Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory

Paulo Vitor da Silva Santiago; Francisco Régis Vieira Alves

doi:10.30935/conmaths/12112

CONTEMPORARY MATHEMATICS AND SCIENCE EDUCATION

Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory

Paulo Vitor da Silva Santiago ¹ ^* , Francisco Régis Vieira Alves ²

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Contemporary Mathematics and Science Education, Volume 3, Issue 2, Article No: ep22013

https://doi.org/10.30935/conmaths/12112

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Abstract

This research aims to present the results of a mathematical investigation in the teaching of affine function with the support of the GeoGebra software, analyzed from the perspective of the theory of conceptual fields in the context of hybrid teaching, using the teaching methodology inverted classroom changing the traditional way of teaching. The applied research methodology was the case study, which was structured with a class of 38 high school students from a Brazilian full-time public school. The proposed activity was developed from the construction called affine function (interactive activity), available on the GeoGebra platform, and was structured in two meetings, one remotely and the other in person. The results show us the need to investigate the study of the affine function using digital technology in a more dynamic design in GeoGebra.

Keywords: GeoGebra, affine function, theory of conceptual fields, digital technology, math teaching

References

Alves, F. R. V. (2019). A vertente Francesa de estudos da didática profissional: Implicações para a atividade do professor de matemática [The French branch of professional didactics studies: Implications for the activity of the mathematics teacher]. Vidya, 39(1), 255-275.
Araújo, J. R. de. (2021). Conversão entre os registros de representação gráfico e algébrico da função afim: Análise a partir da interpretação global de propriedades figurais [Conversion between graphical and algebraic representation records of the affine function: Analysis from the global interpretation of figural properties] [Master’s thesis, Universidade Federal de Pernambuco, Recife].
Bacich, L. (2016). Ensino híbrido: Relato de formação e prática docente para a personalização e o uso integrado das tecnologias digitais na educação [Blended teaching: Report of teacher training and practice for the personalization and integrated use of digital technologies in education]. In Proceedings of the Simpósio Internacional de Educação e Comunicação-SIMEDUC [International Symposium on Education and Communication].
Bardin, L. (1977). Análise de conteúdo [Content analysis]. Edições 70.
Batista, G. E., Staudt, E., Zabadal, J. R. S., & Tauceda, K. C. (2021). Resolução de problemas abertos considerando a aprendizagem significativa e teoria de campos conceituais: Uma proposta para ensinar física quântica no ensino médio [Open-ended problem solving considering meaningful learning and conceptual field theory: A proposal for teaching quantum physics in high school]. Experiências em Ensio de Ciências [Experiences in Science Teaching], 16(3).
Campos, M. S., Altoé, R. O., & Silva, L. S. F. da. (2021). Formulação de problemas de função afim: Preferências, saberes e vivências dos estudantes [Formulation of affine function problems: Preferences, knowledge and experiences of students]. Revista de Educação Matemática [Mathematics Education Magazine], 18. https://doi.org/10.37001/remat25269062v18id531
Common National Curriculum Base. (2018). Base Nacional Comum Curricular. http://basenacionalcomum.mec.gov.br/
Correa, M. M., Meneghetti, C. M. S., & Poffal, C. A. (2020). Resolução de problemas envolvendo função afim e semelhança de triângulos [Solving problems involving affine function and similarity of triangles]. Ensino da Matemática em Debate [Teaching Mathematics in Debate], 7(3), 28-46. https://doi.org/10.23925/2358-4122.2020v7i3p28-46
Eloi, Q. C., & Andrade, V. L. V. X. de. (2022). Lei de formação da função afim: um estudo à luz do contrato didático potencial [Law of formation of the affine function: a study in the light of the potential didactic contract]. Vidya, 42(1), 55-73. https://doi.org/10.37781/vidya.v42i1.3805
Gil, A. C. (2002). Como elaborar projetos de pesquisa [How to design research projects]. Atlas.
Jimenez, J. B. (2021). Uma sequência didática para o ensino e aprendizagem da função afim com o uso da robótica estrutural [A didactic sequence for the teaching and learning of affine function using structural robotics] [Master’s thesis, Universidade Católica de São Paulo].
Mello, A. L. de., & Colombo, J. A. A. (2021). Ensino de função afim através da resolução de problemas: Uma intervenção no ensino médio [Affine function teaching through problem solving: An intervention in high school]. Revista Ensin@ UFMS [Ensin@ UFMS Magazine], 2, 67-89. https://doi.org/10.55028/revens.v2iEsp..13906
National Institute of Educational Studies and Research Anísio Teixeira. (2019). Programa internacional de avaliação de estudantes [Program for international student assessment]. Brazilian Ministry of Education. http://portal.inep.gov.br/pisa
Oliveira, F. de. F. (2021). Modelagem matemática e a calculadora gráfica geogebra no estudo da função afim [Mathematical modeling and the geogebra graphing calculator in the study of the affine function] [Master’s thesis, Universidade Federal Rural do Semiárido, Mossoró].
Oliveira, S. L. de., & Romão, E. C. (2018). Sequência didática para o ensino de função afim utilizando aprendizagem baseada em projetos [Didactic sequence for teaching affine function using project-based learning]. ACTIO: Docência em Ciências [ACTIO: Teaching in Science], 3(3). https://doi.org/10.3895/actio.v3n3.7485
Oliveira, T. S. P. de., Silva, D. C. S., & Lima, A. C. D. S. (2021). O software GeoGebra no ensino da função quadrática [The GeoGebra software in teaching the quadratic function]. Boletim Cearense de Educação e História da Matemática [Ceará Bulletin of Education and History of Mathematics], 8(23), 861-876. https://doi.org/10.30938/bocehm.v8i23.4954
Ortega, M. V., Rodriguez, G. A. A., & Nieto Sanchez, Z. C. (2020). Transposición didáctica para apoyar la enseñanza de la función lineal y afín para estudiantes de cálculo usando las NTIC [Didactic transposition to support the teaching of the linear and affine function for calculus students using NICTs]. Revista Aglala [Aglala Magazine], 11(2).
Pavanelo, E., & Lima, R. (2017). Sala de aula invertida: A análise de uma experiência na disciplina de cálculo I [Flipped classroom: The analysis of an experience in calculus I]. Bolema, 31(58), 739-759. https://doi.org/10.1590/1980-4415v31n58a11
Silva, C. F. da. (2021). Ensino aprendizagem de função afim via exploração, resolução e proposição de problemas com o uso do aplicativo Desmos em contexto remote [Teaching affine function learning via exploration, problem solving and posing with the use of the Desmos application in a remote context] [PhD dissertation, Universidade Estadual da Paraíba, Campina Grande].
Silva, F. dos. S., & Pitanga, J. S. (2018). Sequência de ensino: Uma proposta de resolução de problemas na integração do software geogebra no estudo da função afim no 9º ano [Teaching sequence: A proposal to solve problems in the integration of geogebra software in the study of the affine function in the 9th grade]. Revista Sergipana de Matemática e Educação Matemática [Sergipe Magazine of Mathematics and Mathematics Education], 3(1). https://doi.org/10.34179/revisem.v3i1.7293
Vergnaud, G. (1990). La théorie des champs conceptuels [Conceptual field theory]. Recherches en Didactique des Mathématiques [Research in Didactics of Mathematics], 1(23), 133-170.
Vergnaud, G. (2009). O que é aprender [What is learning?]. In M. Bittar, & C. A. Muniz (Eds.), A aprendizagem matemática na perspectiva da teoria dos campos conceituais [Mathematical learning from the perspective of conceptual fields theory] (pp. 13-35). CRV.
Yin, R. K. (2001). Estudo de caso: Planejamento e métodos [Case study: Planning and methods]. Bookman.
Ziatdinov, R., & Valles Júnior, J. R. (2022). Síntese de modelagem, visualização e programação em GeoGebra como uma abordagem eficaz para o ensino e aprendizagem de tópicos STEM [Synthesis of modeling, visualization and programming in GeoGebra as an effective approach to teaching and learning STEM Topics]. Mathematics, 10(398). https://doi.org/10.3390/math10030398

Citation

Santiago, P. V. D. S., & Alves, F. R. V. (2022). Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory. Contemporary Mathematics and Science Education, 3(2), ep22013. https://doi.org/10.30935/conmaths/12112

Santiago, P. V. D. S., and Alves, F. R. V. (2022). Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory. Contemporary Mathematics and Science Education, 3(2), ep22013. https://doi.org/10.30935/conmaths/12112

Santiago PVDS, Alves FRV. Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory. Contemporary Mathematics and Science Education. 2022;3(2), ep22013. https://doi.org/10.30935/conmaths/12112

Santiago, Paulo Vitor da Silva, and Francisco Régis Vieira Alves. "Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory". Contemporary Mathematics and Science Education 2022 3 no. 2 (2022): ep22013. https://doi.org/10.30935/conmaths/12112

Santiago, Paulo Vitor da Silva et al. "Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory". Contemporary Mathematics and Science Education, vol. 3, no. 2, 2022, ep22013. https://doi.org/10.30935/conmaths/12112

Santiago PVDS, Alves FRV. Affine Functions Using GeoGebra: An Investigation From the Perspective of Conceptual Fields Theory. Contemporary Mathematics and Science Education. 2022;3(2):ep22013. https://doi.org/10.30935/conmaths/12112