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A Didactical Analysis of Teaching Practices Around Differentials Equations in Tunisian School Context

Received: 1 September 2021     Accepted: 22 September 2021     Published: 12 October 2021
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Abstract

The teaching of differential equations is often viewed from an interdisciplinary perspective that justifies the rationale for this notion in the secondary cycle. The history of the teaching of this notion in the Tunisian educational system shows a diversity of approaches which seem to evolve in the direction of modeling extra-mathematical situations and dialectic between semiotics registers. This research is part of the anthropological theory of didactics and analyzes the didactic transposition process developed by the Tunisian institution around differential equations over successive reforms. Three dimensions of analysis were taken into account in this study: a historical-epistemological dimension which makes it possible to identify the dynamic nature of the notion of differential equation through the stages of its constitution and to determine its meaning through the problems addressed in teaching and their development, an institutional dimension addressed by ecology and praxeology analyses based on the programs and official textbooks. Current institutional practices allow us to glimpse a dynamic at scale relating to the teaching of this notion. This aspect is nourished by sets of frameworks, flexibility between registers and interdisciplinary praxeology mobilized upstream and downstream of the work of algebraic resolution. Professional entry allows us to question the constraints for their effective implementation in classes. This dimension is analyzed from ten student notebooks considered as a first revealer of teaching practices in terms of resistance or change. This analysis of the notebooks make it possible to discover the main characteristics of the institutional relationship. The result of the analysis shows that the personal relationship of teachers perceived through the analysis of their didactic preparation with the object of knowledge differential equations, is not suitable to institutional relationship with this same object of knowledge.

Published in Science Journal of Education (Volume 9, Issue 5)
DOI 10.11648/j.sjedu.20210905.13
Page(s) 157-169
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Differential Equation, Mathematical and Didactical Praxeology, Institutional Practices, Teaching Practices

References
[1] Artaud, M. (1997). Introduction à l’approche écologique du didactique. L’écologie des organisations mathématiques et didactiques, In Bailleul et al. (eds.), Actes de la IXème Ecole d’Eté de Didactique des Mathématiques 1997, pp. 101-139. Houlgate.
[2] Artigue, M. (1989a). Une recherche d’ingénierie didactique sur l’enseignement des équations différentielles du premier cycle universitaire, Cahier du séminaire de Didactique des Maths et de l’Informatique de Grenoble, IMAG, pp. 183-209.
[3] Artigue, M. (1989b). Ingénierie didactique, Recherches en Didactique des Mathématiques, vol. 9, n°3, pp. 281-308. La pensée Sauvage. Grenoble.
[4] Assude, T. (2004). Etude du curriculum de mathématiques entre changements et résistances, Liens entre écologie et économie didactique. Actes du séminaire national de didactique des mathématiques. ARDM et IREM pp 317-334, Paris 7.
[5] Ben Nejma S. (2009). D’une réforme à ses effets sur les pratiques enseignantes: une étude de cas en algèbre dans le contexte scolaire tunisien. Thèse des universités de Paris 7 et de Tunis.
[6] Ben Nejma, S. (2010). Quel impact d’une évolution du curriculum officiel sur les pratiques enseignantes ? Etude de cas dans le contexte tunisien. Petit x, 82, 5-30.
[7] Ben Nejma, S. (2012). Pratiques enseignantes et changements curriculaires: une étude de cas en algèbre élémentaire. Dans J.-L. Dorier et S. Coutat (dir.), Enseignement des mathématiques et contrat social: enjeux et défis pour le 21e siècle. Actes du colloque EMF 2012 (p. 1133-1142). Université de Genève, Genève.
[8] Ben Nejma, S. (2020). Exploitation de l'histoire dans une analyse didactique du développement de la pensée fonctionnelle au début de l'enseignement secondaire tunisien. Revue Québécoise de didactique des mathématiques. Vol 1. pp 38-69.
[9] Bloch, I. (2000). L'enseignement de l'analyse à la charnière lycée / université: connaissances, savoirs, et conditions relatives à la validation. Thèse, Université Bordeaux 1.
[10] Chau O. et Pluvinage F (1999). Comparaison de compétences dans les approches algébriques, qualitative et informatique des équations différentielles ordinaires en première année universitaire. Recherche en didactique des mathématiques. Vol. 19, n° 2, p. 195-220.
[11] Chevallard, Y. (1998). Analyse des pratiques enseignantes et didactique des mathématiques: L’approche anthropologique. Actes de l’U. E. de la Rochelle.
[12] Chevallard, Y. (1991). La transposition didactique. Du savoir savant au savoir enseigné. Grenoble. La pensée sauvage.
[13] Chevallard, Y. (1997). Familière et problématique, la figure du professeur, Recherches en Didactique des Mathématiques 17 (3), 17-54.
[14] Chevallard, Y. (1999). Analyse des pratiques enseignantes en théorie anthropologique du didactique, Revue de didactique des mathématiques, 19 (2), 221-266. Grenoble. La pensée Sauvage.
[15] Chevallard, Y. (2002). Organiser l’étude 1. Structures et Fonctions. In J-L. Dorier& al. (eds) Actes de la 11ième Ecole d’été de didactique des mathématiques -Corps- 21-30 Août 2001. Recherches en Didactique des Mathématiques.
[16] Chaachoua, A. (1997). Fonctions du dessin dans l’enseignement de la géométrie dans l’espace. Etude d’un cas: la vie des problèmes de construction et rapports des enseignants à ces problèmes, Thèse de doctorat, Université Joseph Fourier- Grenoble.
[17] Coulange, L., Ben Nejma, S., Constantin, C. et Lenfant, (2012). Des pratiques enseignantes aux apprentissages des élèves en algèbre. Dans L, Coulange et-P Drouhard. JL, Dorieret A, Robert (dir), Enseignement de l’algèbre, Bilan et perspectives, Recherches en didactique des mathématiques-H-S (pp. 57-79). Grenoble: La Pensée Sauvage.
[18] Douday, R. (1986). Jeux de cadres et dialectique outil-objet, Recherches en Didactique des Mathématiques, vol. 7, n°2. La pensée Sauvage, Grenoble.
[19] Duval, R. (1993). Registres de représentation sémiotique et fonctionnement cognitif de la pensée, Annales de Didactique et de Sciences Cognitive, n°5, pp. 37-65. IREM de Strasbourg.
[20] Jabrane, A (2019). Une élude didactique de l’évolution de l’enseignement des équations différentielles en terminale scientifique et son impact sur les pratiques enseignantes dans le contexte tunisien. Mémoire de master de recherche en didactique des mathématiques-ISEFC-UVT.
[21] Lacasta, E. (1995). Les graphiques cartésiens de fonctions dans l'enseignement secondaire des mathématiques: illusions et contrôles, thèse de doctorat. Université de Bordeaux 1.
[22] Ravel, L. (2003). Les programmes à la classe: Etude de la transposition didactique interne, thèse de doctorat. Université Joseph Fourrier, Grenoble.
[23] Rajonson, L. (1988). L’analyser écologique des conditions et des contraintes dans l’étude des phénomènes de transposition didactique: trois études de cas. Thèse de troisième cycle, Université d’Aix-Marseille II.
[24] Saglam, A. (2004). Les équations différentielles en mathématiques et en physique: étude des conditions de leur enseignement et caractérisation des rapports personnels des étudiants de première année d’université à cet objet de savoir, Thèse de doctorat, Université Joseph Fourier, Grenoble I.
[25] Wanner, G. (1988) Les Équations différentielles ont 350 ans. L’enseignement Mathématique, 34, 365-385.
[26] Tunisian Manual. (1965), Algebra, sixth year of Secondary Education, Section: Mathematics, Volume 2, Republic of Tunisia, State Secretariat for National Education, pedagogical office Edition STD.
[27] Tunisian Manuel. (1979), Mathematics, 6th year of Secondary Education, Section: Industrial Technique, Volume 1, Republic of Tunisia, Ministry of National Education, CNP (Experimental Edition 1979).
[28] Tunisian Manuel. (1993), Mathematics, 7th year of Secondary Education, Section: Math-Sciences, Math-Technique, Republic of Tunisia, Ministry of Education and Science CNP, code 222734.
[29] Manuel Tunisien. (2002), Mathématiques, 7ème année de l’Enseignement Secondaire, Section: Mathématiques, Tome 1, République Tunisienne, ministère de l’éducation CNP, code 222445.
[30] Official secondary education programs. (1959), Mathematics, Republic of Tunisia, Ministry of National Education.
[31] Official secondary education curricula (1968). Mathematics, Republic of Tunisia, State Secretariat for National Education.
[32] Official secondary education programs. (1970), Mathematics, Republic of Tunisia, Ministry of Education, Youth and Sports, (Applicable from September 16, 1970).
[33] Official secondary education programs. (1982), Mathematics, Republic of Tunisia, Ministry of National Education. National Pedagogical Center (CNP).
[34] Official secondary education programs. (2004), Mathematics, Republic of Tunisia, Ministry of National Education. General Directorate of Programs and Continuing Education. https://sigmaths.net/Reader.php?var=manuels/4M_t1.pdf
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    Sonia Ben Nejma, Anis Jabrane. (2021). A Didactical Analysis of Teaching Practices Around Differentials Equations in Tunisian School Context. Science Journal of Education, 9(5), 157-169. https://doi.org/10.11648/j.sjedu.20210905.13

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    Sonia Ben Nejma; Anis Jabrane. A Didactical Analysis of Teaching Practices Around Differentials Equations in Tunisian School Context. Sci. J. Educ. 2021, 9(5), 157-169. doi: 10.11648/j.sjedu.20210905.13

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    AMA Style

    Sonia Ben Nejma, Anis Jabrane. A Didactical Analysis of Teaching Practices Around Differentials Equations in Tunisian School Context. Sci J Educ. 2021;9(5):157-169. doi: 10.11648/j.sjedu.20210905.13

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  • @article{10.11648/j.sjedu.20210905.13,
      author = {Sonia Ben Nejma and Anis Jabrane},
      title = {A Didactical Analysis of Teaching Practices Around Differentials Equations in Tunisian School Context},
      journal = {Science Journal of Education},
      volume = {9},
      number = {5},
      pages = {157-169},
      doi = {10.11648/j.sjedu.20210905.13},
      url = {https://doi.org/10.11648/j.sjedu.20210905.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjedu.20210905.13},
      abstract = {The teaching of differential equations is often viewed from an interdisciplinary perspective that justifies the rationale for this notion in the secondary cycle. The history of the teaching of this notion in the Tunisian educational system shows a diversity of approaches which seem to evolve in the direction of modeling extra-mathematical situations and dialectic between semiotics registers. This research is part of the anthropological theory of didactics and analyzes the didactic transposition process developed by the Tunisian institution around differential equations over successive reforms. Three dimensions of analysis were taken into account in this study: a historical-epistemological dimension which makes it possible to identify the dynamic nature of the notion of differential equation through the stages of its constitution and to determine its meaning through the problems addressed in teaching and their development, an institutional dimension addressed by ecology and praxeology analyses based on the programs and official textbooks. Current institutional practices allow us to glimpse a dynamic at scale relating to the teaching of this notion. This aspect is nourished by sets of frameworks, flexibility between registers and interdisciplinary praxeology mobilized upstream and downstream of the work of algebraic resolution. Professional entry allows us to question the constraints for their effective implementation in classes. This dimension is analyzed from ten student notebooks considered as a first revealer of teaching practices in terms of resistance or change. This analysis of the notebooks make it possible to discover the main characteristics of the institutional relationship. The result of the analysis shows that the personal relationship of teachers perceived through the analysis of their didactic preparation with the object of knowledge differential equations, is not suitable to institutional relationship with this same object of knowledge.},
     year = {2021}
    }
    

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    AB  - The teaching of differential equations is often viewed from an interdisciplinary perspective that justifies the rationale for this notion in the secondary cycle. The history of the teaching of this notion in the Tunisian educational system shows a diversity of approaches which seem to evolve in the direction of modeling extra-mathematical situations and dialectic between semiotics registers. This research is part of the anthropological theory of didactics and analyzes the didactic transposition process developed by the Tunisian institution around differential equations over successive reforms. Three dimensions of analysis were taken into account in this study: a historical-epistemological dimension which makes it possible to identify the dynamic nature of the notion of differential equation through the stages of its constitution and to determine its meaning through the problems addressed in teaching and their development, an institutional dimension addressed by ecology and praxeology analyses based on the programs and official textbooks. Current institutional practices allow us to glimpse a dynamic at scale relating to the teaching of this notion. This aspect is nourished by sets of frameworks, flexibility between registers and interdisciplinary praxeology mobilized upstream and downstream of the work of algebraic resolution. Professional entry allows us to question the constraints for their effective implementation in classes. This dimension is analyzed from ten student notebooks considered as a first revealer of teaching practices in terms of resistance or change. This analysis of the notebooks make it possible to discover the main characteristics of the institutional relationship. The result of the analysis shows that the personal relationship of teachers perceived through the analysis of their didactic preparation with the object of knowledge differential equations, is not suitable to institutional relationship with this same object of knowledge.
    VL  - 9
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Author Information
  • Department of Mathematics, University of Carthage, LARINA, Tunisia

  • Department of Didactic, Virtual University Tunis, Tunis, Tunisia

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