Um estudo das lentes teóricas e metodológicas envolvendo práticas pedagógicas de professores que ensinam geometria
Palavras-chave:
Wertsch. Ação mediada. Educação matemática. Pesquisa bibliográfica.
Resumo
Objetivou-se identificar e caracterizar as relações entre as lentes teóricas, as ferramentas culturais e os agentes que constituem a prática pedagógica de professores que ensinam geometria. Para tal, realizou-se uma revisão sistemática de literatura, composta por 30 artigos. Apesar de ter se constatado a presença de diversos conteúdos de geometria em variados níveis de ensino, os resultados indicaram tendências em abordar o conhecimento e a atuação docente sem a consideração de seus aspectos subjetivos, o que foi corroborado pelas ferramentas culturais, pelos instrumentos de constituição de dados utilizados e pela ocorrência de pesquisas quantitativas. Ressalta-se a necessidade de abordar mais profundamente a ação mediada que é a prática pedagógica de professores que ensinam geometria, integrando os aspectos práticos e subjetivos que a compõem, principalmente em pesquisas realizadas no Brasil.
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Referências
AARON, Wendy Rose; HERBST, Patricio Guillermo. The teacher’s perspective on the separation between conjecturing and proving in high school geometry classrooms. Journal of Mathematics Teacher Education, [S. l.], v. 22, p. 231-256, nov. 2017.
ADLER, Jill; MWADZAANGATI, Lisnet; TAKKER, Shikha. From defining as assertion to defining as explaining meaning: teachers’ learning through theory-informed lesson study. International Journal for Lesson & Learning Studies, [S. l.], v. 12, n. 1, p. 38-51, 2023.
ANDREWS, Paul; XENOFONTOS, Constantinos. Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers. Journal of Mathematics Teacher Education, [S. l.], v. 18, p. 299-325, 2015.
ARDIÇ, Mehmet Alper; ISLEYEN, Tevfik. Secondary school mathematics teachers' and students' views on computer assisted mathematics instruction in Turkey: Mathematica example. Malaysian Online Journal of Educational Technology, [S. l.], v. 5, n. 1, p. 46-64, 2017.
BALDRY, Fay et al. The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem‑solving lesson. Journal of Mathematics Teacher Education, [S. l.], v. 26, p. 129-153, 2023.
BARBOSA, Jonei Cerqueira. Abordagens teóricas e metodológicas na Educação Matemática: aproximações e distanciamentos. In: OLIVEIRA, Andréia Maria Pereira; ORTIGÃO, Maria Isabel Ramalho (org.). Abordagens teóricas e metodológicas nas pesquisas em Educação Matemática. Brasília: SBEM, 2018. p. 17-57. v. 13.
BENNING, Isaac. Enacting core practices of effective mathematics pedagogy with GeoGebra. Mathematics Teacher Education and Development, Brisbane, v. 23, n. 2, p. 102-127, 2021.
BOZKURT, Gülay; UYGAN, Candas. Lesson hiccups during the development of teaching schemes: a novice technology‑using mathematics teacher’s professional instrumental genesis of dynamic geometry. ZDM, [S. l.], v. 52, p. 1349-1363, 2020.
BRODIE, Karin; SANNI, Rasheed. We won't know it since we don't teach it: Interactions between teachers' knowledge and practice. African Journal of Research in Mathematics, Science and Technology Education, [S. l.], v. 18, n. 2, p. 188-197, 2014.
CAYTON, Charity et al. Pivotal teaching moments in technology-intensive secondary geometry classrooms. Journal of Mathematics Teacher Education, [S. l.], v. 20, p. 75-100, 2017.
CHO, Yi -An; TEE, Fui-Due. Complementing mathematics teachers’ horizon content knowledge with an elementary-on-advanced aspect. Pedagogical Research, Belgrado, v. 3, n. 1, 2018.
DIMMEL, Justin K.; HERBST, Patricio Guillermo. Proof transcription in high school geometry: A study of what teachers recognize as normative when students present proofs at the board. Educational Studies in Mathematics, [S. l.], v. 105, p. 71-89, 2020.
ERICKSON, Ander; HERBST, Patricio Guillermo. Will teachers create opportunities for discussion when teaching proof in a geometry classroom? International Journal of Science and Mathematics Education, Taiwan, v. 16, n. 1, p. 167-181, jan. 2018.
GUMIERO, Bárbara Silva; PAZUCH, Vinícius. Tecnologias digitais e o ensino de triângulos: uma revisão sistemática da literatura. Revista Brasileira de Estudos Pedagógicos, Brasília, v. 105, n. 1, p. e5980, 16 out. 2024.
HERBST, Patricio Guillermo et al. How can teaching simulations help us study at scale the tensions mathematics teachers have to manage when considering policy recommendations? Educational Studies in Mathematics, [S. l.], v. 110, p. 1-21, 2022.
HERBST, Patricio Guillermo; KO, Inah; MILEWSKI, Amanda. A heuristic approach to assess change in mathematical knowledge for teaching geometry after a practice-based professional learning intervention. Research in Mathematics Education, [S. l.], v. 22, n. 2, p. 188-208, 2020.
HERBST, Patricio Guillermo; KOSKO, Karl W. Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: a comparison of responses to animations and videos. Journal of Mathematics Teacher Education, [S. l.], v. 17, p. 515-537, 2014.
KIYICI, Ozan Deniz; DIKKARTIN ÖVEZ, Filiz Tuba. Examination of technology acceptance and TPACK competencies of mathematics teachers who are involved in distance education practices during the pandemic process. Journal of Educational Technology & Online Learning, Baliquesir, v. 4, n. 4, p. 805-821, 2021.
KOMATSU, Kotaro. Fostering empirical examination after proof construction in secondary school geometry. Educational Studies in Mathematics, [S. l.], v. 96, p. 129-144, 2017.
KUL, Umit. Influences of technology integrated professional development course on mathematics teachers. European Journal of Educational Research, Enschede, v. 7, n. 2, p. 233-243, 2018.
LENTE. In: DLP – Dicionário da Língua Portuguesa da Academia Brasileira de Letras. Rio de Janeiro: Academia Brasileira de Letras, 2025. Disponível em: https://servbib.academia.org.br/dlp/verbete.xhtml?entrada=lente. Acesso em: 9 abr. 2025.
MAVANI, Deepak; MAVANI, Beena; SCHÄFER, Marc. A case study of two selected teachers as they integrated dynamic geometry software as a visualization tool in teaching geometry. African Journal of Research in Mathematics, Science and Technology Education, [S. l.], v. 22, n. 3, p. 297-307, 2018.
MORAN, Mariana et al. O ensino da geometria: entrevista com a professora Regina Maria Pavanello. Educação Matemática em Revista, Brasília, v. 28, n. 79, p. 1-11, abr./jun. 2023.
MWADZAANGATI, Lisnet; ADLER, Jill; KAZIMA, Mercy. Mathematics mediational means and learner centeredness: Insights from ‘traditional’ malawian secondary school geometry lessons. African Journal of Research in Mathematics, Science and Technology Education, [S. l.], v. 26, n. 1, p. 1-12, 2022.
NÓVOA, António. Conhecimento profissional docente e formação de professores. Revista Brasileira de Educação, Rio de Janeiro, v. 27, p. e270129, 2022.
NURGABYL, Duisebek; SATKULOV, Baktiyar; KAGAZBAYEVA, Aspet. Formation and development of mathematical literacy in the context of evaluative – Study tasks of PISA. Journal of Mathematics Education, Irvine, v. 14, n. 4, p. 701-722, 2023.
ROBUTTI, Ornella; PRODROMOU, Theodosia; ALDON, Gilles. Teachers’ involvement in designing MERLO items: Boundary crossing. Digital Experiences in Mathematics Education, [S. l.], v. 7, p. 276-300, 2021.
SCHWARTS, Gil; KARSENTY, Ronnie. “Can this happen only in Japan?”: mathematics teachers reflect on a videotaped lesson in a cross‑cultural context. Journal of Mathematics Teacher Education, [S. l.], v. 23, p. 527-554, 2020.
SEAGO, Nanette M. et al. Impacting teachers’ understanding of geometric similarity: results from field testing of the learning and teaching geometry professional development materials. Professional Development in Education, [S. l.], v. 40, n. 4, p. 627-653, 2014.
SILVA, Elio Rubens de Freitas; SILVA, Adelmo Carvalho da. Práticas pedagógicas de professores que ensinam matemática nos anos finais do Ensino Fundamental. Revista de Ensino de Ciências e Matemática, São Paulo, v. 13, n. 2, p. 1-26, abr./jun. 2022.
SUNZUMA, Gladys et al. In-service Zimbabwean teachers' views on the utility value of diagrams in the teaching and learning of geometry. International Journal on Math, Science and Technology Education, Helsinki, v. 8, n. 1, p. 1-18, 2020.
SUNZUMA, Gladys; MAHARAJ, Aneshkumar. In-service mathematics teachers’ knowledge and awareness of ethnomathematics approaches. International Journal of Mathematical Education in Science and Technology, [S. l.], v. 52, n. 7, p. 1063-1078, 2021.
TIROSH, Dina et al. Using theories and research to analyze a case: Learning about example use. Journal of Mathematics Teacher Education, [S. l.], v. 22, p. 205-225, 2019.
WEISS, Michael; HERBST, Patricio Guillermo. The role of theory building in the teaching of secondary geometry. Educacional Studies in Mathematics, [S. l.], v. 89, p. 205-229, 2015.
WERTSCH, James V. Voices of the mind: a sociocultural approach to mediated action. Cambridge: Harvard University Press, 1991.
WERTSCH, James V. Mind as action. New York: Oxford University Press, 1998.
YILDIZ, Avni; BALTACI, Serdal. Reflections from the lesson study for the development of techno-pedagogical competencies in teaching fractal Geometry. European Journal of Educational Research, Enschede, n. 6, v. 1, p. 41-50, 2017.
ZAKARYAN, Diana; SOSA, Leticia. Conocimiento del profesor de secundaria de la práctica matemática en clases de geometría. Educación Matemática, Cidade do México, v. 33, n. 1, p. 71-97, abr. 2021.
ADLER, Jill; MWADZAANGATI, Lisnet; TAKKER, Shikha. From defining as assertion to defining as explaining meaning: teachers’ learning through theory-informed lesson study. International Journal for Lesson & Learning Studies, [S. l.], v. 12, n. 1, p. 38-51, 2023.
ANDREWS, Paul; XENOFONTOS, Constantinos. Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers. Journal of Mathematics Teacher Education, [S. l.], v. 18, p. 299-325, 2015.
ARDIÇ, Mehmet Alper; ISLEYEN, Tevfik. Secondary school mathematics teachers' and students' views on computer assisted mathematics instruction in Turkey: Mathematica example. Malaysian Online Journal of Educational Technology, [S. l.], v. 5, n. 1, p. 46-64, 2017.
BALDRY, Fay et al. The use of carefully planned board work to support the productive discussion of multiple student responses in a Japanese problem‑solving lesson. Journal of Mathematics Teacher Education, [S. l.], v. 26, p. 129-153, 2023.
BARBOSA, Jonei Cerqueira. Abordagens teóricas e metodológicas na Educação Matemática: aproximações e distanciamentos. In: OLIVEIRA, Andréia Maria Pereira; ORTIGÃO, Maria Isabel Ramalho (org.). Abordagens teóricas e metodológicas nas pesquisas em Educação Matemática. Brasília: SBEM, 2018. p. 17-57. v. 13.
BENNING, Isaac. Enacting core practices of effective mathematics pedagogy with GeoGebra. Mathematics Teacher Education and Development, Brisbane, v. 23, n. 2, p. 102-127, 2021.
BOZKURT, Gülay; UYGAN, Candas. Lesson hiccups during the development of teaching schemes: a novice technology‑using mathematics teacher’s professional instrumental genesis of dynamic geometry. ZDM, [S. l.], v. 52, p. 1349-1363, 2020.
BRODIE, Karin; SANNI, Rasheed. We won't know it since we don't teach it: Interactions between teachers' knowledge and practice. African Journal of Research in Mathematics, Science and Technology Education, [S. l.], v. 18, n. 2, p. 188-197, 2014.
CAYTON, Charity et al. Pivotal teaching moments in technology-intensive secondary geometry classrooms. Journal of Mathematics Teacher Education, [S. l.], v. 20, p. 75-100, 2017.
CHO, Yi -An; TEE, Fui-Due. Complementing mathematics teachers’ horizon content knowledge with an elementary-on-advanced aspect. Pedagogical Research, Belgrado, v. 3, n. 1, 2018.
DIMMEL, Justin K.; HERBST, Patricio Guillermo. Proof transcription in high school geometry: A study of what teachers recognize as normative when students present proofs at the board. Educational Studies in Mathematics, [S. l.], v. 105, p. 71-89, 2020.
ERICKSON, Ander; HERBST, Patricio Guillermo. Will teachers create opportunities for discussion when teaching proof in a geometry classroom? International Journal of Science and Mathematics Education, Taiwan, v. 16, n. 1, p. 167-181, jan. 2018.
GUMIERO, Bárbara Silva; PAZUCH, Vinícius. Tecnologias digitais e o ensino de triângulos: uma revisão sistemática da literatura. Revista Brasileira de Estudos Pedagógicos, Brasília, v. 105, n. 1, p. e5980, 16 out. 2024.
HERBST, Patricio Guillermo et al. How can teaching simulations help us study at scale the tensions mathematics teachers have to manage when considering policy recommendations? Educational Studies in Mathematics, [S. l.], v. 110, p. 1-21, 2022.
HERBST, Patricio Guillermo; KO, Inah; MILEWSKI, Amanda. A heuristic approach to assess change in mathematical knowledge for teaching geometry after a practice-based professional learning intervention. Research in Mathematics Education, [S. l.], v. 22, n. 2, p. 188-208, 2020.
HERBST, Patricio Guillermo; KOSKO, Karl W. Using representations of practice to elicit mathematics teachers’ tacit knowledge of practice: a comparison of responses to animations and videos. Journal of Mathematics Teacher Education, [S. l.], v. 17, p. 515-537, 2014.
KIYICI, Ozan Deniz; DIKKARTIN ÖVEZ, Filiz Tuba. Examination of technology acceptance and TPACK competencies of mathematics teachers who are involved in distance education practices during the pandemic process. Journal of Educational Technology & Online Learning, Baliquesir, v. 4, n. 4, p. 805-821, 2021.
KOMATSU, Kotaro. Fostering empirical examination after proof construction in secondary school geometry. Educational Studies in Mathematics, [S. l.], v. 96, p. 129-144, 2017.
KUL, Umit. Influences of technology integrated professional development course on mathematics teachers. European Journal of Educational Research, Enschede, v. 7, n. 2, p. 233-243, 2018.
LENTE. In: DLP – Dicionário da Língua Portuguesa da Academia Brasileira de Letras. Rio de Janeiro: Academia Brasileira de Letras, 2025. Disponível em: https://servbib.academia.org.br/dlp/verbete.xhtml?entrada=lente. Acesso em: 9 abr. 2025.
MAVANI, Deepak; MAVANI, Beena; SCHÄFER, Marc. A case study of two selected teachers as they integrated dynamic geometry software as a visualization tool in teaching geometry. African Journal of Research in Mathematics, Science and Technology Education, [S. l.], v. 22, n. 3, p. 297-307, 2018.
MORAN, Mariana et al. O ensino da geometria: entrevista com a professora Regina Maria Pavanello. Educação Matemática em Revista, Brasília, v. 28, n. 79, p. 1-11, abr./jun. 2023.
MWADZAANGATI, Lisnet; ADLER, Jill; KAZIMA, Mercy. Mathematics mediational means and learner centeredness: Insights from ‘traditional’ malawian secondary school geometry lessons. African Journal of Research in Mathematics, Science and Technology Education, [S. l.], v. 26, n. 1, p. 1-12, 2022.
NÓVOA, António. Conhecimento profissional docente e formação de professores. Revista Brasileira de Educação, Rio de Janeiro, v. 27, p. e270129, 2022.
NURGABYL, Duisebek; SATKULOV, Baktiyar; KAGAZBAYEVA, Aspet. Formation and development of mathematical literacy in the context of evaluative – Study tasks of PISA. Journal of Mathematics Education, Irvine, v. 14, n. 4, p. 701-722, 2023.
ROBUTTI, Ornella; PRODROMOU, Theodosia; ALDON, Gilles. Teachers’ involvement in designing MERLO items: Boundary crossing. Digital Experiences in Mathematics Education, [S. l.], v. 7, p. 276-300, 2021.
SCHWARTS, Gil; KARSENTY, Ronnie. “Can this happen only in Japan?”: mathematics teachers reflect on a videotaped lesson in a cross‑cultural context. Journal of Mathematics Teacher Education, [S. l.], v. 23, p. 527-554, 2020.
SEAGO, Nanette M. et al. Impacting teachers’ understanding of geometric similarity: results from field testing of the learning and teaching geometry professional development materials. Professional Development in Education, [S. l.], v. 40, n. 4, p. 627-653, 2014.
SILVA, Elio Rubens de Freitas; SILVA, Adelmo Carvalho da. Práticas pedagógicas de professores que ensinam matemática nos anos finais do Ensino Fundamental. Revista de Ensino de Ciências e Matemática, São Paulo, v. 13, n. 2, p. 1-26, abr./jun. 2022.
SUNZUMA, Gladys et al. In-service Zimbabwean teachers' views on the utility value of diagrams in the teaching and learning of geometry. International Journal on Math, Science and Technology Education, Helsinki, v. 8, n. 1, p. 1-18, 2020.
SUNZUMA, Gladys; MAHARAJ, Aneshkumar. In-service mathematics teachers’ knowledge and awareness of ethnomathematics approaches. International Journal of Mathematical Education in Science and Technology, [S. l.], v. 52, n. 7, p. 1063-1078, 2021.
TIROSH, Dina et al. Using theories and research to analyze a case: Learning about example use. Journal of Mathematics Teacher Education, [S. l.], v. 22, p. 205-225, 2019.
WEISS, Michael; HERBST, Patricio Guillermo. The role of theory building in the teaching of secondary geometry. Educacional Studies in Mathematics, [S. l.], v. 89, p. 205-229, 2015.
WERTSCH, James V. Voices of the mind: a sociocultural approach to mediated action. Cambridge: Harvard University Press, 1991.
WERTSCH, James V. Mind as action. New York: Oxford University Press, 1998.
YILDIZ, Avni; BALTACI, Serdal. Reflections from the lesson study for the development of techno-pedagogical competencies in teaching fractal Geometry. European Journal of Educational Research, Enschede, n. 6, v. 1, p. 41-50, 2017.
ZAKARYAN, Diana; SOSA, Leticia. Conocimiento del profesor de secundaria de la práctica matemática en clases de geometría. Educación Matemática, Cidade do México, v. 33, n. 1, p. 71-97, abr. 2021.
Publicado
2026-05-30
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NASCIMBEN DELMONDI MUNHOZ, N.; PAZUCH, V. Um estudo das lentes teóricas e metodológicas envolvendo práticas pedagógicas de professores que ensinam geometria. Revemop, v. 8, p. e2026013, 30 maio 2026.
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Copyright (c) 2026 Natalia Nascimben Delmondi Munhoz, Vinícius Pazuch
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