Research Article

Quadratic Functions and PhET: An Investigation from the Perspective of the Theory of Figural Concepts

Renata Teófilo de Sousa 1 * , Francisco Régis Vieira Alves 1
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1 Federal Institute of Education, Science and Technology of Ceará, BRAZIL* Corresponding Author
Contemporary Mathematics and Science Education, 3(1), 2022, ep22010, https://doi.org/10.30935/conmaths/11929
Published: 27 March 2022
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ABSTRACT

This work aims to present the results of an investigation in the teaching of quadratic function with the help of the PhET Colorado simulator, analyzed from the perspective of the theory of figural concepts in the context of hybrid teaching, using the teaching methodology flipped classroom. The research methodology used was the case study, which was developed with a group of 45 high school students from a Brazilian public school. The proposed activity was developed from the simulation called “graphing quadratics”, available in the PhET, and was developed in two stages, one in a virtual way and the other in person. The results show us the need to explore the study of the quadratic function using technology from a more dynamic perspective. We reinforce the importance of the manipulation performed in the simulator to understand the relationship between the coefficients a, b and c of the function and the behavior of its graph, being a potential resource in the learning of this subject by the students.

CITATION (APA)

de Sousa, R. T., & Alves, F. R. V. (2022). Quadratic Functions and PhET: An Investigation from the Perspective of the Theory of Figural Concepts. Contemporary Mathematics and Science Education, 3(1), ep22010. https://doi.org/10.30935/conmaths/11929

REFERENCES

  1. Alves, F. R. V., & Borges Neto, H. (2011). Efraim Fischbein’s contribution to mathematics education and teacher training. Revista Conexão, Ciência e Tecnologia [Connection, Science and Technology Magazine], 5(1), 38-54. https://doi.org/10.21439/conexoes.v5i1.441
  2. Arruda, E. P. (2020). Emergency remote education: Elements for public policies in Brazilian education in COVID-19 times. EmRede–Revista de Educação a Distância [EmRede-Journal of Distance Education], 7(1), 257-275. https://doi.org/10.53628/emrede.v7.1.621
  3. Bacich, L., Tanzi Neto, A., & Trevisani, F. M. (2015). Ensino híbrido: Personalização e tecnologia na educação [Blended learning: Personalization and technology in education]. Penso.
  4. Bardin, L. (1977). Análise de conteúdo [Content analysis]. Edições 70.
  5. Bohrer, A., & Tinti, D. S. (2021). Mapping of studies on the quadratic function in contexts of mathematics teaching and/or learning. Educação Matemática Pesquisa [Mathematics Education Research], 23(1), 201-230. https://doi.org/10.23925/1983-3156.2021v23i1p201-230
  6. Borke, M. (2021). Student teachers’ knowledge of students’ difficulties with the concept of function. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 670-695. https://doi.org/10.31129/LUMAT.9.1.1661
  7. Brito, R. G. S., Branco, M. N., & Brito, E. M. S. (2019). Student difficulty solving quadratic equation in high school: A quantitative research. Science and Knowledge in Focus, 2(1), 5-17. https://doi.org/10.18468/sc.knowl.focus.2019v2n1.p05-17
  8. Calil, A. M., Veiga, J., & Carvalho, C. V. A. (2010). GRAPHMATICA software application in the teaching of polynomial functions of a degree in 9th grade in elementary school. Revista Práxis [Praxis Magazine], II, 4, 17-27. https://doi.org/10.25119/praxis-2-4-923
  9. Celestino, K. G., & Pacheco, E. R. (2010). Observações sobre Bhaskara [Notes on Bhaskara]. In Anais do EAIC-Encontro Anual de Iniciação Científica [Anais do EAIC–Annual Scientific Initiation Meeting] (pp. 1-4). https://anais.unicentro.br/xixeaic/pdf/1576.pdf
  10. Feltes, C. M., & Puhl, C. S. (2016). Graph of the quadratic function: A proposal for potentially significant education. Scientia cum Industria [Knowledge with Industries], 4(4), 202-206. https://doi.org/10.18226/23185279.v4iss4p202
  11. Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139-162. https://doi.org/10.1007/BF01273689
  12. Fischbein, E. (1999). Intuitions and schemata in mathematical reasoning. Educational Studies in Mathematics, 38(11), 11-50. https://doi.org/10.1023/A:1003488222875
  13. Gil, A. C. (2002). Como elaborar projetos de pesquisa [How to design research projects]. Atlas.
  14. Gomes, I. C. P. (2020). Flipped classroom: a disruptive hybrid model? In Proceedings of CIET:EnPED:2020 - Congresso Internacional De Educação e Tecnologias e Encontro de Pesquisadores em Educação à Distância. https://cietenped.ufscar.br/submissao/index.php/2020/article/view/1382
  15. Maciel, C. R. M. (2018). A construção do conhecimento matemático com uso das TIC [The construction of mathematical knowledge with the use of ICTs] [Master’s thesis, University of Madeira].
  16. Mariotti, M. A., & Cerulli, M. (2001). Semiotic mediation for algebra teaching and learning. In Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (pp. 225-232).
  17. Ministério da Educação do Brasil. (2018). Base Nacional Comum Curricular [Curricular Common National Base]. http://basenacionalcomum.mec.gov.br/
  18. Moran, J. (2015). Mudando a educação com metodologias ativas [Changing education with active methodologies]. In C. A. Souza, & O. E. T. Morales (Eds.), Coleção mídias contemporâneas. Convergências midiáticas, educação e cidadania: Aproximações jovens [Contemporary media collection. Media convergences, education and citizenship: Approximations for young people] (pp. 15-33). UEPG/PROEX.
  19. National Institute of Educational Studies and Research Anísio Teixeira. (2019). Programa Internacional de Avaliação de Estudantes [Programme for International Student Assessment]. Brazilian Ministry of Education. http://portal.inep.gov.br/pisa
  20. Nobre, S. (2006). Equações algébricas: Uma abordagem histórica sobre o processo de resolução da equação de segundo grau [Algebraic equations: A historical approach to the process of solving the quadratic equation]. In C. C. Silva (Ed.), Estudo de história e filosofia das ciências: Subsídio para aplicação no ensino [Study of history and philosophy of science: Subsidy for application in teaching]. Ed. Livraria da Física.
  21. Oliveira, G. P., & Pereira, A. C. C. (2021). O uso pedagógico de objetos de aprendizagem na formação inicial e continuada: Construindo conceitos [The pedagogical use of learning objects in initial and continuing education: Building concepts]. In M. G. V. Silva, & C. A. S. Almeida (Eds.), Novas abordagens no ensino de ciências e matemática: soluções didáticas e tecnologias digitais [New approaches in science and mathematics teaching: Didactic solutions and digital technologies] (pp. 183-197). Imprensa Universitária UFC [UFC University Press]. http://www.repositorio.ufc.br/handle/riufc/59311
  22. Parameswaran, R. (2007). On understanding the notion of limits and infinitesimal quantities. International Journal of Science and Mathematics Education, 5, 193-216. https://doi.org/10.1007/s10763-006-9050-y
  23. Prado, E. M. S. (2014). Um novo olhar sobre o ensino de equação e função do segundo grau [A new look at teaching equation and function in high school] [Master’s thesis, State University of North Fluminense Darcy Ribeiro].
  24. Reis, E. F., & Rehfeldt, M. J. R. (2019). Software PhET and mathematics: Possibility for the teaching and learning of the multiplication. REnCiMa–Revista de Ensino de Ciências e Matemática [REnCiMa–Journal of Science and Mathematics Teaching], 10(1), 194-208. https://doi.org/10.26843/rencima.v10i1.1557
  25. Ribeiro, A. J., & Cury, H. N. (2015). Álgebra para a formação do professor [Algebra for teacher training]. Autêntica Editora [Authentic Publisher].
  26. Silva, L. G., Felício, C. M., & Ferreira, J. C. (2021). Mathematical modeling: Contributions in the teaching of quadratic function in basic and professional education. Ensino Da Matemática em Debate [Teaching Mathematics in Debate], 8(2), 138-156. https://doi.org/10.23925/2358-4122.2021v8i2p138-156
  27. Smole, K. S., & Diniz, M. I. (2013). Matemática: Ensino médio [Mathematics: High school]. Saraiva.
  28. Sousa, R. T., Alves, F. R. V., & Azevedo, I. F. (2022). A teoria dos conceitos figurais e o GeoGebra no estudo de parábolas: Uma experiência com graduandos em matemática. [The theory of figural concepts and GeoGebra in the study of parables: An experience with undergraduate students in Mathematics]. Revista Internacional de Pesquisa em Educação Matemática [International Journal of Research in Mathematics Education], 12(2), 122-143. https://doi.org/10.37001/ripem.v12i2.2893
  29. University of Colorado. (2020). PhET interactive simulations. https://phet.colorado.edu/pt_BR/
  30. Vieira, R. P. M., Alves, F. R. V., & Catarino, P. M. M. C. (2021). Teaching quadratic function through PheT Colorado and didactic engineering. Revista de Educação Matemática [Mathematics Education Magazine], 18, 1-19. https://doi.org/10.37001/remat25269062v17id522