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

Year 2022, Volume: 23 Issue: 4, 853 - 871, 01.12.2022

Gülnur Özbek , Erdoğan Köse

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

Cited By: 4

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.

Keywords

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

Thanks

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

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.

Keywords

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

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