527.
• Khomais, S. (2014). Enhancing preschool children's number knowledge: The suitability of an intervention programme for Saudi practice. Early Child Development and Care, 184 (1), 32-49. https://doi.org/10.1080/03004430.2013.768238.
• Kilickaya, A., & Avci, C. (2021). The impact of Big Math for Little Kids on children’s number skills. Ankara University Journal of Faculty of Educational Sciences, 54(3), 777-803. https://doi.org/10.30964/auebfd.931541.
• Klein, A., Starkey, P., & Ramirez, A. (2002). Pre-K mathematics curriculum. Scott Foresman.
• Klein, A., Starkey, P., Deflorio, L., & Brown, E. T. (2011). Scaling up an effective Pre-K mathematics intervention: Mediators and child outcomes. https://www.sree.org/conferences/2011/program/downloads/abstracts/186.pdf .
• Kroesbergen, E. J., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. A meta-analysis. Remedial and Special Education, 24(2), 97-114. https://doi.org/10.1177/07419325030240020501.
• Kunsch, C. A., Jitendra, A. K., & Sood, S. (2007). The effects of peer-mediated instruction in mathematics for students with learning problems: A research synthesis. Learning Disabilities Research and Practice, 22(1), 1-12.
• Lipsey, M. W., & Wilson, D. (2001). Practical meta-analysis. Sage.
• Malofeeva, E. V. (2005). Meta-analysis of mathematics instruction with young children (Unpublished doctoral dissertation). University of Notre Dame, Notre Dame, IN.
• Methe, S. A., Kilgus, S. P., Neiman, C., & Chris Riley Tillman, T. (2012). Meta-analysis of interventions for basic mathematics computation in single-case research. Journal of Behavioral Education, 21(3), 230-253. https://doi.org/10.1007/s10864-012- 9161-1.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded Sourcebook. (2nd ed). Sage.
• Moher, D., Liberati, A., Tetzlaff, J., Altman, D. G., & The PRISMA Group (2009). Preferred reporting items for systematic reviews and meta-analyses: The PRISMA Statement. PLoS Medicine, 6(7),1-6.
• Mononen, R., Aunio, P., Koponen, T., & Aro, M. (2014) A review of early numeracy interventions for children at risk in mathematics. International Journal of Early Childhood Special Education, 6(1), 25–54.
• Morgan, P., & Wu, Q. (2011). Kindergarten children's growth trajectories in reading and mathematics: Who falls increasingly behind? Journal of Learning Disabilities, 44(5). 472-488. https://doi.org/10.1177/0022219411414010.
• Morgenlander, M., & Manlapig, L. (2006). Big Math for Little Kids workshops: Background and content. In annual meeting of the American Educational Research Association. San Francisco.
• Mullen, B., Muellerleile, P. & Bryant, B. (2001). Cumulative meta-analysis: A consideration of indicators of sufficiency and stability. Personality and Social Psychology Bulletin, 27(11), 1450–1462. https://doi.org/10.1177/01461672012711006
• Mwaura, P. A. M., Sylva, K., & Malmberg, L. E. (2008). Evaluating the Madrasa preschool programme in East Africa: a quasi-experimental study. International Journal of Early Years Education, 16(3), 237-255.
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. https://www.nctm.org/Standards-and-Positions/Principles-and-Standards/.
• National Council of Teachers of Mathematics (NCTM). (2010). Early childhood mathematics: Promoting good beginnings. https://www.naeyc.org/files/naeyc/file/positions/psmath.pd
• Navarro Soria, I., Álvarez Teruel, J.D., Granados Alós, L., & Lavigne Cerván, R. (2021). Early detection of academic performance during primary education using the Spanish Primary School Aptitude Test (AEI) battery. Frontiers in Psychology, 11, 1-10. https://doi.org/10.3389/fpsyg.2020.630803.
• Nicoll, B. (2007). Assessing research based curricula. International Journal of Arts and Sciences, 2, 2-4.
• O’Dell, R. S. (2005). The nature of implementation of an innovative Pre-K mathematics curriculum (Unpublished doctoral dissertation). The State University of New York, USA.
• Orwin, R. G. (1983). A fail-safe N for effect size in meta-analysis. Journal of Educational Statistics, 8(2), 157-159. https://doi.org/10.2307/1164923.
• Ozcan, Z. Ç., & Dogan, H. (2018). A longitudinal study of early math skills, reading comprehension and mathematical problem solving. Pegem Journal of Education and Instruction, 8(1), 01-18. http://dx.doi.org/10.14527/pegegog.2018.001.
• Papadakis, S., Kalogiannakis, M., & Zaranis, N. (2017). Improving mathematics teaching in kindergarten with realistic mathematical education. Early Childhood Education Journal, 45(3), 369-378. https://doi.org/10.1007/s10643-015-0768-4.
• Petticrew, M., & Roberts, H. (2006). Systematic reviews in the social sciences: A practical guide. Blackwell Publishing. https://doi.org/10.1002/9780470754887.
• Presser, L. A., 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.
• Rosenthal, R. (1979). The file drawer problem and tolerance for null results. Psychological Bulletin, 86(3), 638-641. https://doi.org/10.1037/0033-2909.86.3.638.
• Rothstein, H. R., Sutton, A. J., & Borenstein, M. (2005). Publication bias in meta-analysis: Prevention, assessment and adjustments. John Wiley & Sons, Ltd.
• Sarama, J., & Clements, D. H. (2002). Building Blocks for young children's mathematical development. Journal of Educational Computing Research, 27(1), 93-110 https://doi.org/10.2190/F85E-QQXB-UAX4-BMBJ.
• Sarama, J., & Clements, D. H. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89. https://doi.org/10.1207/s15327833mtl0602_1.
• Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research. Learning trajectories for young children. Routledge.
• Scalise, N., Daubert, N. A., & Ramani, G. B. (2017). Narrowing the early mathematics gap: A play-based intervention to promote Head Start preschoolers' number skills. Journal of Numerical Cognition, 3(3), 559-581.
• Sedgwick, P. M. (2013). Meta-analyses: how to read a funnel plot. BMJ Clinical Research, 346, f1342. https://doi.org/10.1136/bmj.f1342.
• Shadish, W. R., & Haddock, C. K. (2009). Combining estimates of effect size. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.). The handbook of research synthesis and meta-analysis (pp. 257-277). Russell Sage Foundation.
• Sollom, M. (2021). A Quasi-experimental study on social emotional learning and primary prevention. Journal of Educational and Developmental Psychology, 11(2),1-16. https://doi.org/10.5539/jedp.v11n2p1.
• 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. https://doi.org/10.1016/j.ecresq.2004.01.002.
• Sterne, J. A. C., Sutton, A. J., Ioannidis, J. P. A., Terrin, N., Jones, D. R., Lau, J., … Higgins, J. P. T. (2011). Recommendations for examining and interpreting funnel plot asymmetry in meta-analyses of randomised controlled trials. BMJ, 343, d4002. https://doi.org/10.1136/bmj.d4002.
• Sterne, J. A., & Harbord, R. M. (2004). Funnel plots in meta-analysis. The Stata Journal: Promoting Communications on Statistics and Stata, 4(2), 127-141. https://doi.org/10.1177/1536867X0400400204.
• Sullivan, G. M., & Feinn, R. (2012). Using effect size-or why the p value is not enough. Journal of Graduate Medical Education, 4(3), 279-282. https://doi.org/10.4300/JGME-D-12-00156.1
• Sutton, A. J. (2009). Publication bias. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.) The handbook of research synthesis and meta-analysis (pp. 435-452) Russell Sage Foundation.
• Swanson, H. L., Hoskyn, M., & Lee, C. (1999). Interventions for students with learning disabilities: A meta-analysis of treatment outcomes. Guilford Press.
• Thabane, L., Mbuagbaw, L., Zhang, S., Samaan, Z., Marcucci, M., Ye, C., Thabane, M., Giangregorio, L., Dennis, B., Kosa, D., Borg Debono, V., Dillenburg, R., Fruci, V., Bawor, M., Lee, J., Wells, G., & Goldsmith, C. H. (2013). A tutorial on sensitivity analyses in clinical trials: The what, why, when and how. BMC Medical Research Methodology, 13. https://doi.org/10.1186/1471-2288-13-92. Article 92.
• VanDerHeyden, A., & Snyder, P. (2006). Integrating frameworks from early childhood intervention and school psychology to accelerate growth for all young children. School Psychology Review, 35(4), 519-534. https://doi.org/10.1080/02796015.2006.12087959.
• Vevea, J. L. & Woods, C. M. (2005). Publication bias in research synthesis: Sensitivity analysis using a priori weight functions. Psychol Methods, 10(4), 428-43. https://doi.org/10.1037/1082-989X.10.4.428.
• Weber, S. M. (2009). The effects of a teacher-guided library selection program on fourth-grade reading achievement [Doctoral dissertation, Capella University]. ProQuest Dissertations Publishing.
• Xin, Y. P., & Jitendra, A. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. Journal of Special Education, 32(4), 207-225. https://doi.org/10.1177/002246699903200402.
• Young, J., & Loveridge, M. (2004). Effectson early numeracy of a program using number books and games. Early Childhood Research Quarterly, 19, 82-98.
• Zippert, E. L., Douglas, A. A., Tian, F., & Rittle Johnson, B. (2021). Helping preschoolers learn math: The impact of emphasizing the patterns in objects and numbers. Journal of Educational Psychology, 113(7), 1370-1386. https://doi.org/10.1037/edu0000656.