Development of computational thinking and geometric reasoning in the 7th grade: Results from a teaching experiment
DOI:
https://doi.org/10.48489/quadrante.37328Keywords:
integration tasks, computational thinking practices, geometric reasoning processes, hypothetical learning trajectoryAbstract
Computational Thinking (CT) has been considered an essential skill in school curricula, especially in Mathematics. However, there is still a limited understanding of how it can be developed in an integrated way with other essential mathematical knowledge. This study investigated the possibility of integrating the development of computational thinking and geometric reasoning within the subtopic of Operations with Figures, in the 7th grade. The Design Research methodology was used, employing a Teaching Experiment approach guided by a conjecture and based on exploratory tasks to develop, simultaneously, CT and geometric reasoning. The results showed that intentionally combining CT and Geometry enables the development and mobilization of knowledge across both domains, in an integrated, cyclical, and iterative way. However, achievement levels varied, with challenges observed in connecting CT and geometric reasoning, influenced by the complexity of concepts, familiarity with programming platforms, and geometric reasoning processes. The study concludes that integration is feasible and beneficial but requires adaptable approaches that consider students' cognitive development and include an inquiry-based approach. It is recommended to initially use unplugged tasks to facilitate the transition to digital tools.
References
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. https://doi.org/10.1145/1929887.1929905
Baumgartner, E., Bell, P., Brophy, S., Hoadley, C., Hsi, S., Joseph, D., Orrill, C., Puntambekar, S., Sandoval, W., & Tabak, I. (2003). Design-Based Research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8. https://doi.org/10.3102/0013189X032001005
Bell, T., & Vahrenhold, J. (2018). CS unplugged—How is it used, and does it work? Lecture Notes in Computer Science, 11011 LNCS, 497–521. https://doi.org/10.1007/978-3-319-98355-4_29
Benton, L., Saunders, P., Kalas, I., Hoyles, C., & Noss, R. (2018). Designing for learning mathematics through programming: A case study of pupils engaging with place value. International Journal of Child-Computer Interaction, 16, 68–76. https://doi.org/10.1016/J.IJCCI.2017.12.004
Bocconi, S., Chioccariello, A., Kampylis, P., Dagiené, V., Wastiau, P., Engelhardt, K., Earp, J., Horvath, M.A., Jasutė, E., Malagoli, C., Masiulionytė-Dagienė, V., & Stupurienė, G. (2022). Reviewing computational thinking in compulsory education. State of play and practices from computing education. In A. Santos, R. Cachia, N. Giannoutsou, & Y. Punie (Eds.), Publications Office of the European Union. Joint Research Centre. https://doi.org/10.2760/126955
Bouck, E. C., & Yadav, A. (2020). Providing access and opportunity for computational thinking and computer science to support mathematics for students with disabilities. Journal of Special Education Technology, 37(1), 151–160. http://dx.doi.org/10.30191/ETS.202304_26(2).0010
Canavarro, A. P., Mestre, C., Gomes, D., Santos, E., Santos, L., Brunheira, L., Vicente, M., Gouveia, M. J., Correia, P., Marques, P., & Espadeiro, G. (2021). Aprendizagens Essenciais de Matemática para o Ensino Básico. ME-DGE.
Carreira, S., Jones, K., Amado, N., Jacinto, H., & Nobre, S. (2016). Youngsters solving mathematics problems with technology. [Mathematics Education in the Digital Era]. Springer.
Chen, C. L., & Herbst, P. (2013). The interplay among gestures, discourse, and diagrams in students’ geometrical reasoning. Educational Studies in Mathematics, 83(2), 285–307.
CS Unplugged (n.d.). Classic Computer Science Unplugged. Retrieved July 31, 2024, from https://classic.csunplugged.org/
del Olmo-Muñoz, J., Cózar-Gutiérrez, R., & González-Calero, J. A. (2020). Computational thinking through unplugged activities in early years of Primary Education. Computers & Education, 150, 103832. https://doi.org/10.1016/j.compedu.2020.103832
Díaz, A., Gutiérrez, Á., & Jaime, A. (2016). Estudio de los niveles de razonamiento de Van Hiele en alumnos de centros de enseñanza vulnerables de educación media en Chile. Enseñanza de Las Ciencias. Revista de Investigación y Experiencias Didácticas, 34(1), 107–128. https://doi.org/10.5565/rev/ensciencias.1664
Espadeiro, R. G. (2022). O Pensamento Computacional no currículo de Matemática. Educação e Matemática, 162, 5–10.
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/10.3102/0013189X12463051
Gualdrón, É. (2014). Descriptores específicos de los niveles de Van Hiele en el aprendizaje de la semejanza de polígonos. Revista Científica, 3(20), 26. https://doi.org/10.14483/23448350.7686
Gusmão, T. C. R. S., & Font, V. (2021). Ciclo de estudo e desenho de tarefas. Educação Matemática Pesquisa, 22(3), 666–697. https://doi.org/10.23925/1983-3156.2020v22i3p666-697
Gutiérrez, A., & Jaime, A. (1998). On the Assessment of the Van Hiele Levels of Reasoning. Focus on Learning Problems in Mathematics, 20(1&2), 27–46. Center for Teaching/Learning of Mathematics.
Gutiérrez, A., Jaime, A., & Fortuny, J. M. (1991). An Alternative Paradigm to Evaluate the Acquisition of the van Hiele Levels. Journal for Research in Mathematics Education, 22(3), 237–251. https://doi.org/10.2307/749076
Instituto de Avaliação Educativa (2018). Provas de Aferição do Ensino Básico. Relatório Nacional: 2016 e 2017. IAVE. https://iave.pt/wp-content/uploads/2020/02/METOD_Relatorio_PA_2016-2017_form.pdf
Instituto de Avaliação Educativa (2021). Estudo de aferição amostral do Ensino Básico 2021: Volume II – Descrição qualitativa dos desempenhos. IAVE. https://iave.pt/wp-content/uploads/2022/05/relatorio_estudo_amostral_EB_Vol-II_2021_27maio22.pdf
Israel, M., & Lash, T. (2019). From classroom lessons to exploratory learning progressions: mathematics + computational thinking. Interactive Learning Environments 28(3), 362–382. https://doi.org/10.1080/10494820.2019.1674879
Jacinto, H. (2017). A atividade de resolução de problemas de matemática com tecnologias e a fluência tecno-matemática de jovens do século XXI [Tese de doutoramento, Universidade de Lisboa]. Repositório da Universidade de Lisboa, Portugal. https://repositorio.ul.pt/handle/10451/29860
Kelly, A. E., & Lesh, R. A. (2000). Multitiered Teaching Experiments. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (Issue III, pp. 231–279). Lawrence Erlbaum Associates.
Kiray, S. A. (2012). A new model for the integration of science and mathematics: The balance model. Energy Education Science and Tecnology Part B: Social and Educational Studies, 4(3), 1181–1196. https://files.eric.ed.gov/fulltext/ED546468.pdf
Machuqueiro, F., & Piedade, J. (2023). Exploring the potential of modern board games to support computational thinking. 2023 International Symposium on Computers in Education (SIIE) (pp. 1–8). https://doi.org/10.1109/SIIE59826.2023.10423693
Ng, O. L., & Cui, Z. (2021). Examining primary students’ mathematical problem-solving in a programming context: Towards computationally enhanced mathematics education. ZDM Mathematics Education, 53, 847–860. https://doi.org/10.1007/s11858-020-01200-7
Nordby, S., Bjerke, A., & Mifsud, L. (2022). Computational Thinking in the Primary Mathematics Classroom: A Systematic Review. Digital Experiences in Mathematics Education, 8, 27–49. https://doi.org/10.1007/s40751-022-00102-5
Oliva, T., Jacinto, H., & Oliveira, H. (2024, July 7-14). Developing computational and algebraic thinking in early grades: A systematic literature review. The 15th International Congress on Mathematical Education [Conference presentation]. Sydney, Australia.
Oliveira, H., Menezes, L., & Canavarro, A. P. (2013). Conceptualizando o ensino exploratório da Matemática: Contributos da prática de uma professora do 3. º ciclo para a elaboração de um quadro de referência. Quadrante, 22(2), 29–54. https://doi.org/10.48489/quadrante.22895
Pinto, É. G., & Rodríguez, Á. G. (2007). Una aproximación a los descriptores de los niveles de razonamiento de van hiele para la semejanza. Investigación En Educación Matemática XI: Comunicaciones de los grupos de investigación del XI Simposio de la SEIEM, (pp. 369–380). https://www.uv.es/angel.gutierrez/textos.html
Ponte, J. (2005). Gestão curricular em Matemática In GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11–34). APM.
Rodríguez-Martínez, J. A., González-Calero, J. A., & Sáez-López, J. M. (2020). Computational thinking and mathematics using Scratch: An experiment with sixth-grade students. Interactive Learning Environments, 28(3), 316–327. https://doi.org/10.1080/10494820.2019.1612448
Santos, L., Raposo, S., Cardoso, A., Correia, P., & Espadeiro, R. G. (2022). Coletânea de tarefas - Tema Geometria (7.º ano de escolaridade). DGE. https://aem.dge.mec.pt/sites/default/files/resources/geometria.pdf
Schleicher, A. (2018). PISA 2021 Mathematics Framework (First Draft). OECD. https://www.okykla2030.lt/wp-content/uploads/2018/12/GB-2018-4-PISA-2021-Mathematics-Framework-First-Draft.pdf
Sentance, S., Waite, J., & Kallia, M. (2019). Teaching computer programming with PRIMM: a sociocultural perspective. Computer Science Education, 29(3), 136–176. https://doi.org/10.1080/08993408.2019.1608781
Seo, Y. H., & Kim, J. H. (2016). Analyzing the effects of coding education through pair programming for the computational thinking and creativity of elementary school students. Indian Journal of Science and Technology, 9(46), 1–5. https://doi.org/10.17485/ijst/2016/v9i46/107837
Sinclair, N., & Patterson, M. (2018). The dynamic geometrisation of computer programming. Mathematical Thinking and Learning, 20(1), 54–74. https:// doi. org/ 10. 1080/ 10986 065. 2018. 14035 41
Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics teaching in the middle school, 3(4), 268–275.
Stigberg, H., & Stigberg, S. (2020). Teaching programming and mathematics in practice: A case study from a Swedish primary school. Policy Futures in Education, 18(4), 483–496. https://doi.org/10.1177/1478210319894785
Vojkuvkova, I. (2012). The Van Hiele model of geometric thinking. In J. Šafránková & J. Pavlů (Eds.), WDS’12 Proceedings of Contributed Papers - Part I (pp. 72–75). Matfyzpress.
Watson, A., & Ohtani, M. (Eds.)(2015). Task design in mathematics education: An ICMI study 22. Springer.
Weintrop, D., Beheshti, E., Horn, M., Orton, K., Kemi, J., Trouille, L., & Wilensky, U. (2016). Defining Computational Thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25, 127–147. https://doi.org/10.1007/s10956-015-9581-5
Wilkerson, M. H. & Fenwick, M. (2017). The practice of using mathematics and computational thinking. In C. V. Schwarz, C. Passmore, & B. J. Reiser (Eds.), Helping students make sense of the world using next generation science and engineering practices (pp. 181–204). NSTA Press.
Wing, J. M. (2006). Computational Thinking. Communications of the ACM, 49(3), 33–35. https://doi.org/10.1145/1118178.1118212
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(3). https://doi.org/10.1186/s40594-023-00396-w
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