Progressive mathematics of functions in secondary school students using a free-fall activity

Rosa Isela González-Polo; Apolo Castaneda

doi:10.29333/iejme/14108

Full Text (PDF)

Rosa Isela González-Polo ¹ , Apolo Castaneda ² ^*

More Detail

¹ Universidad Autónoma del Estado de México, Toluca, MEXICO² Instituto Politécnico Nacional, Mexico City, MEXICO^* Corresponding Author

Abstract

This article aims to analyze the process of the progressive mathematization of the concept of the function by secondary school students through the resolution of a free fall situation. A free-fall mathematical situation was designed and experimented using the Tracker software to obtain movement data. Worksheets and conversations were collected between students and the teacher, and experiments and class discussions were filmed. The analysis consisted of identifying the development from informal strategies associated with the context of the problem to formal procedures. The results show that the process brings meanings to mathematical ideas such as variation, variables, and the relationship between variables, allows coordination and transition between representations and contributes to the learning of functions as a representation of the variation of physical phenomena.

Keywords

progressive mathematization
functions
free fall
software

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 19, Issue 1, February 2024, Article No: em0765

https://doi.org/10.29333/iejme/14108

Publication date: 05 Jan 2024

Article Views: 934

Article Downloads: 940

Open Access References How to cite this article

References

Arzarello, F., & Robutti, O. (2004). Introduction. Approaching functions through motion experiments. Educational Studies in Mathematics, 57(3), 305-308.
Best, M., & Bikner-Ahsbahs, A. (2017). The function concept at the transition to upper secondary school level: Tasks for a situation of change. ZDM-Mathematics Education, 49(6), 865-880. https://doi.org/10.1007/s11858-017-0880-6
Biehler, R. (2005). Reconstruction of meaning as a didactical task: The concept of function as an example. In J. Kilpatrick, C. Hoyles, O. Skovsmose, & P. Valero (Eds.), Meaning in mathematics education (pp. 61-81). Springer. https://doi.org/10.1007/0-387-24040-3_5
Breidenbach, D., Hawks, J., Nichols, D., & Dubinsky, E. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23(3), 247-285. https://doi.org/10.1007/BF02309532
Bressan, A., Gallego, M., Perez, S., & Zolkower, Z. (2016). La educación matemática realista. Bases teóricas [Realistic mathematics education. Theoretical bases]. Enero 2016. https://documen.site/download/educacion-matematica-realista-bases-teoricas_pdf
Chinnappan, M., & Thomas, M. (2003). Teachers’ function schemas and their role in modelling. Mathematics Education Research Journal, 15(2), 151-170. https://doi.org/10.1007/BF03217376
Clement, J. (1989). The concept of variation and misconceptions in Cartesian graphing. Focus on Learning Problems in Mathematics, 11(1-2), 77-87.
de L’Hôpital, G. F. A. M. (1768). Analyse des infiniment petits pour l’intelligence des lignes courbes ... suivie d’un nouveau commentaire pour l’intelligence des endroits les plus difficiles de cet ouvrage [Analysis of the infinitely small for the intelligence of curved lines ... followed by a new commentary for the intelligence of the most difficult places in this work]. Chez la Veuve Girard & François.
Doorman, M., Drijvers, P., Gravameijer, K., Boon, P., & Reed, H. (2012). Tool use and the development of the function concept: From repeated calculations to functional thinking. International Journal of Science and Mathematics Education, 10(6), 1243-1267. https://doi.org/10.1007/s10763-012-9329-0
Duval, R. (2006). Cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1-2), 103-131. https://doi.org/10.1007/s10649-006-0400-z
Eisenberg, T. (2002). Functions and associated learning difficulties. In D. Tall (Ed.), Advanced mathematical thinking (pp. 140-152). Springer. https://doi.org/10.1007/0-306-47203-1_9
Falcade, R., Laborde, C., & Mariotti, M. A. (2007). Approaching functions: Cabri tools as instruments of semiotic mediation. Educational Studies in Mathematics, 66(3), 317-333. https://doi.org/10.1007/s10649-006-9072-y
Fischbein, E. (2002). Intuition in science and mathematics: An educational approach. Kluwer Academic Publisher. https://doi.org/10.1007/0-306-47237-6
Freudenthal, H. (2002). Revisiting mathematics education–China lectures. Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47202-3
Gravemeijer, K. (1994). Developing realistic mathematics education. CD-β Press/Freudenthal Institute, Utrecht University. https://www.fisme.science.uu.nl/publicaties/literatuur/1994_gravemeijer_dissertation_0_222.pdf
Gravemeijer, K. (2007). Emergent modelling as a precursor to mathematical modelling. In W. Blum, P. L. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 137-144). Springer. https://doi.org/10.1007/978-0-387-29822-1_12
Hazzan, O., & Goldenberg, E. P. (1997). Students’ understanding of the notion of function in dynamic geometry environments. International Journal of Computers for Mathematical Learning, 1(3), 263-291. https://doi.org/10.1007/BF00182618
Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36(4), 20-32. https://doi.org/10.1016/j.jmathb.2014.08.003
Kaur, B., Wong, L. F., & Govindani, S. N. (2020). Graphing linear equations–A comparison of the opportunity-to-learn in textbooks using the Singapore and the Dutch approaches to teaching equations. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics visions on and experiences with realistic mathematics education (pp. 97-111). Springer. https://doi.org/10.1007/978-3-030-20223-1_7
Kjeldsen, T. H., & Lützen, J. (2015). Interactions between mathematics and physics: The history of the concept of function–Teaching with and about nature of mathematics. Science & Education, 24(5-6), 543-559. https://doi.org/10.1007/s11191-015-9746-x
Michelsen, C. (2006). Functions: A modelling tool in mathematics and science. ZDM, 38(3), 269-280. https://doi.org/10.1007/BF02652810
Niss, M. A. (2014). Functions learning and teaching. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 238-241). Springer. https://doi.org/10.1007/978-94-007-4978-8_96
Ortega, M., Puig, L., & Albarracin, L. (2019). The influence of technology on the mathematical modelling of physical phenomena. In G. A. Stillman, & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 161-177). Springer. https://doi.org/10.1007/978-3-030-14931-4_9
Sajka, M. (2003). A secondary school student’s understanding of the concept of function: A case study. Educational Studies in Mathematics, 53(3), 229-254. https://doi.org/10.1023/A:1026033415747
Scherer, P. (2020). Low achievers in mathematics Ideas from the Netherlands for developing a competence-oriented view. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics visions on and experiences with realistic mathematics education (pp. 113-132). Springer. https://doi.org/10.1007/978-3-030-20223-1_8
Selter, C., & Walter, D. (2020). Supporting mathematical learning processes by means of mathematics conferences and mathematics language tools. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics visions on and experiences with realistic mathematics education (pp. 229-254). Springer. https://doi.org/10.1007/978-3-030-20223-1_13
SEP. (1999). Fichero de actividades didácticas matemáticas. Educación secundaria [File of mathematical teaching activities. Secondary education]. Secretaría de Educación Pública [Secretary of Public Education].
SEP. (2017). Aprendizajes clave para la educación integral [Key learnings for comprehensive education]. Secretaría de Educación Pública [Secretary of Public Education].
Streefland, L. (1990). Realistic Mathematics Education (RME). What does it mean? In K. Gravemeijer, M. Van den Heuvel-Panhuizen, & L. Streefland (Eds.), Contexts, free productions, tests, and geometry in Realistic Mathematics Education (pp. 1-9). Utrecht University, Freudenthal Institute.
Sun, X., & He, W. (2020). Realistic mathematics education in the Chinese context–Some personal reflection. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics visions on and experiences with realistic mathematics education (pp. 167-188). Springer. https://doi.org/10.1007/978-3-030-20223-1_10
Van Den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9-35. https://doi.org/10.1023/B:EDUC.0000005212.03219.dc
Van Den Heuvel-Panhuizen, M. (2020). Seen through other eyes–Opening up new vistas in realistic mathematics education through visions and experiences from other countries. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics visions on and experiences with realistic mathematics education (pp. 1-20). Springer. https://doi.org/10.1007/978-3-030-20223-1_1
Van Den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_170
Wittmann, E. C. (2020). The impact of Hans Freudenthal and the Freudenthal Institute on the project mathe 2000. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands didactics of mathematics visions on and experiences with realistic mahematics education (pp. 63-69). https://doi.org/10.1007/978-3-030-20223-1_4

How to cite this article

APA

González-Polo, R. I., & Castaneda, A. (2024). Progressive mathematics of functions in secondary school students using a free-fall activity. International Electronic Journal of Mathematics Education, 19(1), em0765. https://doi.org/10.29333/iejme/14108

Vancouver

González-Polo RI, Castaneda A. Progressive mathematics of functions in secondary school students using a free-fall activity. INT ELECT J MATH ED. 2024;19(1):em0765. https://doi.org/10.29333/iejme/14108

AMA

González-Polo RI, Castaneda A. Progressive mathematics of functions in secondary school students using a free-fall activity. INT ELECT J MATH ED. 2024;19(1), em0765. https://doi.org/10.29333/iejme/14108

Chicago

González-Polo, Rosa Isela, and Apolo Castaneda. "Progressive mathematics of functions in secondary school students using a free-fall activity". International Electronic Journal of Mathematics Education 2024 19 no. 1 (2024): em0765. https://doi.org/10.29333/iejme/14108

Harvard

González-Polo, R. I., and Castaneda, A. (2024). Progressive mathematics of functions in secondary school students using a free-fall activity. International Electronic Journal of Mathematics Education, 19(1), em0765. https://doi.org/10.29333/iejme/14108

MLA

González-Polo, Rosa Isela et al. "Progressive mathematics of functions in secondary school students using a free-fall activity". International Electronic Journal of Mathematics Education, vol. 19, no. 1, 2024, em0765. https://doi.org/10.29333/iejme/14108