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

Yıl 2022, Cilt: 23 Sayı: 4, 853 - 871, 01.12.2022

Gülnur Özbek Erdoğan Köse

https://doi.org/10.21565/ozelegitimdergisi.874247

Cited By: 1

Öz

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.

Anahtar Kelimeler

Özel yetenekliler, matematiksel modelleme, modelleme yeterlikleri, ölçek geliştirme, faktör analizi

Teşekkür

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

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

Öz

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.

Anahtar Kelimeler

Gifted and talented students, mathematical modeling, modeling competencies, scale development, factor analysis

Kaynakça

• Adıgüzel, O. C. (2016). Eğitim programlarının geliştirilmesinde ihtiyaç analizi el kitabı. Anı Yayıncılık.
• Alpar, R. (2012). Uygulamalı istatistik ve geçerlik-güvenirlik. Detay Yayıncılık.
• Antonius, S., Haines, C., Jensen, T. H., Niss, M., & Burkhardt, H. (2007). Classroom activities and the teacher. In Modelling and applications in mathematics education (pp. 295-308). Springer.
• Biccard, P., & Wessels, D. (2011). Development of affective modelling competencies in primary school learners. Pythagoras, 32(1), 9. DOI: 10.4102/pythagoras.v32i1.20.
• 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
• Blomhøj, M., & Kjeldsen, T. H. (2006). Teaching mathematical modelling through project work. Zentralblatt für Didaktik der Mathematik, 38, 163-177. https://doi.org/10.1007/BF02655887
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser et al. (Eds.), Trends in teaching and learning of mathematical modelling (ICTMA 14) (pp. 15–30). Springer.
• Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction. Educational studies in mathematics, 22, 37-68. https://doi.org/10.1007/BF00302716
• Blum, W., Galbraith, P. L., Henn, H. W., & Niss, M. (2007). Modelling and applications in mathematics education (pp. 3-33). Springer.
• 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
• Brand, S. (2014). Effects of a holistic versus an atomistic modelling approach on students’ mathematical modelling competencies. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the joint meeting of PME 38 and PME-NA 36, Vol. 2 (pp. 185 191). PME.
• Brown, T. A. (2015). Confirmatory factor analysis for applied research.(Second Edition). Guilford publications.
• Bukova Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme. Pegem Akademi.
• Büyüköztürk, Ş. (2012). Sosyal bilimler için veri analizi el kitabı: İstatistik, araştırma deseni, SPSS uygulamaları ve yorum. Pegem Yayınları
• Campbell, J. R., Cho, S., & Tirri, K. A. H. (2018). Mathematics and science olympiad studies: The outcomes of olympiads and contributing factors to talent development of olympians. International Journal for Talent Development and Creativity, 5(2), 49-60. https://files.eric.ed.gov/fulltext/EJ1301497.pdf
• Comrey, A. L., & Lee, H. B. (1992). A first course in factor analysis (2nd ed.). Erlbaum.
• Cresswell, J. W. (2016). Araştırma deseni nitel, nicel ve karma yöntem yaklaşımları. (S. B. Demir, Çeviri Ed.) Eğiten Kitap.
• Cresswell, J.W. & Plano Clark, V. L. (2015). Karma yöntem araştırmaları tasarımı ve yürütmesi. (Y. Dede ve S. B. Demir, Çeviri Ed.) Anı Yayıncılık.
• Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2010). Multivariate statistics for the social sciences: SPSS and LISREL applications. Pegem Akademi.
• Dağyar, M., Kasalak, G., & Özbek, G. (2022). Gifted and talented youth leadership, perfectionism, and lifelong learning, International Journal of Curriculum and Instruction, 14(1), 566-596. http://ijci.wcci-international.org/index.php/IJCI/article/view/839/450
• Dewey, J. (1910). How we think. D. C. Heath.
• Dewey, J. (1997). Experience and education. First Touchstone Edition
• Eraslan, A., & Kant, S. (2015). Modeling processes of 4th-year middle-school students and the difficulties encountered. Educational Sciences: Theory & Practice, 15(3). https://doi.org/10.12738/estp.2015.3.2556
• 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.
• Kaiser G. (2020) Mathematical Modelling and Applications in Education. In Lerman S. (Eds.) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_101
• 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.
• Kline, R.B. (2005). Principles and practice of structural equation modelling. Guilford.
• Koyuncu, I., Guzeller, C. O., & Akyuz, D. (2016). The development of a self-efficacy scale for mathematical modeling competencies. International Journal of Assessment Tools in Education, 4(1), 19-36. https://doi.org/10.21449/ijate.256552
• Lesh R. & Caylor B. (2007). Introduction To Special Issue: Modeling As Application Versus Modeling As A Way To Create Mathematics. International Journal of Computers for Mathematical Learning. 12(3), 173-194. DOI:10.1007/s10758-007-9121-3
• Lesh R., Hoover M., Hole B., Kelly A. & Post T. (2000). Principles for Developing Thought-Revealing Activities for Students and Teachers, Handbook of Research Design in Mathematics and Science Education, Eds: Anthony Kelly, Richard Lesh, Mahwah, Lawrence Erlbaum Associates. s. 591-645.
• Lesh, R., Young, R., & Fennewald, T. (2010). Modeling in k-16 mathematics classrooms–and beyond. In Modeling students' mathematical modeling competencies (pp. 275-283). Springer.
• Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38, 113-142. https://doi.org/10.1007/BF02655885
• Maaß, K., & Gurlitt, J. (2011). LEMA–Professional development of teachers in relation to mathematical modelling. In Trends in teaching and learning of mathematical modelling (pp. 629-639). Springer.
• Maaß, K., & Mischo, C. (2011). Implementing modelling into day-to-day teaching practice–The project STRATUM and its framework. Journal Für Mathematik-Didaktik, 32, 103-131. https://doi.org/10.1007/s13138-010-0015-x
• Manuel, D., & Freiman, V. (2017). Differentiating instruction using a virtual environment: A study of mathematical problem posing among gifted and talented learners. Global Education Review, 4(1). 78-98.
• Mertler, C. A., & Vannatta, R. A. (2005). Advanced and multivariate statistical methods: Practical application and interpretation (3th ed.). Pyrczak Publishing
• Mihaela Singer, F., Jensen Sheffield, L., Freiman, V., & Brandl, M. (2016). Research on and activities for mathematically gifted students. Springer Nature.
• Millî Eğitim Bakanlığı [Ministry of National Education]. (2019). Bilim ve Sanat Merkezleri Yönergesi [Science and Art Centers Law]. http://mevzuat.meb.gov.tr/html/bilimsanat/yonerge.pdf
• Mumcu, H. Y., & Baki, A. (2017). Matematiği kullanma aktivitelerinde matematiksel modellemenin yorumlanması. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 36(1), 7-33. DOI: 10.7822/omuefd.327387
• Ornstein, A. C., & Hunkins, F. P. (2016). Curriculum: Foundations, principles, and issues (7th Ed.). Pearson Education.
• Özdamar, K. (2004). Paket programlar ile istatistiksel veri analizi (çok değişkenli analizler). Kaan.
• 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.
• Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Test of significance and descriptive goodness-of-fit measures. Methods of Psychological Research-Online, 8(2), 23-74. http://www.mpr-online.de
• Schumacker, R. E., & Lomax, R. G. (1996). A beginner’s guide to structural equation modeling. (First edition). Lawrence Erlbaum Associates, Inc.
• Sekerák, J. (2010). Phases of mathematical modelling and competence of high school students. The teaching of Mathematics, (25), 105-112.
• Sheffield, L. J. (2018). Commentary paper: a reflection on mathematical creativity and giftedness. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness (pp. 405-428). Springer.
• Sümer, N., (2000). Yapısal eşitlik modelleri: Temel kavramlar ve örnek uygulamalar. Türk Psikoloji Yazıları, 3(6), 49-74.
• Şencan, H. (2005). Sosyal ve davranışsal ölçümlerde güvenilirlik ve geçerlilik. (1.Baskı). 107-113, 166-169, 381-390, Seçkin Yayınevi.
• Tabachnick, B. G., & Fidell, L. S. (2001). Using multivariate statistics. Allyn and Bacon. Needham Heights, MA.
• Tavşancıl, E. (2005). Tutumların ölçülmesi ve SPSS ile veri analizi. Nobel.
• Tekin Dede, A. (2017). Modelleme yeterlikleri ile sınıf düzeyi ve matematik başarısı arasındaki ilişkilerin incelenmesi. Elementary Education Online, 16(3). 1201-1219. http://ilkogretim-online.org.tr/index.php/io/article/view/2454
• Tekin Dede, A., & Yılmaz, S. (2015). 6. Sınıf öğrencilerinin bilişsel modelleme yeterlikleri nasıl geliştirilebilir?.International Journal of New Trends in Arts, Sports & Science Education (IJTASE), 4(1), 49-63
• Tekin Dede, A. & Bukova Güzel, E. (2014). Model oluşturma etkinlikleri: Kuramsal yapısı ve bir örneği. Ondokuz Mayıs Üniversitesi Eğitim Fakültesi Dergisi, 33(1), 95-111. DOI: 10.7822/egt298
• Wang, J. J., Halberda, J., & Feigenson, L. (2017). Approximate number sense correlates with math performance in gifted adolescents. Acta Psychologica, 176, 78–84. DOI: 10.1016/j.actpsy.2017.03.014
• Yılmaz, V. & Çelik, H. E. (2009). LISREL ile yapısal eşitlik modellemesi-1. PegemA.
• Zedan R., & Bitar J. (2017). Mathematically gifted students: Their characteristics and unique needs. European Journal of Education Studies, 3(4), 236-260. http://dx.doi.org/10.46827/ejes.v0i0.571