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Abstract

This study examines the outcomes of implementing a teaching unit that integrates problem-solving with the history of mathematics to improve fifth-grade students' understanding of fractions at an educational institution in Yopal, Colombia. Utilizing an educational action research methodology, the study commenced with a diagnostic assessment to identify learning gaps, followed by the design and implementation of a didactic unit. This unit comprised three activities embedded in historical contexts to facilitate the learning of fractions, with its effectiveness assessed through an exit test. Conducted with 32 fifth-grade students, the research employed diagnostic and exit tests to evaluate student performance before and after the activities. The results demonstrated that the teaching unit significantly enhanced students' abilities to understand and apply fractions, as evidenced by their improved performance in the activities within the didactic unit.

Keywords

Didactic Unit Education Fractions History of Mathematics Pólya Method

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Torres-Peña, R. C., Peña-González, D., & Ariza, E. A. (2024). Enhancing fraction learning through problem-solving and historical context: A didactic unit approach. Journal on Mathematics Education, 15(3), 815–834. https://doi.org/10.22342/jme.v15i3.pp815-834
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References

  1. Álvarez, E. J. (2017). Diseño de una unidad didáctica para el aprendizaje cooperativo de números racionales en 2º de la ESO. Master's thesis in Education. Universidad Internacional de la Rioja.
  2. Ambròs, A. (2009). La programación de unidades didácticas. Aula de Innovación Educativa, 180, 26-32. http://www.ub.edu/dllenpantalla/sites/default/files/3%20%20AU%20188%20Alba%20Ambròs%20programar%20por%20competencias.pdf
  3. Arenas-Peñaloza & Rodríguez-Vásquez. (2021). Enseñanza y aprendizaje del concepto de fracción en la educación primaria: estado del arte. Cultura Educación Sociedad, 12(2), 22-60. https://doi.org/10.17981/cultedusoc.12.2.2021.03
  4. Arteaga, M. B., & Macías, S. J. (2016). Didáctica de las Matemáticas en la Educación infantil. Editorial Universidad Internacional de La Rioja, S. A. First edition. Spain.
  5. Ausubel, D. P. (1976). Psicología educativa: Un punto de vista cognoscitivo. Trillas Editorial. Mexico.
  6. Azman, N. A., & Maat, S. M. (2021). Integration of the history of mathematics in mathematics education: A systematic literature review. International Journal of Academic Research in Business and Social Sciences, 11(4), 1035-1057. http://dx.doi.org/10.6007/IJARBSS/v11-i4/9768
  7. Babakr, Z. H., Mohamedamin, P., & Kakamad, K. (2019). Piaget’s cognitive developmental theory: Critical review. Education Quarterly Reviews, 2(3), 517-524. https://doi.org/10.31014/aior.1993.02.03.84
  8. Björklund, C., & Palmér, H. (2022). Teaching toddlers the meaning of numbers—connecting modes of mathematical representations in book reading. Educational Studies in Mathematics, 110, 525–544. https://doi.org/10.1007/s10649-022-10147-3
  9. Butto, Z. C. (2013). El aprendizaje de fracciones en educación primaria: Una propuesta de enseñanza en dos ambientes. Horizontes Pedagógicos, 15(1), 33-45. https://dialnet.unirioja.es/descarga/articulo/4892957.pdf
  10. Cañabate, D., Bubnys, R., Nogué, L., Martínez-Mínguez, L., Nieva, C., & Colomer, J. (2021). Cooperative learning to reduce inequalities: Instructional approaches and dimensions. Sustainability, 13(18), 10234. https://doi.org/10.3390/su131810234
  11. Charalambous, C. Y., Philippou, G. N., & Kyriakides, L. (2008). Tracing the development of preservice teachers’ efficacy beliefs in teaching mathematics during fieldwork. Educational Studies in Mathematics, 67, 125-142. https://doi.org/10.1007/s10649-007-9084-2
  12. Chotimah, C., & Festiyed. (2020). Meta-analysis of the effect of using PhET interactive simulations on worksheets on high school students' physics learning outcomes. Journal of Physics: Conference Series, 1481(1), 012093. https://doi.org/10.1088/1742-6596/1481/1/012093
  13. Díaz, P. J. (2017). Importance of Phet simulation in teaching and learning equivalent fractions. Revista Educación y Desarrollo Social, 11(1), 48-63. https://doi.org/10.18359/reds.2011
  14. Dominguez, H., Crespo, S., del Valle, T., Adams Corral, M., Coupe, M., Gonzalez, G., & Ormazabal, Y. (2020). Learning to transform, transforming to learn: Children’s creative thinking with fractions. Journal of Humanistic Mathematics, 10(2), 76-101. https://doi.org/10.5642/jhummath.202002.06
  15. Ebby, C., Hulbert, E., & Broadhead, R. (2020). A focus on addition and subtraction. Bringing Mathematics Education Research to the Classroom. Routledge. https://doi.org/10.4324/9781003038337
  16. Fandiño, M. (2009). Las fracciones: Aspectos conceptuales y Didácticos. Didácticas Magisterio. 222 p.
  17. Fauzi, I., Rakhmat, C., & Budiman, N. (2023). Complex thinking: How are students' mathematical problem-solving skills in elementary school?. Bulletin of Science Education, 3(3), 228-240. http://dx.doi.org/10.51278/bse.v3i3.916
  18. Gaviria, U. G. (2016). Estrategia didáctica para trabajar el concepto de fracción como relación Parte-Todo en grado quinto, teniendo en cuenta su origen histórico. Master's Thesis. Universidad Nacional de Colombia
  19. Getenet, S., & Callingham, R. (2021). Teaching interrelated concepts of fraction for understanding and teacher’s pedagogical content knowledge. Mathematics Education Research Journal, 33, 201–221. https://doi.org/10.1007/s13394-019-00275-0
  20. Gómez, R. M. (2019). Identificación de dificultades en el proceso de enseñanza-aprendizaje de las fracciones y la resolución de problemas en Educación Primaria. Master's thesis in Specific Didactics. Universitat Jaume. http://hdl.handle.net/10234/184791
  21. Hariyani, M., Herman, T., Suryadi, D., & Prabawanto, S. (2022). Exploration of student learning obstacles in solving fraction problems in elementary school. International Journal of Educational Methodology, 8(3), 505-515. https://doi.org/10.12973/ijem.8.3.505
  22. Lamon, S. (2020). Teaching Fractions and Ratios for Understanding. Routledge.
  23. Latorre, A. (2007). La investigación-acción: conocer y cambiar la práctica educativa. Barcelona, España. Graó Editorial. https://www.uv.mx/rmipe/files/2019/07/La-investigacion-accion-conocer-y-cambiar-la-practica-educativa.pdf
  24. Loc, N.P., Tong, D.H., & Chau, P.T. (2017). Identifying concept fraction of primary school students: The investigation in Vietnam. Educational Research and Reviews, 12(8), 531-539. https://doi.org/10.5897/ERR2017.3220
  25. López, B. F., Rentería, M. L., & Vergara, M. F. (2016). El aprendizaje de las operaciones básicas matemáticas en educación primaria, mediado por ambientes virtuales de aprendizaje. *Universidad Pontificia Bolivariana Maestría En Ciencias Naturales y Matemáticas*.
  26. Ospina, N., & García, O.J. (2019). Propuesta de una unidad didáctica como estrategia para la resolución de problemas a partir de una estructura aditiva a una estructura multiplicativa para lograr aprendizajes significativos en niños y niñas del grado tercero de la básica primaria. Master's Thesis in Education. Universidad del Tolima.
  27. Pearn, C., Stephens, M., & Pierce, R. (2022). Algebraic reasoning in years 5 and 6: Classifying its emergence and progression using reverse fraction tasks. ZDM Mathematics Education, 54, 1257–1271. https://doi.org/10.1007/s11858-022-01426-7
  28. Piaget, J. (1988). Psicologia evolutive de Jean Piaget. Fourth edition. Mexico: Editorial Paidós Mexicana, S. A.
  29. Polotskaia, E., & Savard, A. (2021). Some multiplicative structures in elementary education: A view from relational paradigm. Educational Studies in Mathematics, 106, 447–469. https://doi.org/10.1007/s10649-020-09979-8
  30. Pólya, G. (1969). How to Solve it?. Trillas.
  31. Phuong, N.T., & Loc, N.P. (2020). Solving word problems involving “ratio” concept of the fifth-grade students: A study in Vietnam. Universal Journal of Educational Research, 8(7), 2937-2945. http://doi.org/10.13189/ujer.2020.080722
  32. Reséndiz, B. E., & González, S. C. (2018). Teaching fractions in third-grade elementary students: Discourse analysis and pedagogical practices. Revista Internacional de Ciencias Sociales y Humanidades SOCIOTAM, 28(1), 109-138. https://www.redalyc.org/jatsRepo/654/65457048006/html/index.html
  33. Ronen, I.K. (2020). Action research as a methodology for professional development in leading an educational process. Studies in Educational Evaluation, 64. 100826. https://doi.org/10.1016/j.stueduc.2019.100826
  34. Ruíz, R. A., & Lemos, G. D. (2018). Recursos didácticos para la enseñanza de resolución de problemas de suma – resta. La experiencia de primero de Primaria de la Institución Educativa Simón Bolívar de Torno Rojo - Puerto Libertador – Córdoba. Master's thesis. Universidad Santo Tomás.
  35. Salazar, M., & Díaz, L. (2009). La Actividad de Medir Aporta Significados a Fracciones y Razones. Comité Latinoamericano de Matemática Educativa, Acta 22, 207–216.
  36. Salinas, O.D. (2013). Estrategias didácticas para la enseñanza de fracciones en el tercer ciclo de la educación primaria. Universidad Pedagógica Nacional, México. http://200.23.113.51/pdf/29998.pdf
  37. Schubring, G. (2011). Conceptions for relating the evolution of mathematical concepts to mathematics learning—epistemology, history, and semiotics interacting: To the memory of Carl Menger (1902–1985). Educational Studies in Mathematics, 77(1), 79-104. https://doi.org/10.1007/s10649-011-9301-x
  38. Silva, H. A. (2017). Propuesta didáctica para el fortalecimiento del aprendizaje de los números racionales en el grado 601 del Colegio Miguel Antonio Caro I.E.D J.M. a través de la teoría de las situaciones didácticas. Facultad de ciencias de la educación Instituto de postgrados Maestría en Ciencias de la Educación. Énfasis en Orientación Educativa. Repository of the Universidad libre. Retrieved from: https://repository.unilibre.edu.co/handle/10901/10270
  39. United Nations Educational, Scientific and Cultural Organization (UNESCO). (2016). Contributions to the teaching of Mathematics. Available in: https://unesdoc.unesco.org/ark:/48223/pf0000248073
  40. Valdovinos, S. (2014). Desarrollo de habilidades para el aprendizaje de las fracciones por medio de la manipulación de objetos y las tecnologías en los alumnos de quinto grado de primaria. Master's Thesis in Education. Universidad Pedagógica Naciona, Michoacan - México. Available in: http://bibliotecaupn161.com.mx/tesis/221PROYECTODETITULACION.pdf.pdf
  41. Vásquez, T. E., Armenta, C. M., & Romero, F. C. (2019). The fraction as a measure and as an operator: A design experience of didactic activities. Acta Latinoamericana de Matemática Educativa, 32(2), 322-331. http://funes.uniandes.edu.co/14129/1/Vasquez2019La.pdf
  42. Vittori, D. (2021). Which organization for which party? An organizational analysis of the five-star movement. Contemporary Italian Politics, 13(1), 31-48. https://doi.org/10.1080/23248823.2020.1853373
  43. Vygotsky, L. S. (1978). Mind in society: The development of higher mental processes. Harvard University Press.
  44. Wahyu, K., Kuzu, T.E., Subarinah, S., Ratnasari, D., & Mahfudy, S. (2020). Partitive fraction division: Revealing and promoting primary students’ understanding. Journal on Mathematics Education, 11(2), 237-258. http://doi.org/10.22342/jme.11.2.11062.237-258
  45. Yayuk, E., & Husamah, E. (2020). The difficulties of prospective elementary school teachers in item problem solving for mathematics: Polya`s steps. Journal for the Education of Gifted Young Scientists, 8(1), 361-368. https://doi.org/10.17478/jegys.665833