Mathematics teachers’ conceptual knowledge about and for teaching quadrilaterals
DOI:
https://doi.org/10.37001/ripem.v13i2.3395Palavras-chave:
Mathematics Teaching, Geometry, Concept, Exploratory ResearchResumo
The aim of the article is to analyze the conceptual knowledge of a group of mathematics teachers about quadrilaterals and the way they practice their teaching. We conducted exploratory research with 23 teachers who answered an online questionnaire, whose results we analyzed descriptively and categorically. The best-known characteristic of quadrilaterals was that it is a plane figure and the least known was that it is a simple figure. Notable quadrilaterals were mentioned more than irregular shapes. In addition, the presence of irrelevant attributes such as thick line and being rotated made it difficult to recognize some figures. In teaching quadrilaterals (n = 17), four teachers would act as expositors of their ideas. Two teachers would not address the non-examples. Eleven teachers would deal with examples and non-examples. In conclusion, training is needed to understand other examples, non-examples and irrelevant attributes to teach in a way that promotes conceptual development.
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Aydin, U. (2018). Conceptual and procedural angle knowledge: do gender and grade level make a difference? International Journal for Mathematics Teaching and Learning, 19(1), 22-46.
Ball, D. L.; Thames, M. H. & Phelps, G. (2008). Content Knowledge for Teaching. Journal of Teacher Education, 59(5), 389-407.
Bogdan, R.; Biklen, S. (1994). Investigação Qualitativa em Educação. Uma introdução à teoria e aos métodos. Translation by M. J. Alvarez; S. B. Santos & T. M. Baptista. Porto: Porto Editora.
Castilho, G. R.& Proença, M. C. (2018). Análise do conhecimento de licenciandos em matemática sobre o conceito e o ensino de polígono. Revista Prática Docente, 3(1), 32-49.
Clements, D. H.& Battista, M. T. (1992). Geometry and spatial reasoning. In: D. A. Grouws(Ed.). Handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics. (pp. 420-464). New York: Macmillan.
Coll, C.& Valls, E. (1998). A aprendizagem e o ensino dos procedimentos. In: C. Coll; J. I. Pozo; B. Sarabia & E. Valls (Org.). Os conteúdos na reforma: ensino e aprendizagem de conceitos, procedimentos e atitudes. Translation by B. A. Neves (pp. 73-118). Porto Alegre: Artes Médicas.
Dreyfus, T. (1991). Advanced mathematical thinking processes. In: D. Tall (Ed.). Advanced mathematical thinking. (pp. 25-41). Dordrecht: Kluwer.
Fernández-Millán, E. & Molina, M. (2017). Secondary students’ implicit conceptual knowledge of algebraic symbolism: an exploratory study through problem posing. International Electronic Journal of Mathematics Education, 12(3), 799-826.
Fernández-Millán, E. & Molina, M. (2018). Ejemplos y definiciones de ecuaciones: una ventana haciaelconocimiento conceptual de estudiantes de secundaria. PNA, 12(3), 147-172.
Gil. A. C. (2012). Métodos e técnicas de pesquisa social. 6. ed. São Paulo: Atlas.
Gonçalves, B. M.&Proença, M. C. (2020). Análise dos conhecimentos conceitual e procedimental de alunos do primeiro ano do ensino médio sobre equação do 2.º grau. Revista Sergipana de Matemática e EducaçãoMatemática, 5(2), 209-228.
Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis. In: J. Hiebert (Ed.). Conceptual and procedural knowledge: the case of mathematics. (pp. 1-27). Hillsdale, NJ: Erlbaum.
Hoffer, A. (1983). Van Hiele-based research. In: R. Lesh & M. Landau (Eds.). Acquisition of mathematics concepts and processes. (pp. 205-227). New York: Academic Press.
Klausmeier, H. J. & Goodwin, W. (1977). Manual de Psicologia Educacional: aprendizagem e capacidades humanas. Translation by M. C. T. A. Abreu. São Paulo: Harper & Row.
Liang, B. & Castillo-Garsow, C. (2020). Undergraduate Students’ meanings for central angle and inscribed angle. The Mathematics Educator, 29(1), 53–84.
Maia, E. J. & Proença, M. C. (2016). A resolução de problemas no ensino da geometria: dificuldades e limites de graduandos de um curso de pedagogia. Revista Eletrônica de EducaçãoMatemática, 11(2), 402-417.
Pereira, M. C. G. & Proença, M. C. (2019). O conceito de quadriláteros: análise doconhecimento de quatro alunos do sétimo ano do ensino fundamental. Educação Matemática em Revista, 24(62), 108-124.
Pozo, J. I. (1998). A aprendizagem e o ensino de fatos e conceitos. In: C. Coll;J. I. Pozo;B. Sarabia & E. Valls (Orgs.). Os conteúdos na reforma: ensino e aprendizagem de conceitos, procedimentos e atitudes. Translation by B. A. Neves. (pp. 17-71). Porto Alegre: Artes Médicas.
Proença, M. C.; Maia-Afonso, E. J.; Travassos, W. B. & Castilho, G. R. (2020). Resolução de Problemas de Matemática: análise das dificuldades de alunos do 9.º ano do ensino fundamental. Amazônia: Revista de Educação em Ciências e Matemáticas, 16(36), 224-243.
Proença, M. C. & Pirola, N. A. (2011). O conhecimento de polígonos e poliedros: uma análise do desempenho de alunos do ensino médio em exemplos e não-exemplos. Ciência & Educação, 17(1), 199-217.
Proença, M. C. & Pirola, N. A. (2009). Um estudo sobre o desempenho e as dificuldades
apresentadas por alunos do ensino médio na identificação de atributos definidores de
polígonos. Zetetiké, 17(31), 11-45.
Rittle-Johnson, B. & Schneider, M. (2014). Developing conceptual and procedural knowledge of mathematics. In: R. C. Kadosh & A. Dowker (Eds.). Oxford handbook of numerical cognition. (pp. 1118–1134). Oxford, UK: Oxford University Press.
Rittle-Johnson, B.; Schneider, M. & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587–597.
Scheibling-Sève, C.; Pasquinelli, E. & Sander, E. (2020). Assessing conceptual knowledge through solving arithmetic word problems. Educational Studies in Mathematics, 103(3), 293-311.
Schoenfeld, A. H. (1986). On having and using geometric knowledge. In: J. Hiebert (Ed.). Conceptual and procedural knowledge: the case of mathematics. (pp. 225-264). Hillsdale, NJ: Erlbaum.
Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 04-14.
Skemp, R. R. (1971). The psychology of learning mathematics. Middlesex, England: Penguin.
Steele, M. D. (2013). Exploring the mathematical knowledge for teaching geometry and measurement through the design and use of rich assessment tasks. Journal of Mathematics Teacher Education, 16(4), 245-268.
Sunzuma G. & Maharaj A. (2019). In-service Teachers’ geometry content knowledge: implications for how geometry is taught in teacher training institutions. International Electronic Journal of Mathematics Education, 14(3), 633-646.
Yurniwati, Y. & Soleh, D. A. (2019). Geometric conceptual and procedural knowledge of prospective teachers. International Journal of Education and Pedagogy, 1(2), 108-117.
Zabala, A. (1998). A prática educativa: como ensinar. Translation by E. F. F. Rosa. Porto alegre: ArtMed.
Zuya, H. E. (2017). Prospective Teachers’ conceptual and procedural knowledge in mathematics: the case of algebra. American Journal of Educational Research, 5(3), 310-315.
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