Categories and practices involved with computational thinking for the improvement of mathematical problem-solving skills in secondary school
DOI:
https://doi.org/10.15649/2346030X.4408Keywords:
computational thinking, mathematics, pedagogical practicesAbstract
This reflection article shows how computational thinking comprises a set of skills required by today's human capital, linked to a need regarding economic and labor demand in the era of the fourth industrial revolution. In addition, the educational deficiencies in the secondary grades, regarding the training of mathematics and computation, make it necessary to review the categories and practices that can be used in the process of training these skills in secondary school and innovate in the development of these skills. Therefore, from the literature review, three relevant categories associated with computational processes were found, which impact education in mathematical problem-solving skills in secondary school: algorithm programming, problem solving and modeling, through which the skills of computational thinking, problem decomposition, abstraction and algorithm design are developed. Unlike the Pólya method, which has been implemented in many studies to solve mathematical problems by carrying out steps such as: understanding the problem, establishing a plan, executing the plan and reviewing the process to ensure that no mistakes were made, computational thinking allows solving the problem and representing it through codes with mathematical algorithms, with various didactic tools. In this way, computational thinking currently acquires great importance to promote the development of the necessary competencies in the 21st century. The above shows lines of possibilities in new research that seek to develop pedagogical practices for the resolution of problems related to mathematics in secondary school; some of them include coding skills, use of blocks and graphics. This facilitates the internalization of knowledge that guarantees the progressive advancement of students in their mathematical and computational skills and their integral formation.
References
K. V. de Oudeweetering y J. Voogt, "Teachers’ conceptualization and enactment of twenty-first century competences: exploring dimensions for new curricula," The Curriculum Journal, vol. 29, no. 1, pp. 116-133, 2018, doi: 10.1080/09585176.2017.1369136.
OCDE, “Organización para la Cooperación y el Desarrollo Económicos (OCDE) | Cancillería,” Accedido: 10 de enero de 2024. [En línea]. Disponible en: https://www.cancilleria.gov.co/en/internacional/politica/economico/OCDE.
UNESCO, “E2030: educación y habilidades para el siglo XXI; reporte - UNESCO Biblioteca Digital,” Accedido: 12 de febrero de 2024. [En línea]. Disponible en: https://unesdoc.unesco.org/ark:/48223/pf0000250117.
I. J. Salamanca y M. Badilla, "Estudio de marcos referenciales de habilidades para el siglo XXI: un modelo ecosistémico para orientar procesos de innovación educativa," Synergies Chili, vol. 16, pp. 33-48, ago. 2020.
M. Zapata, Pensamiento computacional desconectado. Computational thinking unplugged, 2019, doi: 10.13140/RG.2.2.12945.48481.
D. Weintrop et al., "Defining computational thinking for mathematics and science classrooms," Journal of Science Education and Technology, vol. 25, no. 1, pp. 127-147, 2016, doi: 10.1007/s10956-015-9581-5.
M. Resnick et al., "Scratch: Programming for All," Communications of the ACM, vol. 52, pp. 60-67, nov. 2009, doi: 10.1145/1592761.1592779.
L. Zhang y J. Nouri, "A systematic review of learning computational thinking through Scratch in K-9," Computers & Education, vol. 103607, jun. 2019, doi: 10.1016/j.compedu.2019.103607.
M. Lodi y S. Martini, "Computational Thinking, Between Papert and Wing," Science & Education, vol. 30, ago. 2021, doi: 10.1007/s11191-021-00202-5.
S. Grover y R. Pea, "Computational Thinking: A Competency Whose Time Has Come," 2017, doi: 10.5040/9781350057142.ch-003.
K. M. Rich, E. Spaepen, C. Strickland, y C. Moran, "Synergies and differences in mathematical and computational thinking: implications for integrated instruction," Interactive Learning Environments, abr. 2020, Accedido: 16 de febrero de 2024. [En línea]. Disponible en: https://www.tandfonline.com/doi/abs/10.1080/10494820.2019.1612445.
J. M. Wing, "Computational thinking," Communications of the ACM, vol. 49, no. 3, pp. 33-35, mar. 2006, doi: 10.1145/1118178.1118215.
S. Papert, Mindstorms: children, computers, and powerful ideas, USA: Basic Books, Inc., 1980.
P. Denning, "Remaining trouble spots with computational thinking," Communications of the ACM, vol. 60, pp. 33-39, may 2017, doi: 10.1145/2998438.
H. Ye, B. Liang, O.-L. Ng, y C. S. Chai, "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, vol. 10, no. 1, p. 3, ene. 2023, doi: 10.1186/s40594-023-00396-w.
S. Bocconi et al., "Developing Computational Thinking in Compulsory Education. Implications for policy and practice," EUR - Scientific and Technical Research Reports, dic. 2016, doi: 10.2791/792158.
J. Sumway, L. Welch, J. Kozlowski, J. Midura, y V. Lee, "Kindergarten students’ mathematics knowledge at work: the mathematics for programming robot toys," Mathematical Thinking and Learning, vol. 25, no. 4, Accedido: 26 de enero de 2024. [En línea]. Disponible en: https://www.tandfonline.com/doi/abs/10.1080/10986065.2021.1982666.
Z. Cui y O.-L. Ng, "The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment," Journal of Educational Computing Research, vol. 59, p. 073563312097993, ene. 2021, doi: 10.1177/0735633120979930.
P. O. Gilchrist, A. B. Alexander, A. J. Green, F. E. Sanders, A. Q. Hooker, y D. M. Reif, "Development of a Pandemic Awareness STEM Outreach Curriculum: Utilizing a Computational Thinking Taxonomy Framework," Education Sciences, vol. 11, no. 3, Art. no. 3, mar. 2021, doi: 10.3390/educsci11030109.
C. Pei, D. Weintrop, y U. Wilensky, “Cultivating Computational Thinking Practices and Mathematical Habits of Mind in Lattice Land”, Mathematical Thinking and Learning, vol. 20, pp. 75-89, ene. 2018, doi: 10.1080/10986065.2018.1403543.
C. Selby y J. Woollard, “Computational thinking: the developing definition”, ene. 2013.
Z. Cui y O. Ng, “The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment”, Journal of Educational Computing Research, pp. 1-17, 2021. Accedido: 23 de junio de 2024. [En línea]. Disponible en: https://journals.sagepub.com/doi/abs/10.1177/0735633120979930.
S. Subramaniam, S. M. Maat, y M. S. Mahmud, “Computational thinking in mathematics education: A systematic review”, Cypriot Journal of Educational Sciences, vol. 17, n.o 6, jun. 2022, doi: 10.18844/cjes.v17i6.7494.
S. Wu y Y. Su, “Visual Programming Environments and Computational Thinking Performance of Fifth- and Sixth-Grade Students”, Journal of Educational Computing Research, vol. 59, n.o 6, pp. 1075-1092, oct. 2021, doi: 10.1177/0735633120988807.
K. Bråting y C. Kilhamn, “Exploring the intersection of algebraic and computational thinking”, Mathematical Thinking and Learning, vol. 23, n.o 2, pp. 170-185, abr. 2021, doi: 10.1080/10986065.2020.1779012.
S. Ramaila y H. Shilenge, “Integration of computational thinking activities in Grade 10 mathematics learning”, International Journal of Research in Business and Social Science, vol. 12, n.o 2, mar. 2023, doi: 10.20525/ijrbs.v12i2.2372.
J. Á. R. Ortiz y J. V. Guizado, “Proceso del pensamiento crítico y computacional en el aprendizaje de la Matemática en educación secundaria”, Revista Prisma Social, n.o 41, abr. 2023.
M. Kallia, S. van, P. Drijvers, E. Barendsen, y J. Tolboom, “Characterising computational thinking in mathematics education: a literature-informed Delphi study”, Research in Mathematics Education, vol. 23, n.o 2, pp. 159-187, may 2021, doi: 10.1080/14794802.2020.1852104.
D. Quiroz, J. Carmona, A. Castrillón, y J. Villa, “Integración del Pensamiento Computacional en la educación primaria y secundaria en Latinoamérica: una revisión sistemática de literatura”, Revista de Educación a Distancia, vol. 21, n.o 68, nov. 2021, doi: 10.6018/red.485321.
E. Relkin, L. Ruiter, y M. Bers, “Learning to Code and the Acquisition of Computational Thinking by Young Children”, Computers & Education, vol. 169, p. 104222, abr. 2021, doi: 10.1016/j.compedu.2021.104222.
Z. Ersozlu, M. Swartz, y A. Skourdoumbis, “Developing Computational Thinking through Mathematics: An Evaluative Scientific Mapping”, Education Sciences, vol. 13, n.o 4, abr. 2023, doi: 10.3390/educsci13040422.
V. Nogueira et al., “Towards an inclusive digital literacy: An experimental intervention study in a rural area of Brazil”, Education and Information Technologies, vol. 27, mar. 2022, doi: 10.1007/s10639-021-10711-z.
D. Pérez, M. Román, y E. González, “El pensamiento algorítmico como estrategia didáctica para el desarrollo de habilidades de resolución de problemas en el contexto de la educación básica secundaria”, vol. 23, pp. 1-22, ene. 2023, doi: 10.6018/red.542111.
M. Velasco, “Resolución de problemas algorítmicos y objetos de aprendizaje: una revisión de la literatura”, RIDE Revista Iberoamericana para la Investigación y el Desarrollo Educativo, vol. 10, n.o 20, mar. 2020, doi: 10.23913/ride.v10i20.630.
A. Ioannidou, V. Bennett, A. Repenning, K. H. Koh, y A. Basawapatna, “Computational Thinking Patterns”, Online Submission, ago. 2011.
H. Pérez, “Uso de Scratch como herramienta para el desarrollo del pensamiento computacional en programación I de la carrera de informática de la Universidad Central del Ecuador”, 2017. Accedido: 14 de abril de 2024. [En línea]. Disponible en: http://rua.ua.es/dspace/handle/10045/82731.
I. Alonso, “La resolución de problemas matemáticos. Una alternativa didáctica centrada en la representación”, 2001. doi: 10.13140/RG.2.2.27079.19362.
D. Pinzón, M. Román, y E. González, “El pensamiento algorítmico como estrategia didáctica para el desarrollo de habilidades de resolución de problemas en el contexto de la educación básica secundaria”, vol. 23, pp. 1-22, ene. 2023, doi: 10.6018/red.542111.
J. Shim, “A Study on the Level of Algorithmic Thinking of Students in Elementary and Secondary Schools”. Accedido: 14 de abril de 2024. [En línea]. Disponible en: http://www.kci.go.kr/kciportal/landing/article.kci?arti_id=ART002544204.
G. Polya, How to solve it: A new aspect of mathematical method, Princeton, NJ: Princeton University Press, 1945.
J. D. Bransford y B. S. Stein, The Ideal Problem Solver: A Guide for Improving Thinking, Learning, and Creativity. New York, NY, USA: Freeman, 1984. Accedido: 24 de junio de 2024. [En línea]. Disponible en: https://www.product24swiss.net/?referenceid=1062573.
D. Treffinger y S. Isaksen, "Creative Problem Solving: The History, Development, and Implications for Gifted Education and Talent Development", Gifted Child Quarterly, vol. 49, pp. 342-353, oct. 2005, doi: 10.1177/001698620504900407.
S. Thompson, How to Program It. Accedido: 24 de junio de 2024. [En línea]. Disponible en: https://www.cs.kent.ac.uk/people/staff/sjt/Haskell_craft/HowToProgIt.html.
M. I. Mac Gaul de Jorge, M. F. López, y A. P. del Olmo, "Resolución de problemas computacionales: análisis del proceso de aprendizaje", presentado en III Congreso de Tecnología en Educación y Educación en Tecnología, jun. 2008. Accedido: 24 de junio de 2024. [En línea]. Disponible en: http://sedici.unlp.edu.ar/handle/10915/19049.
I. Alonso, A. Salgado, y A. Blanco, "Sistema básico de habilidades para algoritmizar durante la programación computacional", Magazine de las Ciencias: Revista de Investigación e Innovación. Accedido: 15 de abril de 2024. [En línea]. Disponible en: https://revistas.utb.edu.ec/index.php/magazine/article/view/725.
F. Rojas y H. Solar, "Organización de tareas matemáticas según niveles de complejidad cognitiva: una mirada desde las competencias matemáticas", ene. 2011.
MEN, "Lineamientos Curriculares - ..::Ministerio de Educación Nacional de Colombia::..", Accedido: 24 de junio de 2024. [En línea]. Disponible en: https://www.mineducacion.gov.co/1621/article-89869.html.
MEN, "2007 - ..::Ministerio de Educación Nacional de Colombia::..", Accedido: 24 de junio de 2024. [En línea]. Disponible en: https://www.mineducacion.gov.co/1621/article-166893.html.
MINTIC, "Orientaciones Curriculares de Tecnología e Informática", Colombia Aprende. Accedido: 24 de junio de 2024. [En línea]. Disponible en: https://colombiaaprende.edu.co/contenidos/coleccion/orientaciones-curriculares-de-tecnologia-e-informatica.
W. Blum y D. Leiß, "How do Students and Teachers Deal with Modelling Problems?", en Mathematical Modelling, 2007, pp. 222-231, doi: 10.1533/9780857099419.5.221.
P. Cobb, "Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development", Accedido: 27 de abril de 2024. [En línea]. Disponible en: https://www.researchgate.net/publication/243720204_Where_Is_the_Mind_Constructivist_and_Sociocultural_Perspectives_on_Mathematical_Development.
A. Schoenfeld, "Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics", 1992, pp. 334-370.
H. Freudenthal, Didactical Phenomenology of Mathematical Structures, vol. 1, 2002, doi: 10.1007/0-306-47235-X.
Z. Cui y O. Ng, "The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment", Semantic Scholar. Accedido: 26 de junio de 2024. [En línea]. Disponible en: https://www.semanticscholar.org/paper/The-Interplay-Between-Mathematical-and-Thinking-in-Cui-Ng/94f82e7cf9148ee5cbd7b012b37587a3b0341398.
K. Brennan y M. Resnick, "New frameworks for studying and assessing the development of computational thinking", MIT Media Lab. Accedido: 26 de junio de 2024. [En línea]. Disponible en: https://www.media.mit.edu/publications/new-frameworks-for-studying-and-assessing-the-development-of-computational-thinking/.
Ľ. Valovičová, J. Ondruška, Ľ. Zelenický, V. Chytrý, y J. Medová, "Enhancing Computational Thinking through Interdisciplinary STEAM Activities Using Tablets", Mathematics, vol. 8, n.o 12, Art. n.o 12, dic. 2020, doi: 10.3390/math8122128.
M. Román, J. Pérez, y C. Jiménez, "Which cognitive abilities underlie computational thinking? Criterion validity of the Computational Thinking Test", Accedido: 26 de junio de 2024. [En línea]. Disponible en: https://www.researchgate.net/publication/308654282_Which_cognitive_abilities_underlie_computational_thinking_Criterion_validity_of_the_Computational_Thinking_Test.
J. Rodríguez, J. A. González, y J.-M. Sáez, "Computational thinking and mathematics using Scratch: an experiment with sixth-grade students", Interactive Learning Environments, vol. 28, pp. 1-12, may 2019, doi: 10.1080/10494820.2019.1612448.
W. Ho, C. Looi, W. Huang, P. Seow, y L. Wu, "Computational thinking in mathematics: To be or not to be, that is the question", en Mathematics: Connection and Beyond: Yearbook 2020 Association of Mathematics Educators, World Scientific, 2021, pp. 205-234, doi: 10.1142/9789811236983_0011.
S. Chan, C. Looi, W. Ho, W. Huang, P. Seow, y L. Wu, "Learning Number Patterns through Computational Thinking Activities: A Rasch Model Analysis", Heliyon, vol. 7, p. e07922, sep. 2021, doi: 10.1016/j.heliyon.2021.e07922.
E. Coban y Ö. Korkmaz, "An alternative approach for measuring computational thinking: Performance-based platform", Thinking Skills and Creativity, vol. 42, p. 100929, ago. 2021, doi: 10.1016/j.tsc.2021.100929.
J. Sáez, M. Sevillano, y E. Vásquez, “The effect of programming on primary school students’ mathematical and scientific understanding: educational use of mBot”, Rochester, NY, 8 de mayo de 2022. Accedido: 26 de junio de 2024. [En línea]. Disponible en: https://papers.ssrn.com/abstract=4103579.
N. Sinclair y M. Patterson, “The Dynamic Geometrisation of Computer Programming”, Mathematical Thinking and Learning, vol. 20, pp. 54-74, ene. 2018, doi: 10.1080/10986065.2018.1403541.
O. Kaufmann y B. Stenseth, “Programming in mathematics education”, International Journal of Mathematical Education in Science and Technology, vol. 52, n.o 7, pp. 1029-1048, ago. 2021, doi: 10.1080/0020739X.2020.1736349.
M. Wilkerson, “Construction, categorization, and consensus: Student generated computational artifacts as a context for disciplinary reflection”, Educational Technology Research and Development, vol. 62, pp. 99-121, feb. 2014, doi: 10.1007/s11423-013-9327-0.
S. Psycharis y M. Kallia, “The effects of computer programming on high school students’ reasoning skills and mathematical self-efficacy and problem solving”, Instructional Science, vol. 45, n.o 5, pp. 583-602, 2017, doi: 10.1007/s11251-017-9421-5.
R. Porlán, “Teoría del conocimiento, teoría de la enseñanza y desarrollo profesional (las concepciones epistemológicas de los profesores)”, Universidad de Sevilla, 1991. Accedido: 28 de junio de 2024. [En línea]. Disponible en: https://dialnet.unirioja.es/servlet/tesis?codigo=130281.
A. Gorina, I. Alonso, N. Domecq, y J. Esteven, “Pautas para implementar la enseñanza de la Matemática a través de la resolución de problemas/ Guidelines to implement the teaching of Mathematics through the problem solving”, Revista Maestro y Sociedad, pp. 66-81, abr. 2018.
B. Jonsson, M. Norqvist, Y. Liljekvist, y J. Lithner, “Learning mathematics through algorithmic and creative reasoning”, The Journal of Mathematical Behavior, vol. 36, pp. 20-32, dic. 2014, doi: 10.1016/j.jmathb.2014.08.003.
T. Easton, “Beyond the algorithmization of the sciences”, Commun. ACM, vol. 49, pp. 31-33, may 2006, doi: 10.1145/1125944.1125967.
A. Salgado, I. A. Berenguer, y A. Gorina Sánchez, “Ejemplificación de la solución algorítmica de problemas de programación computacional”, Didasc@lia: Didáctica y Educación, vol. 5, n.o 4 (Octubre-Diciembre), pp. 15-36, 2014.
I. Alonso, “Sistema Básico de Habilidades para la Algoritmización Computacional”, Revista de Investigación, Formación y Desarrollo: Generando Productividad Institucional, vol. 9, p. 14, abr. 2021, doi: 10.34070/rif.v9i1.255.
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