Computational Thinking in Math Education-From Theory to Practice

Yıl 2024, Cilt: 7 Sayı: 3, 214 - 235, 01.11.2024

Rümeysa Beyazhançer

Öz

This study examines the integration of computational thinking (CT) into mathematics education and its impact on teaching processes. The aim of the study is to evaluate the role of CT in mathematics education and its effects on both teachers and students. The study investigates the impact of CT on the understanding of mathematical concepts, the development of problem-solving skills, and the use of technology-supported learning environments. The findings of the research show that the integration of CT into mathematics education equips students with essential skills such as problem-solving, abstraction, and algorithm development. Additionally, CT-based activities help students better understand mathematical concepts and relate these concepts to daily life. Teachers have been able to use technology and computer-supported educational tools more effectively by applying CT-based pedagogical practices. This process has provided significant insights into the challenges faced by teachers and how these challenges can be overcome. In conclusion, the integration of CT into mathematics education enhances students' analytical and creative thinking skills and enriches teachers' pedagogical practices. This study emphasizes the importance of CT in education and offers valuable suggestions for the development of teaching strategies.

Anahtar Kelimeler

Computational thinking, Mathematics education, Algorithmic thinking

Matematik Eğitiminde Bilgi İşlemsel Düşünme- Kuramdan Uygulamaya

Öz

Bu çalışma, bilgi işlemsel düşünme (BİD) kavramının matematik eğitimi ile entegrasyonunu ve bu entegrasyonun öğretim süreçleri üzerindeki etkilerini incelemektedir. Çalışmanın amacı, BİD'nin matematik eğitiminde nasıl bir rol oynadığını ve bu sürecin öğretmenler ve öğrenciler üzerindeki etkilerini değerlendirmektir. Çalışma kapsamında, BİD'nin matematiksel kavramların anlaşılmasına, problem çözme becerilerinin gelişimine ve teknoloji destekli öğrenme ortamlarının kullanımına olan etkileri incelenmiştir. Araştırmanın bulguları, BİD'nin matematik eğitimine entegrasyonunun öğrencilere problem çözme, soyutlama ve algoritma geliştirme gibi önemli becerileri kazandırdığını göstermektedir. Ayrıca, BİD tabanlı etkinlikler, öğrencilerin matematiksel kavramları daha iyi anlamalarını ve bu kavramları günlük hayatla ilişkilendirmelerini sağlamaktadır. Öğretmenler ise BİD tabanlı pedagojik uygulamaları kullanarak teknoloji ve bilgisayar destekli eğitim araçlarını daha etkili bir şekilde kullanabilmişlerdir. Bu süreçte öğretmenlerin karşılaştığı zorluklar ve bu zorlukların nasıl aşılabileceği konusunda önemli bilgiler elde edilmiştir. Sonuç olarak, BİD'nin matematik eğitimine entegrasyonu, öğrencilerin analitik ve yaratıcı düşünme becerilerini geliştirmekte ve öğretmenlerin pedagojik uygulamalarını zenginleştirmektedir. Bu çalışma, BİD'nin eğitimdeki önemini vurgulamakta ve öğretim stratejilerinin geliştirilmesine yönelik değerli öneriler sunmaktadır.

Anahtar Kelimeler

Bilgi işlemsel düşünme, Matematik eğitimi, Algoritmik düşünme

Kaynakça

• Abrams, J. P. (2001). Mathematical modeling: teaching the open-ended application of mathematics. The Teaching Mathematical Modeling and the of Representation. 2001 Yearbook, NCTM, (Eds. Cuoco, A.A. and Curcio, F.R.).
• Ang, K., & Tan, C. (2022). Mathematical modelling and computational thinking: Their intersections in STEM education. Journal of STEM Education Research, 5(3), 78-93.
• Barcelos, T. S., Rodrigues, R. A., & Carvalho, L. M. (2018). Computational thinking in K-12: An analysis of empirical literature. Proceedings of the IEEE Frontiers in Education Conference (FIE), 1-9.
• Barr, V., & Stephenson, C. (2011). Bringing computational thinking to K-12: what is involved and what is the role of the computer science education community? ACM Inroads, 2(1), 48-54.
• Bell, T., & Vahrenhold, J. (2018). CS Unplugged—How is it used, and does it work? In Adventures between lower bounds and higher altitudes (pp. 497-521). Springer.
• Berry, J., & Houston, K. (1995). Mathematical modeling. London: Edward Arnold.
• Biccard, P., & Wessels, D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. International Perspectives on the Teaching and Learning of Mathematical Modelling. 1(5), 375-383.
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling (pp. 15–30). Dordrecht: Springer.
• Borromeo Ferri, R. (2006). Theoretical and Empirical Differentiations of Phases in the Modelling Process. In Kaiser, G., Sriraman B. & Blomhoij, M. (Eds.) Zentralblatt für Didaktik der Mathematik. 38(2), 86-95.
• Bråting, K., & Kilhamn, C. (2021). Programming in school mathematics: A historical epistemological perspective on the integration of programming in Swedish school mathematics. Journal of Curriculum Studies, 53(5), 694–710. https://doi.org/10.1080/00220272.2021.1896132
• Brennan, K., & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. In Proceedings of the 2012 annual meeting of the American Educational Research Association, Vancouver, Canada (Vol. 1, p. 25).
• Critten, V., Hagon, H., & Messer, D. (2022). Can pre-school children learn programming and coding through guided play activities? A case study in computational thinking. Early Childhood Education Journal, 50(6), 969–981. https://doi.org/10.1007/s10643-021-01233-z
• Cui, L., & Ng, O. L. (2021). Computational thinking in mathematics education: Investigating the impact of programming on mathematical problem-solving. Journal of Mathematical Education, 52(1), 848.
• De Chenne, H., & Lockwood, E. (2022). Exploring students' use of computational thinking to solve combinatorial problems with Python. Journal of Mathematical Behavior, 66, 100944. https://doi.org/10.1016/j.jmathb.2022.100944
• Denning, P. J. (2005). Beyond Calculation: The Next Fifty Years of Computing. Communications of the ACM, 48(3), 29-32.
• Denning, P. J. (2017). Remaining trouble spots with computational thinking. Communications of the ACM, 60(6), 33-39.
• Eisenberg, M. (2002). Output devices, computation, and the future of mathematical crafts. International Journal of Computers for Mathematical Learning, 7(1), 1–44. https://doi.org/10.1023/A:1013347104484
• Feldhausen, R., Weese, J. L., Bean, N. H., & Bell, R. S. (2018). Collaborative learning in computer science and engineering: A multi-year study of long-term impacts. Journal of Computing in Higher Education, 30(1), 57–82. https://doi.org/10.1007/s12528-018-9163-8
• Foerster, P. (2016). Introducing computational thinking in high school mathematics: Challenges and strategies. Mathematics Teacher, 109(8), 611–615. https://doi.org/10.5951/mathteacher.109.8.0611
• Gadanidis, G., Namukasa, I., & Cendros, R. (2018). Computational thinking in mathematics teacher education. International Journal of Information and Learning Technology, 34(2), 133-139. https://doi.org/10.1108/IJILT-09-2016-0048
• Gal-Ezer, J., & Stephenson, C. (2009). Computer science teacher preparation is critical. ACM Inroads, 1(1), 61-66.
• Grover, S., & Pea, R. (2013). Computational thinking in K–12: A review of the state of the field. Educational Researcher, 42(1), 38-43. https://doi.org/10.3390/educsci13040422
• Hadad, R., Tang, X., Yin, Y., Lin, Q., & Zhai, X. (2020). Developing assessment tools for computational thinking in mathematics education. International Journal of STEM Education, 7(13), 1-15. https://doi.org/10.1186/s40594-020-00225-6.
• Hanid, M. F. A., Mohamad Said, M. N. H., Yahaya, N., & Abdullah, Z. (2022). Enhancing students' understanding of geometric concepts through computational thinking: A case study in secondary education. International Journal of STEM Education, 9(1), 110-120. https://doi.org/10.1186/s40594-022-00323-8
• Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıklama [Yayımlanmamış yüksek lisans tezi]. Dokuz Eylül Üniversitesi, İzmir.
• Hickmott, D., Prieto-Rodriguez, E., & Holmes, K. (2018). A scoping review of studies on computational thinking in K-12 mathematics classrooms. Digital Experiences in Mathematics Education, 4(1), 48-69.
• Hong Kong Curriculum Development Council. (2020). Mathematics education key learning area curriculum guide (Primary 1 - Secondary 6). Hong Kong: Education Bureau.
• Hooshyar, D., Yousefi, E., Lim, H., & Yang, Y. (2021). Development and evaluation of an adaptive educational system for improving students’ computational thinking skills. IEEE Transactions on Learning Technologies, 14(2), 230-242. https://doi.org/10.1109/TLT.2021.3056002
• Hsu, T. C., & Hu, C. (2017). Applying computational thinking to mathematics education: A practical guide for teachers. Computers & Education, 115, 1–14. https://doi.org/10.1016/j.compedu.2017.06.013
• Hsu, T. C., Chang, S. C., & Hung, Y. T. (2018). How to learn and how to teach computational thinking: Suggestions based on a review of literature. Computers & Education, 126, 296-310.
• Hu, C. (2011). Computational thinking: what it might mean and what we might do about it. In Proceedings of the 16th annual joint conference on Innovation and Technology in computer science education (pp. 223-227).
• Huang, H., & Qiao, F. (2022). Exploring the integration of computational thinking in STEM education: A review of tools and practices. Journal of STEM Education, 23(4), 415-430. https://doi.org/10.1007/s10956-022-09945-3
• International Society for Technology in Education. (2016). ISTE standards for students. Arlington, VA: Author.
• Jiang, S., & Wong, L. H. (2022). Facilitating computational thinking through learning by teaching and game design. Journal of Educational Computing Research, 60(2), 355-380.
• Jocius, R., et al. (2021). Jocius, R., Goode, J., & Zhang, S. (2021). Building a virtual community of practice: Teacher learning for computational thinking infusion. TechTrends, 65(5), 718-727. https://doi.org/10.1007/s11528-021-00611-8
• Kahn, K., Sendova, E., Sacristán, A. I., & Noss, R. (2011). Developing mathematical thinking through programming activities: A case study. International Journal of Mathematical Education in Science and Technology, 42(4), 479–495. https://doi.org/10.1080/0020739X.2010.550949
• Kallia, M., van Borkulo, S. P., Drijvers, P., Barendsen, E., & Tolboom, J. (2021). Characterising computational thinking in mathematics education: a literature-informed Delphi study. Research in mathematics education, 23(2), 159-187.
• Kang, Y., & Lee, H. (2020). Computational thinking assessment in K-12 mathematics: Developing and validating a rubric. Journal of Educational Technology & Society, 23(4), 405–417.
• Karaçam, Z. (2013). Sistematik derleme metodolojisi: Sistematik derleme hazırlamak için bir rehber. Dokuz Eylül Üniversitesi Hemşirelik Yüksekokulu Elektronik Dergisi, 6(1), 26-33
• Ke, F. (2014). Designing and integrating purposeful learning in game play: A systematic review. Educational Technology Research and Development, 62(1), 57–82.
• Kong, S. C., & Abelson, H. (2019). Computational thinking education (p. 382). Springer Nature.
• Kotsopoulos, D., Lee, J., & Weber, K. (2017). Developing pedagogical frameworks for computational thinking in mathematics education. Computational Thinking Journal, 10(2), 123–137.
• Krathwohl, D. R. (2002). A revision of Bloom's taxonomy: An overview. Theory into practice, 41(4), 212-218.
• Lee, I., & Malyn-Smith, J. (2020). Integrating computational thinking and science in the elementary classroom. Journal of Research on Technology in Education, 52(1), 1-12.
• Lee, I., & Malyn-Smith, J. (2020). Integrating computational thinking and science in the elementary classroom. Journal of Research on Technology in Education, 52(1), 1–12.
• Lesh, R. A., & Doerr, H. (2003). Foundations of Model and Modelling Perspectives On Mathematic Teaching And Learning. In R. A. Lesh, and H. Doerr (Eds.), Beyond Constructivism: Models and Modelling Perspectives on Mathematics Teaching, Learning and Problem Solving (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum.
• Li, Y., Schoenfeld, A. H., diSessa, A. A., Graesser, A. C., Benson, L. C., English, L. D., & Duschl, R. A. (2020). Computational thinking is more about thinking than computing. Journal for STEM Education Research, 3, 1-18.
• Lockwood, E., & De Chenne, H. (2020). Enriching students' combinatorial reasoning through the use of loops and conditional statements in Python. Journal of Educational Computing Research, 58(4), 763–784. https://doi.org/10.1177/0735633120918173
• Lye, S. Y., & Koh, J. H. L. (2014). Review on teaching and learning of computational thinking through programming: What is next for K-12?. Computers in Human Behavior, 41, 51-61.
• Mason, J. (1988). Modelling: What Do We Really Want Pupils to Learn? In D. Pimm (Ed.), Mathematics, Teachers and Children. (pp. 201-215). London: Hodder & Stoughton.
• Miller, D. (2019). Integrating computational thinking in secondary mathematics education: Challenges and opportunities. Journal of STEM Education Research, 5(1), 45–60. https://doi.org/10.1007/s41979-019-0005-2
• Morelli, R., Uche, C., Lake, P., & Baldwin, L. (2010). Analyzing the effectiveness of robotics to teach computational thinking. Proceedings of the 41st ACM Technical Symposium on Computer Science Education, 144–148. https://doi.org/10.1145/1734263.1734314
• Mousoulides, M., Pittalis, M., & Christou, C. (2006). Improving Mathematical Knowledge Through Modeling in Elementary Schools. In J. Novotna, H. Moraova, M. Kratka and N. Stehlikova (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, 4, 201-208.
• Müller, G., & Wittmann, E. (1984). Der Mathematikunterricht in der Primarstufe. Braunschweig: Vieweg.
• National Research Council. (2010). Report on computational thinking and K-12 education. National Academies Press.
• National Research Council. (2013). Next generation science standards: For states, by states. Washington, DC: The National Academies Press.
• Ng, O. L., & Cui, L. (2021). The integration of computational thinking and mathematical reasoning in secondary education: A case study. Journal of Educational Computing Research, 59(1), 45–67. https://doi.org/10.1177/0735633120938871
• Norris, C., Sullivan, T., Poirot, J., & Soloway, E. (2003). No access, no use, no impact: Snapshot surveys of educational technology in K-12. Journal of Research on Technology in Education, 36(1), 15-27.
• Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. Basic Books, Inc.
• Papert, S. (1993). The children’s machine: Rethinking school in the age of the computer. New York, NY, USA: Basic Books, Inc
• Papert, S. (2006). Keynote leBİDure. Keynote at ICMI 17 Conference in Hanoi, Vietnam. Retrieved from http:// dailypapert.com/wp-content/uploads/2012/05/Seymour-Vietnam-Talk-2006.pdf Accessed 10 Feb 2024.
• Pei, C., Weintrop, D., & Wilkerson, M. H. (2018). Examining the role of computational thinking in mathematical problem-solving. Educational Researcher, 47(5), 329-338.
• Pei, F., Smith, J., & Jones, T. (2018). Computational thinking in geometry: Case studies in secondary education. Computers & Education, 127, 127–142. https://doi.org/10.1016/j.compedu.2018.08.017
• Repenning, A., Webb, D., & Ioannidou, A. (2010). Scalable game design and the development of a checklist for getting computational thinking into public schools. Proceedings of the 41st ACM Technical Symposium on Computer Science Education, 265–269.
• Rodríguez-Martínez, A., González-Calero, J. A., & Pérez-Pérez, C. (2020). Enhancing students’ computational thinking skills: A computational experiment in a secondary school mathematics classroom. Education and Information Technologies, 25(2), 1455-1472.
• Schoenfeld, A. H. (1985). Mathematical Problem Solving. Academic Press Inc.
• Shumway, J. F., Berland, M., & Wilkerson, M. (2021). Computational thinking in K-12: In-service teacher perceptions and practices. Journal of Research on Technology in Education, 53(1), 63-79.
• Shute, V. J., Sun, C., & Asbell-Clarke, J. (2017). Demystifying computational thinking. Educational Research Review, 22, 142-158.
• Sırakaya, M., & Vural, M. (2020). The impact of computational thinking-based activities on students' problem-solving skills and attitudes towards programming. Journal of Education and Learning, 9(2), 115-125. https://doi.org/10.5539/jel.v9n2p115
• Siller, H. S., & Greefrath, G. (2010). Mathematical Modelling In Class Regarding To Technology. CERME 6 – Proceedings of the sixth Congress of the European Society for Research in Mathematics Education. 108-117.
• Sneider, C., Stephenson, C., Schafer, B., Flick, L., & Wolf, M. (2014). Computational thinking in high school science classrooms: Exploring the role of computers in science inquiry. Journal of Science Education and Technology, 23(1), 37-44. https://doi.org/10.1007/s10956-013-9441-z
• Stewart, M., et al. (2021). Exploring the role of computational thinking in mathematical modeling activities for high school students. Journal of Mathematical Behavior, 61, 100804. https://doi.org/10.1016/j.jmathb.2021.100804
• Swaid, S. I. (2015). Bringing computational thinking to STEM education. Procedia Computer Science, 65, 693-698. https://doi.org/10.1016/j.procs.2015.09.030
• Syslo, M. M., & Kwiatkowska, A. B. (2014). Informatics education in Europe: Are we all in the same boat? Proceedings of the ITiCSE Conference, 3–8.
• Tang, X., Yin, Y., Lin, Q., Hadad, R., & Zhai, X. (2020). Assessing computational thinking: A systematic review of empirical studies. Computers & Education, 148, 103798.
• Tekdal, M. (2021). Investigating the integration of computational thinking in Turkish STEM education. Journal of Educational Technology & Society, 24(4), 100-111. https://doi.org/10.1109/EDUCON45650.2021
• Tucker, A., McCowan, D., Deek, F. P., Stephenson, C., & Jones, J. (2006). A model curriculum for K–12 computer science: Final report of the ACM K–12 task force curriculum committee. ACM.
• Voskoglou, M. G. (2006). The Use of Mathematical Modelling as a Tool for Learning Mathematics. Quaderni di Ricerca in Didattica. 16, 53-60.
• Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.
• Webb, N. L. (1997). Research Monograph Number 6: Criteria for Alignment of Expectations and Assessments in Mathematics and Science Education. Council of Chief State School Officers.
• Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25(1), 127-147.
• Wilensky, U. (1995). NetLogo: An environment for simulating complex systems. Center for Connected Learning and Computer-Based Modeling, Northwestern University.
• Wilensky, U., Brady, C., & Horn, M. (2014). Fostering computational literacy in science classrooms: An agent-based approach. Communications of the ACM, 57(8), 24–28. https://doi.org/10.1145/2633031
• Wing, J. M. (2006). Computational thinking. Communications of the ACM, 49(3), 33–35. https://doi.org/10. 1145/1118178.1118215
• Wing, J. M. (2008). Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 366(1881), 3717–3725. https://doi.org/10.1098/rsta.2008.0118
• Wing, J. M. (2011). Research notebook: Computational thinking—what and why. The Link Magazine, Pittsburg,PA: Computer Science. Retrieved from
• Yadav, A., Hong, H., & Stephenson, C. (2014). Computational thinking for all: Pedagogical approaches to embedding 21st-century problem-solving in K-12 classrooms. TechTrends, 58(6), 20–27.
• Ye, H., Liang, B., Ng, O. L., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: a systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10(1), 3
• Yıldız, M., Çiftçi, E., & Karal, H. (2017). Bilişimsel düşünme ve programlama. Eğitim teknolojileri okumaları (1st ed., s. 75-86).
• Yılmaz, K. (2021). Sosyal bilimlerde ve eğitim bilimlerinde sistematik derleme, meta değerlendirme ve bibliyometrik analizler. Manas Sosyal Araştırmalar Dergisi, 10(2), 1457-1490.
• Yuen, J., Lee, J. S. Y., & Chan, K. (2023). Impact of chatbot-assisted language learning on academic performance and motivation. Education and Information Technologies, 28(11), 15223–15243. https://doi.org/10.1007/s10639-022-10879-4.
• Zhang, L., & Nouri, J. (2019). A systematic review of learning computational thinking through Scratch in K-9. Computers & Education, 141, 103607. https://doi.org/10.1016/j.compedu.2019.103607.