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Matematiksel Modelleme Yeterlikleri Ölçeği’nin Geliştirilmesi ve Psikometrik Özelliklerinin Belirlenmesi: Özel Yetenekliler Örneklemi

Year 2022, Volume: 23 Issue: 4, 853 - 871, 01.12.2022
https://doi.org/10.21565/ozelegitimdergisi.874247

Abstract

Giriş: Geliştirilen modeller ile özgün projeler oluşturma açısından kilit bir kavram olan matematiksel modelleme bu yönüyle özel yetenekli gençlerin eğitiminde kullanılmaktadır. Modelleme yeterliklerinin belirlenmesi, gelişimine ihtiyaç duydukları aşamaların tespit edilmesi nasıl eğitim uygulamaları ve program farklılaştırmaları yapılacağına karar verilmesi açısından önemli veriler sağlayacaktır. Araştırmada matematiksel modelleme yeterlikleri ölçeğini geliştirmek ve psikometrik özelliklerini belirlemek amaçlanmaktadır.
Yöntem: Araştırma betimsel bir çalışmadır. Araştırma iki farklı örneklem grubu katılımı ile gerçekleştirilmiştir. İlk grupta 301 katılımcıdan elde edilen verilerle açımlayıcı faktör analizi (AFA) yapılmıştır. İkinci grupta 185 katılımcıdan elde edilen veriler ile doğrulayıcı faktör analizi (DFA) yapılmıştır.
Bulgular: Geliştirilen ölçek ‘Tamamen katılıyorum’, ‘Katılıyorum’, ‘Orta derecede katılıyorum’, ‘Katılmıyorum’ ve ‘Hiç katılmıyorum’ şeklinde derecelendirilmiş olup ters kodlanılması gerekli olan maddeler bulunmamaktadır. Ölçeğin alt faktörlerinin ‘Gerçek yaşam problemini belirlenme’, ‘Problemi anlama ve sadeleştirme’, ‘Matematikselleştirme’, ‘Matematiksel olarak çalışma’ ve ‘Yorumlama ve doğrulama’ olduğu belirlenmiştir. Güvenirliği belirlemek amacıyla hesaplanan Cronbach alfa iç tutarlılık katsayıları ölçeğin bütünü için 0.958 olarak ve sırasıyla alt faktörler için .811, .900, .883, .820 ve .927 olarak hesaplanmıştır. Ölçeğin uyum indeksleri (χ2 / df = 2.00, GFI = .90, RMSEA = .075, SRMR = .063, IFI = .97, NNFI = .97, CFI = .97, NFI = .94, PNFI = .86) belirlenmiştir.
Tartışma: Araştırmanın sonucunda, geliştirilen 5 faktörlü 31 maddelik ölçeğin sonraki çalışmalarda kullanılabilecek yeterli psikometrik özelliklere sahip olduğuna ulaşılmıştır. Geliştirilen ölçek modelleme sürecinde hem bütüncül olarak hem de aşamalarında kısmi olarak ölçüm yapmayı sağlamaktadır. Bu bağlamda bu araştırma kapsamında geliştirilen ölçek ile gerçekleştirmede en iyi olunan aşamalar ile en zorlanılan ve gelişimine ihtiyaç duyulan aşamaların belirlenmesi sağlanabilir.

Thanks

Millî Eğitim Bakanlığı Özel Eğitim ve Rehberlik Hizmetleri Genel Müdürlüğü Araştırma-Geliştirme ve Projeler Daire Başkanlığı

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Determination of Psychometric Characteristics of Mathematical Modeling Competencies Scale: Gifted and Talented Youth

Year 2022, Volume: 23 Issue: 4, 853 - 871, 01.12.2022
https://doi.org/10.21565/ozelegitimdergisi.874247

Abstract

Introduction: It can be claimed that mathematical modeling, which is a key concept in terms of creating original projects with the developed models, is important in the education of gifted youth. Determining their modeling competencies and identifying the stages that they need to develop will provide essential data in terms of deciding on what kind of educational practices and program differentiation will be carried out. The study aims to develop a scale for mathematical modeling competencies and to determine its psychometric properties.
Method: This is a descriptive study which was carried out with the participation of gifted students in two different groups. Exploratory factor analysis (EFA) was performed on the data obtained from 301 participants in the first group, and confirmatory factor analysis (CFA) was performed on the data obtained from 185 participants in the second group.
Findings: The scale includes items to be rated on a level of agreement including “Strongly agree”, “Agree”, “Moderately agree”, “Disagree” and “Strongly disagree”, and there are no items that need reverse coding. The sub-factors of the scale were determined as ‘identifying the real-life problem’, ‘understanding and simplifying the problem’, ‘mathematizing’, ‘working mathematically’ and ‘interpretation and validation’. Cronbach's alpha internal consistency coefficients were calculated as 0.958 for the scale and .811, .900, .883, .820 and .927 for the sub-factors, respectively. Fit indices of the scale (χ2 / df = 2.00, GFI = .90, RMSEA = .075, SRMR = .063, IFI = .97, NNFI = .97, CFI = .97, NFI = .94, PNFI = .86) determined.
Discussion: The developed scale is a 5-point Likert-type scale and there are no items that need to be reverse coded. According to the findings obtained from the analysis, it was concluded that the 31-item scale with a 5-factor structure is a valid and reliable scale. As a result of the research, it was concluded that the 31-item scale with a five-factor structure had sufficient psychometric properties to be used in future studies. The scale helps to measure both as a whole in the modeling process and partially in its stages. In this context, the scale developed within the scope of this research can be used for determining the stages that students are best at and those that require improvement.

References

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  • Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching mathematics and its applications, 22(3), 123-139. https://doi.org/10.1093/teamat/22.3.123
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  • Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38, 86-95. https://doi.org/10.1007/BF02655883
  • Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modeling behavior. Journal für Mathematik-Didaktik, 31, 99-118. https://doi.org/10.1007/s13138-010-0009-8
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  • Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1607-1627. doi: 10.12738/estp.2014.4.2039
  • Erdoğan, F. & Erben, T. (2020). An investigation of the measurement estimation strategies used by gifted students. Journal of Computer and Education Research, 8 (15), 201-223. DOI: 10.18009/jcer.680284
  • Grünewald, S. (2012). Acquirement of Modelling Competencies – First Results of an Empirical Comparison of the Efectiveness of a Holistic Respectively an Atomistic Approach to the Development of (Metacognitive) Modelling Competencies of Students. 12th International Congress on Mathematical Education, 8 July-15 July 2012, COEX, Seoul, Korea.
  • Haines, C., Crouch, R., & Davis, J. (2001). Understanding students' modelling skills. In Modelling and mathematics education (pp. 366-380). Woodhead Publishing.
  • Hidayat R, Zulnaidi H, Syed Zamri SNA (2018). Roles of metacognition and achievement goals in mathematical modeling competency: A structural equation modeling analysis. PLoS ONE 13(11): e0206211. https://doi.org/10.1371/journal.pone.0206211
  • Hooper, D., Coughlan, J., & Mullen, M. R. (2008). Structural equation modelling: guidelines for determining model fit. Electronic Journal of Business Research Methods. 6(1): 53–60.
  • Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118
  • Jöreskog, K. G., & Sörbom, D. (1993). LISREL 8: Structural equation modeling with the SIMPLIS command language. Scientific Software International, Inc.
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  • Kaiser, G., & Grünewald, S. (2015). Promotion of mathematical modelling competencies in the context of modelling projects. In N. H. Lee and D. K. E. Ng (Eds.), Mathematical Modelling: From Theory to Practice (pp. 21-39). World Scientific.
  • Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom—problems and opportunities. In Modelling and applications in mathematics education (pp. 99-108). Springer.
  • Kaiser, G., Schwarz, B., & Tiedemann, S. (2010). Future teachers’ professional knowledge on modeling. In Modeling Students' Mathematical Modeling Competencies (pp. 433-444). Springer.
  • Kelloway, E. K. (1998). Using LISREL for structural equation modeling: A researcher's guide. London: Sage.
  • Kline, P. (1994). An easy guide to factor analysis. Routledge.
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There are 68 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Gülnur Özbek 0000-0001-9395-5022

Erdoğan Köse 0000-0003-0426-0267

Publication Date December 1, 2022
Published in Issue Year 2022 Volume: 23 Issue: 4

Cite

APA Özbek, G., & Köse, E. (2022). Matematiksel Modelleme Yeterlikleri Ölçeği’nin Geliştirilmesi ve Psikometrik Özelliklerinin Belirlenmesi: Özel Yetenekliler Örneklemi. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 23(4), 853-871. https://doi.org/10.21565/ozelegitimdergisi.874247

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