Articulation between the Anthropological Theory of the Didactic and the theory of instrumented activity: Instrumental Approach

Authors

DOI:

https://doi.org/10.30612/tangram.v7i3.18016

Keywords:

Technology in Mathematics Education, Praxeology, Instrumental Genesis

Abstract

This theoretical article aims to discuss how the emergence and need for a theoretical basis that can look at didactic phenomena with the proliferation of digital technological resources for pedagogical use gave rise to the Instrumental Approach (IA), through the articulation between elements of the Anthropological Theory of the Didactic (ATD) and concepts of the theory of instrumented activity. To this end, focus is given to ATD, developed by Yves Chevallard and collaborators, highlighting the praxeologies, made up of (types of) tasks, (types of) technique, technology and theory. Next, are presented concepts such as artifact, instrument, instrumental genesis, instrumentation and instrumentalization, which are part of the theory of instrumented activity proposed by Rabardel. In addition, the concept of scheme is briefly discussed, as it appears in different theoretical frameworks. Finally, we present and discuss the emergence of IA, proposed mainly by Michele Artigue, highlighting the values of instrumented techniques and the differences between paper and pencil techniques and techniques used in technological artifacts. In this way, the articulation between ATD and the instrumental approach is highlighted, which allows us to understand the integration of technological resources in the school environment and how these objects influence student learning and the work of the teacher.

Downloads

Download data is not yet available.

Author Biographies

Maria Ivete Basniak, UNESPAR

Professora adjunta da Universidade Estadual do Paraná (UNESPAR) campus União da Vitória – PR – Brasil. Doutora em Educação pela Universidade Federal do Paraná.

Daysi Julissa García Cuéllar, Pontificia Universidad Católica del Perú (Perú).

Docente de pregrado y posgrado en la Pontificia Universidad Católica del Perú – Lima – Perú. Doctora en Educación Matemática por la Pontificia Universidade Católica de São Paulo.

References

Almouloud, S. A. (2007). Fundamentos da didática da matemática. Ed. UFPR.

Artigue, M. (2002). Learning Mathematics in a CAS environment: the Genesis of a reflection about Instrumention and the dialectics between technical and conceptual work. International Journal for Computers in Mathematical Learning, 7, 245-274. DOI: https://doi.org/10.1023/A:1022103903080

Artigue, M. (2007). Tecnología y enseñanza de las matemáticas: desarrollo y aportaciones de la aproximación instrumental. In: XII Conferência Inter-Americana de Educación Matemática, 13-33.

Artigue, M. (2011). Tecnología y enseñanza de las matemáticas: desarrollo y aportaciones de la aproximación instrumental. Cuadernos de Investigación y Formación en Educación Matemática, 6(8), 13-33.

Bueno, A., Basniak, M. I., & García Cuéllar, D. J. (2023). Escenario animado de Abejas en GeoGebra y la dialéctica esquema-técnica. UNIÓN – Revista Iberoamericana de Educación Matemática, 19(68), 1-21.

Bellemain, F., & Trouche, L. (2019). Compreender o trabalho do professor com os recursos de seu ensino, um questionamento didático e informático. Caminhos da Educação Matemática em Revista/Online, 9(1), 105-144.

Bittar, M. A (2017). Teoria Antropológica do Didático como ferramenta metodológica para análise de livros didáticos. Zetetiké, 25(3), 364-387. https://doi.org/10.20396/zet.v25i3.8648640. DOI: https://doi.org/10.20396/zet.v25i3.8648640

Bosch, M., & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs. Objet d’étude et problématique. Recherches en Didactique des Mathématiques, 19(1), 77-124.

Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 77- 111.

Chevallard, Y. (1999). L’Analyse des pratiques enseignantes en théorie anthropologique du didactique. Recherches en Didactique des Mathématiques, 19(2), 221-266.

Drijvers. P. et al. (2010). Integrating Technology into Mathematics Education: Theoretical Perspectives. In: C. Hoyles, & J. B. C. Lagrange (Ed.). Mathematics Education and Technology-Rethinking the Terrain, (pp. 89-133). Springer. http://dx.doi.org/10.1007%2F978-1-4419-0146-0_7.

Pedreros, M. P. (2012). Modelización de situaciones de movimiento en un sistema algebraico computacional: una aproximación desde la Teoría Antropológica de lo Didáctico y el Enfoque Instrumental. [Dissertação de Mestrado em Educación Matemática]. Universidad del Valle Instituto de Educación y Pedagogía.

Rabardel, P. (1995a). Los hombres y las tecnologías. Visión cognitiva de los instrumentos contemporáneos. Universidad Industrial de Santander.

Rabardel, P. (1995b). Qu’est-ce qu’un instrument ? Appropriation, conceptualisation, mises en situation. Les dossiers de l’ingénierie éducative, 19, 61-65.

Rabardel, P. (2002). Pessoas e tecnologia: uma abordagem cognitiva dos instrumentos contemporâneos. Université paris 8. hal-01020705.

Santos, C. M., & Freitas, J. L. M. (2013). As organizações praxeológicas no ensino de geometria: análise da prática pedagógica de uma professora indígena. XI Encontro Nacional de Educação Matemática.

Santos, C. M., & Freitas, J. L. M. (2017). Contribuições da teoria antropológica do didático na formação de professores de matemática. Revista de Educação em Ciências e Matemática, 13(27), 51-66. http://dx.doi.org/10.18542/amazrecm.v13i27.4281. DOI: https://doi.org/10.18542/amazrecm.v13i27.4281

Trouche, L. (2003). Construction et conduite des instruments dans les apprentissages mathématiques: nécessité des orchestrations. Université Paris VII. hal-00190091.

Trouche, L. (2005). An instrumental approach to mathematics learning in symbolic calculator environments. In: K. Guin, K. Ruthven, & L. Trouche (Eds.). The didactical challenge of symbolic calculators: Turning a computational device into a mathematical instrument. (pp. 137-162). Springer. DOI: https://doi.org/10.1007/0-387-23435-7_7

Trouche, L. (2016). Didactics of Mathematics: Concepts, Roots, Interactions and Dynamics from France. In: J. Monaghan, L. Trouche, & J. M. Borwein (Org). Tools and Mathematics: Instruments for Learning. (pp. 219-256). Springer. https://dx.doi.org/10.1007/978-3-319-02396-0_10. DOI: https://doi.org/10.1007/978-3-319-02396-0_10

Trouche, L. (2018a). Instrumentalization in Mathematics Education. In: S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. DOI: 10.1007/978-3-319- 77487-9_100013-1. DOI: https://doi.org/10.1007/978-3-319-77487-9_100013-1

Trouche, L. (2018b). Instrumentation in Mathematics Education. In: S. Lerman (Ed.), Encyclopedia of Mathematics Education. Springer. DOI: 10.1007/978-3-030-15789-0_80. DOI: https://doi.org/10.1007/978-3-030-15789-0_80

Vergnaud, G. (1996). A trama dos Campos Conceituais na construção dos conhecimentos. Revista do GEMPA, 4(9-19).

Vergnaud, G. (1990). La théorie des champs conceptuels. Recherche en Didactique des Mathématiques, 10(23), 133-170.

Vergnaud, G. (2009). O que é aprender? In: M. Bittar, & C. A. Muniz (Orgs.). A aprendizagem matemática na perspectiva da teoria dos campos conceituais. (pp. 13-26). Editora CRV.

Published

2024-10-01

How to Cite

Bueno, A. C., Basniak, M. I., & Cuéllar, D. J. G. (2024). Articulation between the Anthropological Theory of the Didactic and the theory of instrumented activity: Instrumental Approach. TANGRAM - Revista De Educação Matemática, 7(3), 99–118. https://doi.org/10.30612/tangram.v7i3.18016

Issue

Section

Theoretical articles