Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function
Öz
This study investigates the praxeologies teachers use about the inverse function in the teaching process when the curriculum is changed. A case study, one of the qualitative research methods, was used in the study. The participants of the study were three experienced mathematics teachers. The data were collected by recording the teaching process of the teachers with a video camera and a voice recorder. The praxeological analysis method of the Anthropological Theory of Didactics (ATD) was used in the data analysis. The findings of the study show that teachers use two different praxeologies in the inverse function. The first one is praxeology based on informal mapping with the effect of the dominant definition of the concept of function in the curriculum, and this praxeology was used to introduce the concept of inverse function. The other praxeology, which shows the monoid structure more clearly, emerged due to both a necessity and the necessity to exhibit an approach appropriate to the curriculum in more complex tasks and was shaped as a mixed praxeology. It was determined that teachers did not structure both praxeologies well and made sudden transitions from one praxeology to another.
Anahtar Kelimeler
Anthropological theory of didactics, praxeology, teachers, inverse function, curriculum
Destekleyen Kurum
Anadolu University
Proje Numarası
1408E364
Teşekkür
This work has been supported by Anadolu University Scientific Research Projects Coordination Unit under grant number 1408E364. This article is extracted from my doctorate dissertation entitled “Ecological problems related the function topic in mathematics curriculum (2013) and teachers' praxeology”, supervised by Prof. Dr. Abdulkadir Erdoğan (Ph.D. Dissertation, Anadolu University, Eskişehir, Türkiye, 2018).
Kaynakça
- Artigue, M., & Winsløw, C. (2010). International comparative studies on mathematics education: A viewpoint from the anthropological theory of didactics. Recherches en didactiques des mathématiques, 30(1), 47-82.
- Barbe´, J., Bosch, M., Espinoza, L., & Gascón, J. (2005). Didactic restrictions on the teacher’s practice: The case of limits of functions in Spanish high schools. Educational Studies in Mathematics, 59, 235–268. https://doi.org/10.1007/0-387-30451-7_9
- Barquero, B., Jessen, B.E., Ruiz-Hidalgo, J.F., & Goldin, J. (2023). What theories and methodologies are appropriate for studying phenomena related to mathematics curriculum reforms?. In Y. Shimizu, R. Vithal, (eds.) Mathematics Curriculum Reforms Around the World (pp. 193-217). New ICMI Study Series. Cham: Springer.
- Bosch, M. (2015). Doing research within the anthropological theory of the didactic: The case of school algebra. In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 51–69). Springer.
- Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri [Scientific research methods]. Ankara: Pegem Akademi.
- Cha, I. S. (1999). Mathematical and pedagogical discussions of the function concept. Research in Mathematical Education, 3(1), 35-56.
- Chevallard, Y. (1997). Familière et problématique, la figure du professeur. Recherches en Didactique Des Mathématiques, 17(3), 17–54.
- Chevallard, Y. (1998) Analyse des pratiques enseignantes et didactique des mathématiques: L’approche anthropologique. Recherches en Didactique des Mathématiques, 19(2), 221-266.
- Chevallard, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Ed.), Proceedings of the 4th Conference of the European Society for Research in Mathematics Education (pp. 21–30). Fundemi IQS.
- Chevallard, Y. (2007). Readjusting didactics to a changing epistemology. European Educational Research Journal, 6(2), 131-134.
