HISTORIA DE LA MATEMÁTICA PARA EL DISEÑO DE TAREAS: caracterización de conexiones intramatemáticas asociadas a la clasificación de los grupos de orden cuatro
Palavras-chave:
Investigación histórica, Conexiones matemáticas, Grupos isomorfos, Comprensión conceptual, Educación MatemáticaResumo
Las conexiones matemáticas son competencias necesarias que se deben desarrollar en los estudiantes para la comprensión de conceptos en matemáticas en cualquier nivel educativo. Además, la historia de la matemática es un contexto del que emanan conexiones para la construcción de conocimiento. Por lo cual, en este artículo se presentan algunas conexiones intramatemáticas identificadas al resolver tareas sobre la clasificación de los grupos de orden cuatro fundamentada en un análisis histórico y epistemológico del concepto de grupos isomorfos. La investigación es cualitativa y su diseño es un estudio de caso. Para la recolección de datos se aplicó una entrevista. Los datos se analizaron desde un análisis cualitativo de texto. Los resultados indican que existen, por lo menos, tres conexiones asociadas a los conceptos de grupo, isomorfismo y grupos isomorfos de los siguientes tipos que son comparación a través de características comunes, derivación, procedimiento y relación parte-todo. Se concluye que las tareas diseñadas con una fundamentación histórica favorecen para la apreciación conectada de los conceptos y resultados matemáticos en relación con los problemas e ideas que los generaron, haciendo explícitas las conexiones matemáticas.
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Referências
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Borji, V., Radmehr, F., & Font, V. (2019). The impact of procedural and conceptual teaching on students' mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 52(3), 404-423. http://doi.org/10.1080/0020739X.2019.1688404
Businskas, A. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. (Doctoral dissertation). Simon Fraser University. Canada. Recuperado de: https://summit.sfu.ca/item/9245
Bütüner, S. Ö. (2016). The use of concrete learning objects taken from the history of mathematics in mathematics education. International Journal of Mathematical Education in Science and Technology, 47(8), 1156-1178. https://doi.org/10.1080/0020739X.2016.1184336
Bütüner, S. Ö. (2020). An evaluation of activities based on the use of the history of mathematics as a tool. Journal of Pedagogical Research, 4(2), 139-164. http://dx.doi.org/10.33902/JPR.2020062216
Bütüner, S. Ö. & Baki, A. (2020). The use of history of mathematics in the mathematics classroom: An action study. International Journal of Education in Mathematics, Science and Technology (IJEMST), 8(2), 92-117. https://doi.org/10.46328/ijemst.v8i2.843
Cayley, A. (1854). VII. On the theory of groups, as depending on the symbolic equation θ^n=1. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 7(42), 40-47. https://doi.org/10.1080/14786445408647421
Creswell, J. W. (2014). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. 4 ed. Thousand Oaks: Sage Publications.
Eli, J., Mohr-Schroeder, M., & Lee, C. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
Fauvel, J., & van Maanen, J. (Eds.) (2000). History in mathematics education: the ICMI study. Dordrecht: Kluwer Academic Publishers.
Fleener, M. J., Reeder, S. L., Young, E., & Reynolds, A. M. (2002). History of mathematics: Building relationships for teaching and learning. Action in Teacher Education, 24(3), 73-84. https://doi.org/10.1080/01626620.2002.10734433
Fraser, J. B., & Koop, J. A. (1978). Teachers‟ opinions about some teaching material involving history of mathematics. International Journal of Mathematical Education in Science and Technology, 9(2), 147-151. https://doi.org/10.1080/0020739780090203
Furinghetti, F. (2020). Rethinking history and epistemology in mathematics education*. International Journal of Mathematical Education in Science and Technology, 51(6), 967-994. https://doi.org/10.1080/0020739X.2019.1565454
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
García-García, J., & Dolores-Flores, C. (2021a). Pre- university students' mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/ s13394-019-00286-x
García-García, J., & Dolores-Flores, C. (2021b). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
Gençkaya, Ş., & Tan-Şişman, G. (2021). The use of the history of mathematics in teaching-learning process: The perspectives of faculty members and teachers. Psycho-Educational Research Reviews, 10(2), 241-257. https://doi.org/10.52963/PERR_Biruni_V10.N2.17
Goktepe, S., & Ozdemir, A. S. (2013). An example of using history of mathematics in classes. European Journal of Science and Mathematics Education, 1(3), 125-136. https://doi.org/10.30935/scimath/9392
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.). Conceptual and Procedural Knowledge: the Case of Mathematics (pp. 1-27). Hillsdale: Lawrence Erlbaum Associates.
Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235-261. https://doi.org/10.1007/s10649-008-9174-9
Jankvist, U. T., Mosvold, R., Fauskanger, J., & Jakobsen, A. (2015). Analysing the use of history of mathematics through MKT. International Journal of Mathematical Education in Science and Technology, 46(4), 495-507. https://doi.org/10.1080/0020739X.2014.990528
Kuckartz, U. (2014). Qualitative Text Analysis: A Guide to Methods, Practice and Using Software. Los Angeles: Sage.
McBride, C. C., & Rollins, H. J. (1977). The effects of history of mathematics on attitudes toward mathematics of college algebra students. Journal for Research in Mathematics Education, 8(1), 57-61. https://doi.org/10.2307/748568
Melhuish, K., & Fagan, J. (2018). Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level. In N. H. Wasserman (Ed.). Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers (pp. 19-45). Netherlands: Springer. https://doi.org/10.1007/978-3-319-99214-3_2
Mendes, I. A. (2020). History for the Teaching of Mathematics: Transformation and Mobilization of Mathematical Knowledge for School. Pedagogical Research, 5(3), em0072. https://doi.org/10.29333/pr/8284
Mersin, N., & Durmus, S. (2021). Effects of the Enriched History of Mathematics Course on Prospective Mathematics Teachers. International Journal of Curriculum and Instruction, 13(1), 635-668. Recuperado de: https://files.eric.ed.gov/fulltext/EJ1285556.pdf
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards for School Mathematics: An Overview. National Council of Teachers of Mathematics.
Njie, B., & Asimiran, S. (2014). Case study as a choice in qualitative methodology. IOSR Journal of Research & Method in Education, 4(3), 35-40. https://doi.org/10.9790/7388-04313540
Queiroz, D. S. (2020). HISTÓRIA NA EDUCAÇÃO MATEMÁTICA. Revista De História Da Educação Matemática, 6(1). Recuperado de: https://www.histemat.com.br/index.php/HISTEMAT/article/view/294
Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., & Font, V. (2020). A new view about connections. The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2020.1799254
Singletary, L. M. (2012). Mathematical Connections Made in Practice: An Examination of Teachers’ Beliefs and Practices. (Doctoral dissertation). University of Georgia. Athens. Recuperado de: https://getd.libs.uga.edu/pdfs/singletary_laura_m_201208_phd.pdf
Wang, K., Wang, X. Q., Li, Y., & Rugh, M. S. (2018). A framework for integrating the history of mathematics into teaching in Shanghai. Educational Studies in Mathematics, 98(2), 135-155. https://doi.org/10.1007/s10649-018-9811-x
Borji, V., Radmehr, F., & Font, V. (2019). The impact of procedural and conceptual teaching on students' mathematical performance over time. International Journal of Mathematical Education in Science and Technology, 52(3), 404-423. http://doi.org/10.1080/0020739X.2019.1688404
Businskas, A. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. (Doctoral dissertation). Simon Fraser University. Canada. Recuperado de: https://summit.sfu.ca/item/9245
Bütüner, S. Ö. (2016). The use of concrete learning objects taken from the history of mathematics in mathematics education. International Journal of Mathematical Education in Science and Technology, 47(8), 1156-1178. https://doi.org/10.1080/0020739X.2016.1184336
Bütüner, S. Ö. (2020). An evaluation of activities based on the use of the history of mathematics as a tool. Journal of Pedagogical Research, 4(2), 139-164. http://dx.doi.org/10.33902/JPR.2020062216
Bütüner, S. Ö. & Baki, A. (2020). The use of history of mathematics in the mathematics classroom: An action study. International Journal of Education in Mathematics, Science and Technology (IJEMST), 8(2), 92-117. https://doi.org/10.46328/ijemst.v8i2.843
Cayley, A. (1854). VII. On the theory of groups, as depending on the symbolic equation θ^n=1. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 7(42), 40-47. https://doi.org/10.1080/14786445408647421
Creswell, J. W. (2014). Research Design: Qualitative, Quantitative and Mixed Methods Approaches. 4 ed. Thousand Oaks: Sage Publications.
Eli, J., Mohr-Schroeder, M., & Lee, C. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
Fauvel, J., & van Maanen, J. (Eds.) (2000). History in mathematics education: the ICMI study. Dordrecht: Kluwer Academic Publishers.
Fleener, M. J., Reeder, S. L., Young, E., & Reynolds, A. M. (2002). History of mathematics: Building relationships for teaching and learning. Action in Teacher Education, 24(3), 73-84. https://doi.org/10.1080/01626620.2002.10734433
Fraser, J. B., & Koop, J. A. (1978). Teachers‟ opinions about some teaching material involving history of mathematics. International Journal of Mathematical Education in Science and Technology, 9(2), 147-151. https://doi.org/10.1080/0020739780090203
Furinghetti, F. (2020). Rethinking history and epistemology in mathematics education*. International Journal of Mathematical Education in Science and Technology, 51(6), 967-994. https://doi.org/10.1080/0020739X.2019.1565454
García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
García-García, J., & Dolores-Flores, C. (2021a). Pre- university students' mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33, 1-22. https://doi.org/10.1007/ s13394-019-00286-x
García-García, J., & Dolores-Flores, C. (2021b). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
Gençkaya, Ş., & Tan-Şişman, G. (2021). The use of the history of mathematics in teaching-learning process: The perspectives of faculty members and teachers. Psycho-Educational Research Reviews, 10(2), 241-257. https://doi.org/10.52963/PERR_Biruni_V10.N2.17
Goktepe, S., & Ozdemir, A. S. (2013). An example of using history of mathematics in classes. European Journal of Science and Mathematics Education, 1(3), 125-136. https://doi.org/10.30935/scimath/9392
Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.). Conceptual and Procedural Knowledge: the Case of Mathematics (pp. 1-27). Hillsdale: Lawrence Erlbaum Associates.
Jankvist, U. T. (2009). A categorization of the “whys” and “hows” of using history in mathematics education. Educational Studies in Mathematics, 71(3), 235-261. https://doi.org/10.1007/s10649-008-9174-9
Jankvist, U. T., Mosvold, R., Fauskanger, J., & Jakobsen, A. (2015). Analysing the use of history of mathematics through MKT. International Journal of Mathematical Education in Science and Technology, 46(4), 495-507. https://doi.org/10.1080/0020739X.2014.990528
Kuckartz, U. (2014). Qualitative Text Analysis: A Guide to Methods, Practice and Using Software. Los Angeles: Sage.
McBride, C. C., & Rollins, H. J. (1977). The effects of history of mathematics on attitudes toward mathematics of college algebra students. Journal for Research in Mathematics Education, 8(1), 57-61. https://doi.org/10.2307/748568
Melhuish, K., & Fagan, J. (2018). Connecting the Group Theory Concept Assessment to Core Concepts at the Secondary Level. In N. H. Wasserman (Ed.). Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers (pp. 19-45). Netherlands: Springer. https://doi.org/10.1007/978-3-319-99214-3_2
Mendes, I. A. (2020). History for the Teaching of Mathematics: Transformation and Mobilization of Mathematical Knowledge for School. Pedagogical Research, 5(3), em0072. https://doi.org/10.29333/pr/8284
Mersin, N., & Durmus, S. (2021). Effects of the Enriched History of Mathematics Course on Prospective Mathematics Teachers. International Journal of Curriculum and Instruction, 13(1), 635-668. Recuperado de: https://files.eric.ed.gov/fulltext/EJ1285556.pdf
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and Standards for School Mathematics: An Overview. National Council of Teachers of Mathematics.
Njie, B., & Asimiran, S. (2014). Case study as a choice in qualitative methodology. IOSR Journal of Research & Method in Education, 4(3), 35-40. https://doi.org/10.9790/7388-04313540
Queiroz, D. S. (2020). HISTÓRIA NA EDUCAÇÃO MATEMÁTICA. Revista De História Da Educação Matemática, 6(1). Recuperado de: https://www.histemat.com.br/index.php/HISTEMAT/article/view/294
Rodríguez-Nieto, C., Rodríguez-Vásquez, F. M., & Font, V. (2020). A new view about connections. The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2020.1799254
Singletary, L. M. (2012). Mathematical Connections Made in Practice: An Examination of Teachers’ Beliefs and Practices. (Doctoral dissertation). University of Georgia. Athens. Recuperado de: https://getd.libs.uga.edu/pdfs/singletary_laura_m_201208_phd.pdf
Wang, K., Wang, X. Q., Li, Y., & Rugh, M. S. (2018). A framework for integrating the history of mathematics into teaching in Shanghai. Educational Studies in Mathematics, 98(2), 135-155. https://doi.org/10.1007/s10649-018-9811-x
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2022-04-12
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Zubillaga-Guerrero, E. ., & Rodríguez-Vásquez, F. M. . (2022). HISTORIA DE LA MATEMÁTICA PARA EL DISEÑO DE TAREAS: caracterización de conexiones intramatemáticas asociadas a la clasificación de los grupos de orden cuatro. Revista De História Da Educação Matemática, 8, 1–17. Recuperado de https://www.histemat.com.br/index.php/HISTEMAT/article/view/490
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