Araştırma Makalesi
BibTex RIS Kaynak Göster

Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function

Yıl 2023, Cilt: 11 Sayı: 22, 1089 - 1112, 27.10.2023

Mustafa Gök Abdulkadir Erdoğan

https://doi.org/10.18009/jcer.1361502

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.
  • Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima journal of mathematics education, 12, 71-114. https://www.jasme.jp/hjme/download/05_Yves%20Chevallard.pdf
  • Chevallard, Y. (2022). Challenges and advances in teacher education within the ATD. In Y. Chevallard et al. (Eds.), Advances in the anthropological theory of the didactic (pp. 81-89). Springer. https://doi.org/10.1007/978-3-030-76791-4_7
  • Chevallard, Y., & Bosch, M. (2020). Didactic transposition in mathematics education. In: S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 53-61). Springer.
  • Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 38-43). Springer.
  • Erdogan, A. (2014). Conditions épistémiques de l’étude autonome des élèves relativement à l’algèbre et aux fonctions, en classe de Seconde française [Epistemological condition of the study of functions and algebra, in France]. Recherche en didactique des mathmématiques, 34(2/3), 201-238.
  • Even, R. Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21, 521–544 (1990). https://doi.org/10.1007/BF00315943
  • Fraleigh, J. B. (2014). A first course in abstract algebra (7th ed.). London: Pearson.
  • Garcia, F. J., Pérez, J. G., Higueras, L. R., & Casabó, M. B. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM, 38(3), 226-246.
  • Gellert, U., Barbé, J., & Espinoza, L. (2013). Towards a local integration of theories: Codes and praxeologies in the case of computer-based instruction. Educational Studies in Mathematics, 82, 303–321.
  • Gök, M., Erdoğan, A., & Özdemir Erdoğan, E. (2019). Transpositions of function concept in mathematics curricula and textbooks from the historical development perspective. International Journal of Instruction, 12(1), 1189-1206.
  • Ikram, M., Purwanto, Parta, I.N., & Susanto, H. (2020). Exploring the potential role of reversible reasoning: Cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591-611.
  • Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. San Francisco, CA: John Wiley & Sons.
  • Pansell, A. (2023). Mathematical knowledge for teaching as a didactic praxeology. Frontiers in Education, 8, 1-14.
  • Putra, Z. H. (2020). Didactic transposition of rational numbers: A case from a textbook analysis and prospective elementary teachers’ mathematical and didactic knowledge. Journal of Elementary Education, 13(4), 365-394.
  • Strømskag, H., & Chevallard, Y. (2023). Breaches of the didactic contract as a driving force behind learning and non-learning: A story of flaws and wants. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(1), 52-64.
  • The Ministry of National Education [MoNE]. (2005). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary school mathematics course (9th, 10th, 11th and 12th grades) curriculum]. Ankara: MoNE.
  • The Ministry of National Education [MoNE]. (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary school mathematics course (9th, 10th, 11th and 12th grades) curriculum]. Ankara: MoNE.
  • The Ministry of National Education [MoNE]. (2018). Ortaöğretim fen lisesi matematik dersi (9, 10, 11 ve 12. Sınıflar) öğretim programı [Secondary education science high school mathematics course (Grades 9, 10, 11 and 12) curriculum]. Ankara: MoNE.
  • Topphol, V. (2023). The didactic transposition of the fundamental theorem of calculus. REDIMAT – Journal of Research in Mathematics Education, 12(2), 144-172.
  • Wasserman, N. H. (2017). Making sense of abstract algebra: Exploring secondary teachers’ understandings of inverse functions in relation to its group structure. Mathematical Thinking and Learning, 19(3), 181-201.
  • Weber, K., Mejía-Ramos, J. P., Fukawa-Connelly, T., & Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. The Journal of Mathematical Behavior, 57, 100752.
  • Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263-281.

Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function

Yıl 2023, Cilt: 11 Sayı: 22, 1089 - 1112, 27.10.2023

Mustafa Gök Abdulkadir Erdoğan

https://doi.org/10.18009/jcer.1361502

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

Proje Numarası

1408E364

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.
  • Chevallard, Y. (2019). Introducing the anthropological theory of the didactic: An attempt at a principled approach. Hiroshima journal of mathematics education, 12, 71-114. https://www.jasme.jp/hjme/download/05_Yves%20Chevallard.pdf
  • Chevallard, Y. (2022). Challenges and advances in teacher education within the ATD. In Y. Chevallard et al. (Eds.), Advances in the anthropological theory of the didactic (pp. 81-89). Springer. https://doi.org/10.1007/978-3-030-76791-4_7
  • Chevallard, Y., & Bosch, M. (2020). Didactic transposition in mathematics education. In: S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 53-61). Springer.
  • Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 38-43). Springer.
  • Erdogan, A. (2014). Conditions épistémiques de l’étude autonome des élèves relativement à l’algèbre et aux fonctions, en classe de Seconde française [Epistemological condition of the study of functions and algebra, in France]. Recherche en didactique des mathmématiques, 34(2/3), 201-238.
  • Even, R. Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21, 521–544 (1990). https://doi.org/10.1007/BF00315943
  • Fraleigh, J. B. (2014). A first course in abstract algebra (7th ed.). London: Pearson.
  • Garcia, F. J., Pérez, J. G., Higueras, L. R., & Casabó, M. B. (2006). Mathematical modelling as a tool for the connection of school mathematics. ZDM, 38(3), 226-246.
  • Gellert, U., Barbé, J., & Espinoza, L. (2013). Towards a local integration of theories: Codes and praxeologies in the case of computer-based instruction. Educational Studies in Mathematics, 82, 303–321.
  • Gök, M., Erdoğan, A., & Özdemir Erdoğan, E. (2019). Transpositions of function concept in mathematics curricula and textbooks from the historical development perspective. International Journal of Instruction, 12(1), 1189-1206.
  • Ikram, M., Purwanto, Parta, I.N., & Susanto, H. (2020). Exploring the potential role of reversible reasoning: Cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591-611.
  • Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation. San Francisco, CA: John Wiley & Sons.
  • Pansell, A. (2023). Mathematical knowledge for teaching as a didactic praxeology. Frontiers in Education, 8, 1-14.
  • Putra, Z. H. (2020). Didactic transposition of rational numbers: A case from a textbook analysis and prospective elementary teachers’ mathematical and didactic knowledge. Journal of Elementary Education, 13(4), 365-394.
  • Strømskag, H., & Chevallard, Y. (2023). Breaches of the didactic contract as a driving force behind learning and non-learning: A story of flaws and wants. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(1), 52-64.
  • The Ministry of National Education [MoNE]. (2005). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary school mathematics course (9th, 10th, 11th and 12th grades) curriculum]. Ankara: MoNE.
  • The Ministry of National Education [MoNE]. (2013). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary school mathematics course (9th, 10th, 11th and 12th grades) curriculum]. Ankara: MoNE.
  • The Ministry of National Education [MoNE]. (2018). Ortaöğretim fen lisesi matematik dersi (9, 10, 11 ve 12. Sınıflar) öğretim programı [Secondary education science high school mathematics course (Grades 9, 10, 11 and 12) curriculum]. Ankara: MoNE.
  • Topphol, V. (2023). The didactic transposition of the fundamental theorem of calculus. REDIMAT – Journal of Research in Mathematics Education, 12(2), 144-172.
  • Wasserman, N. H. (2017). Making sense of abstract algebra: Exploring secondary teachers’ understandings of inverse functions in relation to its group structure. Mathematical Thinking and Learning, 19(3), 181-201.
  • Weber, K., Mejía-Ramos, J. P., Fukawa-Connelly, T., & Wasserman, N. (2020). Connecting the learning of advanced mathematics with the teaching of secondary mathematics: Inverse functions, domain restrictions, and the arcsine function. The Journal of Mathematical Behavior, 57, 100752.
  • Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers. Mathematical Thinking and Learning, 12(4), 263-281.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik Eğitimi
Bölüm Araştırma Makalesi
Yazarlar

Mustafa Gök 0000-0001-9349-4078

Abdulkadir Erdoğan 0000-0002-6553-8309

Proje Numarası 1408E364
Erken Görünüm Tarihi 25 Ekim 2023
Yayımlanma Tarihi 27 Ekim 2023
Gönderilme Tarihi 16 Eylül 2023
Kabul Tarihi 23 Ekim 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 11 Sayı: 22

Kaynak Göster

APA Gök, M., & Erdoğan, A. (2023). Didactic Praxeologies Employed by Mathematics Teachers in Teaching the Inverse Function. Journal of Computer and Education Research, 11(22), 1089-1112. https://doi.org/10.18009/jcer.1361502
 Kapak Resmi İndir

Creative Commons Lisansı


Bu eser Creative Commons Atıf 4.0 Uluslararası Lisansı ile lisanslanmıştır.


Değerli Yazarlar,

JCER dergisi 2018 yılından itibaren yayımlanacak sayılarda yazarlarından ORCID bilgilerini isteyecektir. Bu konuda hassasiyet göstermeniz önemle rica olunur.

Önemli: "Yazar adından yapılan yayın/atıf taramalarında isim benzerlikleri, soyadı değişikliği, Türkçe harf içeren isimler, farklı yazımlar, kurum değişiklikleri gibi durumlar sorun oluşturabilmektedir. Bu nedenle araştırmacıların tanımlayıcı kimlik/numara (ID) edinmeleri önem taşımaktadır. ULAKBİM TR Dizin sistemlerinde tanımlayıcı ID bilgilerine yer verilecektir.

Standardizasyonun sağlanabilmesi ve YÖK ile birlikte yürütülecek ortak çalışmalarda ORCID kullanılacağı için, TR Dizin’de yer alan veya yer almak üzere başvuran dergilerin, yazarlardan ORCID bilgilerini talep etmeleri ve dergide/makalelerde bu bilgiye yer vermeleri tavsiye edilmektedir. ORCID, Open Researcher ve Contributor ID'nin kısaltmasıdır.  ORCID, Uluslararası Standart Ad Tanımlayıcı (ISNI) olarak da bilinen ISO Standardı (ISO 27729) ile uyumlu 16 haneli bir numaralı bir URI'dir. http://orcid.org adresinden bireysel ORCID için ücretsiz kayıt oluşturabilirsiniz. "