Matematik Eğitiminde Futschek Modeli Temelinde Algoritmik Düşünme Ölçeği Geliştirilmesi

Yıl 2025, Cilt: 54 Sayı: 3, 1299 - 1340, 31.12.2025

Beytullah Ömer Dumlu , Necla Turanlı

Öz

Çalışmanın amacı öğrencilerin matematiksel problemleri çözerken süreç içerisinde karşılaştıkları problemi anlama, çözüm yolu oluşturma, strateji geliştirme, hataları fark etme, çözüm planı yapma ve değerlendirme gibi bilişsel süreçleri değerlendirebilecek geçerli ve güvenilir bir algoritmik düşünme ölçeği geliştirmektir. Araştırmacılar tarafından alanyazın incelenerek Futschek’in algoritmik düşünme süreci modeli temelinde beşli likert tipinde 42 maddelik bir taslak ölçek oluşturulmuştur. Geliştirilen taslak ölçek, 2024-2025 eğitim-öğretim yılında Tekirdağ ilinin Kapaklı ilçesindeki üç farklı lisede 9. sınıf öğrencisi olarak öğrenim gören 312 kız ve 221 erkek olmak üzere toplam 533 öğrenciye uygulanmıştır. Verilerin analizinde SPSS 27 ve AMOS 24 kullanılarak madde toplam test korelasyonları, Cronbach Alpha güvenirlik, Sperman-Brown Prophecy güvenirlik, bileşik güvenirlik, test-tekrar test güvenirlik katsayısı bulunmuştur. Bunun yanı sıra hipotez testleri, keşfedici faktör analizi ve doğrulayıcı faktör analizi yapılmıştır. Analizler ve uzman görüşleri sonucunda ölçek 25 madde indirilerek asıl ölçek oluşturulmuştur. Sonuç olarak geliştirilen ölçeğin, öğrencilerin problem çözme süreci içerisinde yaşadıkları zorlukları, karar verme aşamalarındaki tercihlerini, stratejileri etkili kullanıp kullanmadıklarını, algoritmik yeterliliklerini ve farkındalık düzeylerini ölçmek için kapsamlı ve işlevsel bir ölçme aracı olarak katkı sağlayacağı söylenebilir.

Anahtar Kelimeler

Algoritmik Düşünme , Algoritma , Problem Çözme , Ölçek Geliştirme , matematik eğitimi

Development of an Algorithmic Thinking Scale Based on the Futschek Model in Mathematics Education

Öz

The aim of the study is to develop a valid and reliable algorithmic thinking scale that can assess cognitive processes such as understanding the problem, creating a solution path, developing strategies, identifying errors, making a solution plan, and evaluating during the process of solving mathematical problems. Based on a review of the literature literature and Futschek's algorithmic thinking process model the researchers designed a draft scale consisting of 42 items on a five-point Likert. The developed draft scale was applied to a total of 533 students, including 312 female and 221 male ninth- grade students, in three different high schools in the Kapaklı district of Tekirdağ province during the 2024-2025 academic year. In the analysis of the data, SPSS 27 and AMOS 24 were used to determine item-total test correlations, Cronbach's Alpha reliability, Spearman-Brown Prophecy reliability, composite reliability, and test-retest reliability coefficients. In addition, hypothesis testings, exploratory factor analysis, and confirmatory factor analysis were performed. As a result of the analyses and expert evaluations, the scale was reduced to 25 items to form the final scale. In conclusion, it can be said that the developed scale is expected contribute as a comprehensive and functional measurement tool to measure the difficulties students experience in the problem-solving processes, their preferences in the decision-making stages, the effectiveness of their strategy use, and their levels of algorithmic competence and awareness.

Anahtar Kelimeler

Algorithmic Thinking , Problem Solving , Algorithm , Scale Development , Mathematics Education

Kaynakça

• Australian Curriculum, Assessment and Reporting Authority. (2015). Australian curriculum: Digital technologies. Australian Curriculum, Assessment and Reporting Authority. https://www.australiancurriculum.edu.au/
• Aksoy, M. (2022). Origami sanat etkinliklerinin algoritma başarısı ve problem çözme becerileri üzerinde etkisi [Yayınlanmamış yüksek lisans tezi]. Süleyman Demirel Üniversitesi.
• Atılgan, H., Kan, A., & Doğan, N. (2013). Eğitimde ölçme ve değerlendirme (6. Bs.). Anı Yayıncılık. Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi. Harf Eğitim Yayıncılığı.
• Batı, A. H., Tetik, C., & Gürpınar, E. (2010). Assessment of the validity and reliability of the Turkish adaptation of the Study Process Questionnaire (R-SPQ-2F). Turkiye Klinikleri Journal of Medical Sciences, 30(5), 1639–1646. https://doi.org/10.5336/medsci.2009-15368
• Baykul, Y. (2010). Eğitimde ve psikolojide ölçme: Klasik test teorisi ve uygulaması (2. Bs.). Pegem Akademi.
• Berikan, B. (2018). Bilgi işlemsel düşünme becerisine yönelik tasarlanan “veri setleriyle problem çözme” öğrenme deneyiminin biçimlendirici değerlendirmesi [Yayımlanmamış doktora tezi]. Gazi Üniversitesi.
• Bethune, K. S., & Wood, C. L. (2013). Effects of coaching on teachers’ use of function-based interventions for students with severe disabilities. Teacher Education and Special Education, 36(2), 97–114. https://doi.org/10.1177/0888406413478637
• Bolarinwa, O. A. (2015). Principles and methods of validity and reliability testing of questionnaires used in social and health science researches. Nigerian Postgraduate Medical Journal, 22(4), 195–201. https://doi.org/10.4103/1117-1936.173959
• Büyüköztürk, Ş. (2003). Sosyal bilimler için veri analizi el kitabı (1. Bs.). Pegem Akademi. https://doi.org/10.17051/io.38688
• Brown, W. (2015). Introduction to algorithmic thinking. https://raptor.martincarlisle.com/Introduction%20to%20Algorithmic%20Thinking.doc
• Bryman, A., & Cramer, D. (2001). Quantitative data analysis with SPSS release 10 for windows: A guide for social scientists. Routledge. https://doi.org/10.4324/9780203471548
• Byrne, B. M. (2010). Structural Equation Modeling with AMOS: Basic Concepts, Applications, and Programming (2nd Ed.). New York: Routledge. https://doi.org/10.4324/9780203805534
• Can, A. A. (2021). İlkokul dördüncü sınıf öğrencilerinin matematik problemi çözmeye ilişkin algılarının metaforlar yoluyla analizi. Uşak Üniversitesi Eğitim Araştırmaları Dergisi, 7(1), 103–118. https://doi.org/10.29065/usakead.882143
• Cangur, S., & Ercan, İ. (2015). Comparison of model fit indices used in structural equation modeling under multivariate normality. Journal of Modern Applied Statistical Methods, 14(1), 152–167. https://doi.org/10.56801/10.56801/v14.i.759
• Clark, D. (2016). Computational and algorithmic thinking, 2011–2015. Australian Mathematics Trust. Comrey, A. L., & Lee, H. L. (1992). A first course in factor analysis. Lawrence Erlbaum Associates. https://doi.org/10.4324/9781315827506
• Creswell, J. W., Plano Clark, V. L., Gutmann, M., & Hanson, W. (2003). Advanced mixed methods research designs. In A. Tashakkori, & C. Teddlie (Eds.), Handbook of mixed methods in social & behavioral research (pp. 209–240). Sage.
• Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. Holt, Rinehart and Winston, Inc. Çokluk, Ö., Şekercioğlu, G., & Büyüköztürk, Ş. (2012). Sosyal bilimler için çok değişkenli istatistik: SPSS ve LISREL uygulamaları (2. Bs.). Pegem Akademi.
• Davcik, N. (2014). The use and misuse of structural equation modeling in management research: A review and critique. Journal of Advances in Management Research, 11(1), 47–81. https://doi.org/10.1108/JAMR-07-2013-0043
• DeVellis, R. F. (2006). Quantitative and issues and approaches: Classical test theory (CTT) and item response theory (IRT). Medical Care, 44(11), 50–59. https://doi.org/10.1097/01.mlr.0000245426.10853.30
• Department for Education. (2013). National curriculum in England: Computing programmes of study. https://www.gov.uk/government/publications/national-curriculum-in-england-computing-programmes-of-study
• Doğruel, L., Masur, P., & Joeckel, S. (2022). Development and validation of an algorithm literacy scale for internet users. Communication Methods and Measures, 16(2), 115–133. https://doi.org/10.1080/19312458.2021.1968361
• Ekici, D. İ., & Balım, A. G. (2013). Ortaokul öğrencileri için problem çözme becerilerine yönelik algı ölçeği: Geçerlilik ve güvenirlik çalışması. Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi, 10(1), 67-86.
• El-Hamamsy, L., Zapata-Cáceres, M., Martín-Barroso, E., Mondada, F., Zufferey, J. D., Bruno, B., & Román-González, M. (2025). The competent Computational Thinking test (cCTt): A valid, reliable and gender-fair test for longitudinal CT studies in grades 3–6. Technology, Knowledge and Learning, 1–55. https://doi.org/10.48550/arXiv.2305.19526
• Erümit, K. A., Karal, H., Şahin, G., Aksoy, D. A., Aksoy, A., & Benzer, A. İ. (2018). Programlama öğretimi için bir model önerisi: Yedi adımda programlama. Eğitim ve Bilim, 44(197), 155–183. https://doi.org/10.15390/EB.2018.7678
• Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299. https://doi.org/10.1037/1082-989X.4.3.272
• Field, A. (2000). Discovering statistics using SPSS for Windows. Sage Publications. Erişim adresi: https://l24.im/f0BVti
• Flores, M. M., & Ganz, J. B. (2007). Effectiveness of direct instruction for teaching statement inference, use of facts, and analogies to students with developmental disabilities and reading delays. Focus on Autism and Other Developmental Disabilities, 22(4), 244– 251. https://doi.org/10.1177/10883576070220040601
• Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39–50. https://doi.org/10.2307/3151312
• Futschek, G. (2006). Algorithmic thinking: The key for understanding computer science. In R. T. Mittermeir (Ed.), Informatics education – The bridge between using and understanding computers (pp. 159–168). Springer. https://doi.org/10.1007/11915355_15
• Futschek, G., & Moschitz, J. (2010). Developing Algorithmic Thinking by Inventing and Playing Algorithms. In Constructionist approaches to creative learning, thinking and education (p. 10). http://hdl.handle.net/20.500.12708/53175
• Futschek, G., & Moschitz, J. (2011,). Learning algorithmic thinking with tangible objects eases transition to computer programming. In R. Mittermeir & M. M. Syslo (Eds.), Informatics in schools: Situation, evolution, and perspectives (pp. 155–164). Springer. https://doi.org/10.1007/978-3-642-24722-4_14
• Garner, S. (2003). Learning resources and tools to aid novices learn programming. Informing Science & Information Technology Education Joint Conference (INSITE), 213–222. https://doi.org/10.28945/2613
• George, D., & Mallery, P. (2003). SPSS for Windows step by step: A simple guide and reference (4th Ed.). Allyn & Bacon.
• Gorsuch, R. L. (1983). Factor analysis. Lawrence Erlbaum Associates. https://doi.org/10.4324/9780203781098
• Gültekin, S. (2017). Testlerde kullanılacak madde türleri, hazırlama ilkeleri ve puanlaması. R. N. Demirtaşlı (Ed.), Eğitimde ölçme ve değerlendirme içinde (4. Bs., ss. 145–222). Anı Yayıncılık.
• Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2009). Multivariate data analysis (7th Ed.). Prentice Hall.
• Hicks, S. C., Bethune, K. S., Wood, C. L., Cooke, N. L., & Mims, P. J. (2011). Effects of direct instruction on the acquisition of prepositions by students with intellectual disabilities. Journal of Applied Behavior Analysis, 44(3), 675–679. https://doi.org/10.1901/jaba.2011.44-675
• Israel, M., Wherfel, Q. M., Pearson, J., Shehab, S., & Tapta, T. (2015). Empowering K-12 students with disabilities to learn computational thinking and computer programming. Teaching Exceptional Children, 48(1), 45-53. https://doi.org/10.1177/0040059915594790
• The International Society for Technology in Education. (2015). Computational thinking leadership toolkit (1st Ed.). ISTE. https://cdn.iste.org/www-root/ct-documents/ct-leadershipt-toolkit.pdf?sfvrsn=4
• Johnson, B., & Turner, L. A. (2003). Data collection strategies in mixed methods research. In A. Tashakkori, & C. Teddlie (Eds.), Handbook of mixed methods in social & behavioral research (pp. 297–319). Sage.
• Joshi, A., Kale, S., Chandel, S., & Pal, D. K. (2015). Likert scale: Explored and explained. British Journal of Applied Science & Technology, 7(4), 396–403. https://doi.org/10.9734/BJAST/2015/14975
• K–12 Computer Science Framework. (2016). K–12 computer science framework. https://k12cs.org/
• Karakuş Aktan, E. D. A., Aslan, C., & Yalçın, A. (2021). Okuma stratejisi eğitiminin matematik dersi problem çözme becerisine etkisi. Ana Dili Eğitimi Dergisi, 9(2), 81–97. https://doi.org/10.16916/aded.851966
• Knight, V. F., Smith, B. R., Spooner, F., & Browder, D. (2012). Using explicit instruction to teach science descriptors to students with autism spectrum disorder. Journal of Autism and Developmental Disorders, 42(3), 378–389. https://doi.org/10.1007/s10803-011- 1258-1
• Kline, R. B. (2011). Hypothesis testing. In Principles and practice of structural equation modeling (3rd Ed., pp. 7, 192-209, 342). The Guilford Press.
• Kline, R. B. (2015). Principles and practice of structural equation modeling (4th ed.). Guilford Press.
• Kocasaraç, H. (2023). Algoritmik düşünme eğitimi.
• Kwon, Y., & Marzec, M. L. (2016). Does worksite culture of health (CoH) matter to employees? Empirical evidence using job-related metrics. Journal of Occupational and Environmental Medicine, 58(5), 448-454. https://doi.org/10.1097/JOM.0000000000000724
• Lawshe, C. H. (1975). A quantitative approach to content validity. Personnel Psychology, 28(4), 563–575. https://doi.org/10.1111/j.1744-6570.1975.tb01393.x
• Milli Eğitim Bakanlığı, (2013). Ortaöğretim matematik dersi (9, 10. 11 ve 12. sınıflar) öğretim programı. TTKB.
• Montague, M., Enders, C., & Dietz, S. (2011). Effects of cognitive strategy instruction on math problem solving of middle school students with learning disabilities. Learning Disability Quarterly, 34(4), 262–272. https://doi.org/10.1177/073194871142176
• Milli Eğitim Bakanlığı, (2024). Ortaöğretim matematik dersi (9, 10. 11 ve 12. sınıflar) öğretim programı. TTKB. National Council of Teachers of Mathematics, (2000). Principles and standards for school mathematics. Author.
• Nunnally, J. C. (1978). Psychometric theory. McGraw Hill.
• Organisation for Economic Co-Operation and Development, (2021). Trends shaping education 2021. OECD Publishing. https://www.oecd.org/en/about/projects/trends-shaping-education.html
• Oğuz, V., & Köksal Akyol, A. (2014). Problem çözme becerisi ölçeği (PÇBÖ) geçerlik ve güvenilirlik çalışması. Çukurova Üniversitesi Eğitim Fakültesi Dergisi, 44(1), 105-122. https://doi.org/10.14812/cuefd.54362
• Okur, S. (2008). Students’ strategies, episodes, and metacognitions in the context of PISA 2003 mathematical literacy items [Unpublished master’s thesis]. Middle East Technical University.
• Polya, G. (1997). Nasıl çözmeli? Matematikte yeni bir boyut (F. Halatçı, Çev.). Sistem Yayıncılık.
• Ritter, F., & Standl, B. (2023). Promoting student competencies in informatics education by combining semantic waves and algorithmic thinking. Informatics in Education, 22(1), 141–160. https://doi.org/10.15388/infedu.2023.07
• Ross, K. A. (1998). Doing and proving: The place of algorithms and proofs in school mathematics. The American Mathematical Monthly, 105(3), 252–255. https://doi.org/10.2307/2589080
• Sarmento, R. P., & Costa, V. (2019). Confirmatory factor analysis: A case study. arXiv. https://doi.org/10.48550/arXiv.1905.05598
• Seçer, İ. (2015). SPSS ve Lisrel ile pratik veri analizi (2. Bs.). Anı Yayıncılık.
• Segura-Orti, E., & Martinez-Olmos, F. J. (2011). Test-retest reliability and minimal detectable change scores for sit-to-stand-to-sit tests, the six-minute walk test, the one-leg heel-rise test, and handgrip strength in people undergoing hemodialysis. Physical Therapy, 91(8), 1244–1252. https://doi.org/10.2522/ptj.20100141
• Sürücü, L., Şeşen, H., & Maşlakçı, A. (2021). SPSS, AMOS ve PROCESS Macro ile ilişkisel, aracı/düzenleyici ve yapısal eşitlik modellemesi (uygulamalı analizler). Detay Yayıncılık.
• Sysło, M. M., & Kwiatkowska, A. B. (2008). The challenging face of informatics education in Poland. In Proceedings of the International Conference on Informatics in Secondary Schools: Evolution and Perspectives (pp. 1–18). Springer. https://doi.org/10.1007/978-3-540-69924-8_1
• Szanto, S. (2002). Developing algorithmic thinking. New Pedagogical Review. http://www.oki.hu/oldal.php?tipus=cikk&kod=2002- 05-mu-Szanto-Algoritmikus
• Tavşancıl, E. (2005). Tutumların ölçülmesi ve SPSS ile veri analizi. Nobel Yayın Dağıtım.
• Terwee, C. B., Bot, S. D. M., de Boer, M. R., van der Windt, D. A. W. M., Knol, D. L., Dekker, J., Bouter, L. M., & de Vet, H. C.
• W. (2007). Quality criteria were proposed for measurement properties of health status questionnaires. Journal of Clinical Epidemiology, 60(1), 34–42. https://doi.org/10.1016/j.jclinepi.2006.03.012
• Tsai, M. J., Liang, J. C., & Hsu, C. Y. (2020). The computational thinking scale for computer literacy education. Journal of Educational Computing Research, 59(29). https://doi.org/10.1177/0735633120972356
• Ural, A., & Kılıç, İ. (2013). Bilimsel araştırma süreci ve SPSS ile veri analizi. Detay Yayıncılık.
• Vasconcelos, J. (2007). Basic Strategy for Algorithmic Problem Solving. http://www.cs.jhu.e du/~jorgev/cs106/ProblemSolving.html
• Vieira, A. L. (2011). Interactive LISREL in Practice. Heidelberg: Springer. http://dx.doi.org/10.1007/978-3-642-18044-6
• Xin, Y. P. (2016). Conceptual model-based problem solving. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems (pp. 231–254). Springer. https://doi.org/10.1007/978-3-319-28023-3_14
• Yadav, A., Ocak, C., & Oliver, A. (2022). Computational thinking and metacognition. TechTrends, 66(4), 405–411. https://doi.org/10.1007/s11528-022-00695-z
• Yıldız, M., Çiftçi, E., & Karal, H. (2017). Bilişimsel düşünme ve programlama. Eğitim Teknolojileri Okumaları, TOJET. http://www.tojet.net/e-book/eto_2017.pdf
• Ziatdinov, R., & Musa, S. (2013). Rapid mental computation system as a tool for algorithmic thinking of elementary school students development. European Research, 25(7), 1105–1110. https://doi.org/10.48550/arXiv.1305.4443
• Zsakó, L., & Szlávi, P. (2012). ICT competences: Algorithmic thinking. Acta Didactica Napocensia, 5(2), 49–58. https://www.learntechlib.org/p/159542/