Contextualization and conjecturing: elements of design of didactic sequences for the learning of Mathematics at a University level

LUIS CARLOS ROMERO, ALEJANDRO LEURO, MARIA CAMILA CARVAJAL

Abstract

In this paper we present the results of a research developed with the purpose of identifying some elements for the design of teaching sequences that promote reasoning and conjecture-based activities in undergraduate students. The methodology employed corresponds to a teaching experiment, in which the proposed activities were designed according to the theory of Mathematics in the Context of Science. The results obtained allow us to identify the relationship between the resolution process of the contextualized events and the formulation of conjectures, and to recognize the usefulness of the design of contextualized events to foster conjecturing processes for engineering students.

Keywords

Conjecturing, Math modelling, Mathematics in the context of Science, differential equations, contextualized event

Full Text:

PDF

References

Ainley, J., Pratt, D., & Hansen, A. (2006). Connecting engagement and focus in pedagogic task design. British Educational Research Journal, 32(1), 23-38. https://doi.org/10.1080/01411920500401971.

Aravena Díaz, M. D., Díaz Levicoy, D., Rodríguez Alveal, F., & Cárcamo Mansilla, N. (2022). Estudio de caso y modelado matemático en la formación de ingenieros. Caracterización de habilidades STEM. Ingeniare. Revista Chilena de Ingeniería, 30(1), 37-56. http://dx.doi.org/10.4067/S0718-33052022000100037.

Asempapa, R. (2018). Assessing teachers’ knowledge of mathematical modeling: Results from an initial scale development. Journal of Mathematics Education, 11(1), 1-16. http://dx.doi.org/10.26711/007577152790017

Asempapa, R., & Sturgill, D. J. (2019). Mathematical modeling: Issues and challenges in mathematics education and teaching. Journal of Mathematics Research, 11(5), 71-81 http://dx.doi.org/10.5539/jmr.v11n5p71.

Astawa, I., Budayasa, I. K., & Juniati, D. (2018). The process of student cognition in constructing mathematical conjecture. Journal on Mathematics Education, 9(1), 15-26. http://dx.doi.org/10.22342/jme.9.1.4278.15-26.

Caicedo, E., & Chacón, G. (2020). Aprendizaje de las ecuaciones diferenciales desde un enfoque cualitativo. Praxis & Saber, 11(26). https://doi.org/10.19053/22160159.v11.n26.2020.9856.

Camarena, P. (2013). A treinta años de la teoría educativa "Matemática en el Contexto de las Ciencias". Innovación Educativa, 13(62), 17-44. https://www.scielo.org.mx/pdf/ie/v13n62/v13n62a3.pdf.

Camarena, P. (2021). Teoría de la Matemática en el Contexto de las Ciencias. Edunse Editorial Universitaria. https://www.edunse.unse.edu.ar/libros/digitales/teoria-matematica.pdf.

Cañadas, M. C., Deulofeu-Piquet, J., Figueiras, L., Reid, D. A., & Yevdokimov, O. (2008). Perspectivas teóricas en el proceso de elaboración de conjeturas e implicaciones para la práctica: tipos y pasos. Revista Enseñanza de las Ciencias, 26(3), 431-441.

Cárdenas-Oliveros, J. A., Rodriguez-Borges, C. G., Pérez-Rodríguez, J. A., & Valencia-Zambrano, X. H. (2022). Desarrollo del pensamiento crítico: Metodología para fomentar el aprendizaje en ingeniería. Revista de Ciencias Sociales (Ve), XXVIII(4), 512-530. https://www.redalyc.org/journal/280/28073811032/html/.

Confrey, J. (2006). The evolution of design studies as methodology. In R. K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 135-151). Cambridge University Press.

Dierdorp, A., Bakker, A., Eijkelhof, H., & van Maanen, J. (2011). Authentic practices as contexts for learning to draw inferences beyond correlated data. Mathematical Thinking and Learning, 13(1-2), 132-151.

Doerr, H., Ärlebäck, J., & Costello Staniec, A. (2014). Design and effectiveness of modeling‐based mathematics in a summer bridge program. Journal of Engineering Education, 103(1), 92-114. http://dx.doi.org/10.1002/jee.20037.

Garcia-Barrera, A. (2015). Importancia de la competencia argumentativa en el ámbito educativo: una propuesta para su enseñanza a través del role playing online. RED-Revista de Educación a Distancia, 1(45), 1-20. http://dx.doi.org/10.6018/red/45/alba.

Guzmán-Cedillo, Y., & Flores, R. (2020). La competencia argumentativa como meta en contextos educativos. Revisión de la literatura. Educar, 56(1), 15-34. https://doi.org/10.5565/rev/educar.1009.

Henriques, A., & Martins, M. (2022). Mathematical reasoning in linear systems learning: A higher education exploratory teaching experiment with prospective teachers. Avances de Investigación en Educación Matemática, 21, 65-85. http://dx.doi.org/10.35763/aiem21.4238.

Komatsu, K., & Jones, K. (2022). Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning. Educational Studies in Mathematics, 109(3), 567-591. https://doi.org/10.1007/s10649-021-10086-5.

Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM, 43(3), 325-336. http://dx.doi.org/10.1007/s11858-011-0329-2.

Lincoln, Y. S., Guba, E. G., & Pilotta, J. J. (1985). Naturalistic Inquiry. Beverly Hills, CA: Sage. http://dx.doi.org/10.1016/0147-1767(85)90062-8.

Mendoza, S. M., Ramírez, P., & Serpa, A. M. (2021). Errores y dificultades vinculadas al razonamiento cuantitativo entre estudiantes de nuevo ingreso en la carrera de ingeniería. Revista Boletín Redipe, 10(11), 379-399. https://doi.org/10.36260/rbr.v10i11.1545.

Molina, M., Castro, E., Molina, J. L., & Castro, E. (2011). Un acercamiento a la investigación de diseño a través de los experimentos de enseñanza. Enseñanza de las Ciencias: Revista de Investigación y Experiencias Didácticas, 29(1), 75-88.

Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational Studies in Mathematics, 67, 37-58 https://doi.org/10.1007/s10649-007-9083-3.

Romero, L. C., & Camargo, L. (2022). Potencial del modelo de tareas tecno-pedagógicas para promover procesos de conjeturación en estudiantes universitarios. PNA, 16(2), 141-166. https://doi.org/10.30827/pna.v16i2.21334.

Rangel-Arzola, J. E., & Ortiz-Buitrago, J. (2022). Modelización matemática, programación lineal y vídeos en la formación de ingenieros. Matemáticas, Educación y Sociedad, 5(3), 40-59.

Sharhorodska, O., Alvarez, A. P., & Alpaca, N. B. (2018). Las matemáticas y la formación del ingeniero, como una relación simbiótica. Revista Referencia Pedagógica, 6(2), 175-189.

Shenton, A. (2004). Strategies for ensuring trustworthiness in qualitative research projects. Education for Information, 22(2), 63-75. https://doi.org/10.3233/EFI-2004-22201.

Solar, H., Ortiz, A., Aravena, M., & Goizueta, M. (2023). Relaciones entre la argumentación y la modelación en el aula de matemáticas. Bolema: Boletim de Educação Matemática, 37, 500-531. http://dx.doi.org/10.1590/1980-4415v37n76a07.

Stahl, N., & King, J. (2020). Expanding approaches for research: Understanding and using trustworthiness in qualitative research. Journal of Developmental Education, 44(1), 26-28. https://www.jstor.org/stable/45381095.

Torres, D., & Montiel, G. (2020). La desarticulación matemática en Ingeniería. Una alternativa para su estudio y atención, desde la Matemática Educativa. Nóesis. Revista de ciencias sociales, 29(58-1), 24-55. https://doi.org/10.20983/noesis.2020.3.2.

Trench, M., Oberholzer, N., & Minervino, R. (2009). Dissolving the analogical paradox: Retrieval under a production paradigm is highly constrained by superficial similarity. In In B. Kokinov, K. Holyoak & D. Gentner (Eds), New Frontiers in Analogy Research (pp. 443-452). Sofia: NBU Series in Cognitive Science.

Triantafillou, C., Psycharis, G., Potari, D., Bakogianni, D., & Spiliotopoulou, V. (2021). Teacher educators’ activity aiming to support inquiry through mathematics and science teacher collaboration. International Journal of Science and Mathematics Education, 19(1), 21-37. https://doi.org/10.1007/s10763-021-10153-6.

Vos, P. (2015). Authenticity in extra-curricular Mathematics activities: Researching authenticity as a social construct. In G. Stillman, W. Blum & M. Salett Biembengut (Eds), Mathematical modelling in education research and practice. International perspectives on the teaching and learning of mathematical modelling (pp. 105-113). Springer, Cham. https://doi.org/10.1007/978-3-319-18272-8_8.

Wake, G. (2014). Making sense of and with mathematics: The interface between academic mathematics and mathematics in practice. Educational Studies in Mathematics, 86(2), 271-290. https://doi.org/10.1007/s10649-014-9540-8.

Wake, G. (2015). Preparing for workplace numeracy: A modelling perspective. ZDM, 47(4), 675-689. https://doi.org/10.1007/s11858-015-0704-5.

Wardani, P. L., Dafik, & Tirta, I. M. (2019). The analysis of research-based learning implementation in improving students conjecturing skills in solving local antimagic vertex dynamic coloring. Journal of Physics: Conference Series, 1211(1). http://dx.doi.org/10.1088/1742-6596/1211/1/012090.


DOI: https://doi.org/10.26220/rev.5424

View Counter: Abstract | 183 | times, and PDF | 76 | times



Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Re S M ICT E | ISSN: 1792-3999 (electronic), 1791-261X (print) | Laboratory of Didactics of Sciences, Mathematics and ICT, Department of Educational Sciences and Early Childhood Education - University of Patras.

Pasithee | Library & Information Center | University of Patras