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Abstract

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the Onto-semiotic Approach. The methodology was qualitative-descriptive where data was collected through interviews based on a task. Subsequently, following the joint analysis method of both theories, the mathematical activity of the participants when they solved the task was analyzed. The results show that, teacher and students established a system of connections of feature type, different representations, meanings, part-whole, procedural and implications in terms of practices, processes, objects, and semiotic functions that relate them. However, some students presented difficulties caused by some incorrect mathematical connection such as stating that the maximum height of the projectile is the time obtained with the critical number, errors in performing arithmetic calculations when evaluating the function, graphically representing the quadratic function as a straight line and use the general formula in an inappropriate way that prevents the procedural connection from being made.

Keywords

Derivative Mathematical Connections Mathematics Education Onto-Semiotic Approach Projectile

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Rodríguez-Nieto, C. A., Font, V. ., Rodríguez-Vásquez, F. M. ., & Pino-Fan, L. R. . (2023). Onto-semiotic analysis of one teacher’s and university students’ mathematical connections when problem-solving about launching a projectile. Journal on Mathematics Education, 14(3), 563–584. https://doi.org/10.22342/jme.v14i3.pp563-584
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References

  1. Amaya, T. (2020). Evaluación de la faceta epistémica del conocimiento didáctico-matemático de futuros profesores de matemáticas en el desarrollo de una clase utilizando funciones. Bolema: Mathematics Education Bulletin, 34, 110-131. https://doi.org/10.1590/1980-4415v34n66a06
  2. Antonio, R., Escudero, D. I., & Flores, E. (2019). An introduction to the concept of derivative in high school students. Educación matemática, 31(1), 258-280. https://doi.org/10.24844/em3101.10
  3. Arenas-Peñaloza, J. A., & Rodríguez-Vásquez, F. M. (2022). Understanding ratio through the Pirie-Kieren model. Acta Scientiae, 24(4), 24-56. https://doi.org/10.17648/acta.scientiae.6826
  4. Berry, J., & Nyman, M. (2003). Promoting students’ graphical understanding of the calculus. The Journal of Mathematical Behavior, 22(4), 479–495. https://doi.org/10.1016/j.jmathb.2003.09.006
  5. Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
  6. Businskas, A. M. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. Unpublished PhD Thesis. Simon Fraser University. Canada.
  7. Campo-Meneses, K. G., Font, V., García-García, J., & Sánchez, A. (2021). Mathematical connections activated in high school students’ practice solving tasks on the exponential and logarithmic functions. EURASIA Journal of Mathematics, Science and Technology Education, 17(9), em1998. https://doi.org/10.29333/ejmste/11126
  8. Campo-Meneses, K., & García-García, J. (2020). Explorando las conexiones matemáticas asociadas a la función exponencial y logarítmica en estudiantes universitarios colombianos. Revista Educación Matemática, 32(3), 209-240. https://doi.org/10.24844/em3203.08
  9. Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education. London and New York: Routledge. https://doi.org/10.4324/9780203224342
  10. Coxford, A.F. (1995). The case for connections. In P. A. House & A.F. Coxford (Eds.), Connecting mathematics across the curriculum. Reston, VA: National Council of Teachers of Mathematics.
  11. Dolores-Flores, C., & García-García, J. (2017). Conexiones Intramatemáticas y Extramatemáticas que se producen al Resolver Problemas de Cálculo en Contexto: un Estudio de Casos en el Nivel Superior. Boletim de Educação Matemática, 31(57), 158–180. https://doi.org/10.1590/1980-4415v31n57a08
  12. Dolores-Flores, C., Rivera-López, M. I., & García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematics Education in Science and Technology, 50(3), 369–389. https://doi.org/10.1080/0020739X.2018.1507050
  13. Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (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
  14. Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2013). Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry. School Science and Mathematics, 113(3), 120–134. https://doi.org/10.1111/ssm.12009
  15. Evitts, T. (2004). Investigating the mathematical connections that preservice teachers use and develop while solving problems from reform curricula. (Unpublished doctoral dissertation). Pennsylvania State University College of Education. EE. UU.
  16. Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1), 97–124. https://doi.org/10.1007/s10649-012-9411-0
  17. Font, V., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educational Studies in Mathematics, 91(1), 107-122. https://doi.org/10.1007/s10649-015-9639-6
  18. Frías, A., & Castro, E. (2007). Influencia del número de conexiones en la representación simbólica de problemas aritméticos de dos pasos. PNA, 2(1), 29-41. https://doi.org/10.30827/pna.v2i1.6203
  19. Fuentealba, C., Badillo, E., Sánchez-Matamoros, G., & Cárcamo, A. (2018). The understanding of the derivative concept in higher education. EURASIA Journal of Mathematics, Science and Technology Education, 15(2), 1-15. https://doi.org/10.29333/ejmste/100640
  20. García-García, J., & Dolores-Flores, C. (2019). García-García, J., & Dolores-Flores, C. (2021). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1-22. https://doi.org/10.1007/s13394-019-00286-x
  21. García-García, J., & Dolores-Flores, C. (2020). 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
  22. Godino, J. D., & Batanero, C. (1994). Significado institucional y personal de los objetos matemáticos. Recherches en didactique des Mathématiques, 14(3), 325-355. https://revue-rdm.com/1994/significado-institucional-y/
  23. Godino, J. D., Batanero, C., & Font, V. (2019). The onto-semiotic approach: Implications for the prescriptive character of didactics. For the Learning of Mathematics, 39(1), 37-42.
  24. Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM-The International Journal on Mathematics Education, 39(1-2), 127-135. https://doi.org/10.1007/s11858-006-0004-1
  25. Goldin, G. A. (2000). A scientific perspective on structured, task-based interviews in mathematics education research. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 517-545). Lawrence Erlbaum Associates.
  26. Kayhan, M., Yalvaç, B., & Yeltekin, E. (2017). 8th Grade Student's Skill of Connecting Mathematics to Real Life. Journal of Education and Training Studies, 5(10), 158-166. https://doi.org/10.11114/jets.v5i10.2614
  27. Mhlolo, M.K., Venkat, H., & Schäfer, M. (2012). The nature and quality of the mathematical connections teachers make. Pythagoras, 33(1), 1-9. http://dx.doi.org/10.4102/pythagoras.v33i1.22
  28. Moon, K., Brenner, M. E., Jacob, B., & Okamoto, Y. (2013). Prospective secondary mathematics teachers’ understanding and cognitive difficulties in making connections among representations. Mathematical Thinking and Learning, 15(3), 201-227. https://doi.org/10.1080/10986065.2013.794322
  29. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
  30. Pino-Fan, L. R., Godino, J. D., & Font, V. (2015). Una propuesta para el análisis de las prácticas matemáticas de futuros profesores sobre derivadas [A proposal for the analysis of the mathematical practices of future teachers on derivatives]. Bolema. Mathematics Education Bulletin, 29(51), 60-89. https://doi.org/10.1590/1980-4415v29n51a04
  31. Pino-Fan, L. R., Godino, J. D., & Font, V. (2018). Assessing key epistemic features of didactic mathematical knowledge of prospective teachers: The case of the derivative. Journal of Mathematics Teacher Education, 21, 63-94. https://doi.org/10. 1007/s10857-016-9349-8
  32. Pino-Fan, L. R., Guzmán, I., Font, V., & Duval, R. (2017). Analysis of the underlying cognitive activity in the resolution of a task on derivability of the absolute-value function: Two theoretical perspectives. PNA, 11(2), 97-124. https://doi.org/10.30827/pna.v11i2. 6076
  33. Rodríguez-Nieto, C. A., Font, V., Borji, V., & Rodríguez-Vásquez, F. M. (2021a). Mathematical connections from a networking theory between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 53(9), 2364– 2390. https://doi.org/10.1080/0020739X.2021.1875071
  34. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., Font, V., & Morales-Carballo, A. (2021b). Una visión desde el networking TAC-EOS sobre el papel de las conexiones matemáticas en la comprensión de la derivada [A view from the TAC-EOS network on the role of mathematical connections in understanding the derivative]. Revemop, 3, e202115, 1-32. https://doi.org/10.33532/revemop. e202115
  35. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & García-García, J. (2021c). Pre-service mathematics teachers’ mathematical connections in the context of problem-solving about the derivative. Turkish Journal of Computer and Mathematics Education, 12(1), 202-220. https://doi.org/10.16949/turkbilmat.797182
  36. Rodríguez-Nieto, C. A., Rodríguez-Vásquez, F. M., & Font, V. (2022a). 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, 53(6), 1231–1256. https://doi.org/10.1080/0020739X.2020.1799254
  37. Rodríguez-Nieto, C. A., Font, V., & Rodríguez-Vásquez, F. M. (2022b). Literature review on networking of theories developed in mathematics education context. EURASIA Journal of Mathematics, Science and Technology Education, 18(11), em2179. https://doi.org/10.29333/ejmste/12513
  38. Sari, P., Hadiyan, A., & Antari, D. (2018). Exploring derivatives by means of GeoGebra. International Journal on Emerging Mathematics Education, 2(1), 65-78. http://dx.doi.org/10.12928/ijeme.v2i1.8670
  39. Sánchez-Matamoros, G., Fernández, C., & Llinares, S. (2015). Developing pre-service teachers’ noticing of students’ understanding of the derivative concept. International journal of science and mathematics education, 13(6), 1305-1329. https://doi.org/10.1007/s10763-014-9544-y
  40. Vargas, M. F., Fernández-Plaza, J. A., & Ruiz-Hidalgo, J. F. (2020). Significado de derivada en las tareas de los libros de 1° de Bachillerato [Meaning of derivative in the book tasks of 1st of “Bachillerato”]. Bolema: Mathematics Education Bulletin, 34, 911-933. https://doi.org/10.1590/1980-4415v34n68a04
  41. Yavuz-Mumcu, H. (2018). Matematiksel ilişkilendirme becerisinin kuramsal boyutta incelenmesi: türev kavramı örneği. Turkish Journal of Computer and Mathematics Education, 9(2), 211-248. https://doi.org/10.16949/turkbilmat.379891
  42. Zubillaga-Guerrero, E., Rodríguez-Vásquez, F.M., & Romero-Valencia, J. (2021). Case study on intra-mathematical connections when solving tasks associated with the classification of groups of primeorder. REDIMAT – Journal of Research in Mathematics Education, 10(3),269-295. doi: 10.17583/redimat.8794