Noticing de futuros professores de Matemática no contexto da classificação hierárquica de quadriláteros
DOI:
https://doi.org/10.46312/1zzefr59Palavras-chave:
Noticing Docente, Formação Inicial de Professores de Matemática, Classificação Hierárquica de QuadriláterosResumo
Este artigo discute o noticing de futuros professores de Matemática (FPM) sobre o pensamento de um aluno relativo à classificação hierárquica de quadriláteros. A investigação envolveu a discussão, com os FPM, de aspectos teóricos da aprendizagem em geometria, seguida da análise de registros escritos produzidos por um aluno em uma tarefa de classificação de quadriláteros. A partir de uma análise qualitativa e interpretativa, os resultados indicam que os FPM reconheceram erros e dificuldades do estudante; interpretaram tais dificuldades à luz do fenômeno prototípico, da classificação partitiva e de limitações relacionadas às definições geométricas; sugeriram questionamentos, recursos visuais e exemplos diversificados como estratégias de superação dos erros e dificuldades reconhecidos do estudante. Conclui-se, assim, que o noticing evidenciado concentrou-se em aspectos relevantes da estrutura hierárquica da classificação dos quadriláteros, ressaltando a importância de ações formativas articulando fundamentação teórica e análise de práticas escolares para potencializar o desenvolvimento desta capacidade profissional docente.
Referências
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BALDINGER, Erin E. Reasoning about student written work through self-comparison: how pre-service secondary teachers use their own solutions to analyze student work. Mathematical Thinking and Learning, [s. l.], v. 22, n. 1, p. 56–78, 2 Jan. 2019. https://doi.org/10.1080/10986065.2019.1624930
CABRAL, Joana; OLIVEIRA, Hélia; MENDES, Fátima. O conhecimento matemático de futuras educadoras e professoras sobre sequências repetitivas e a capacidade de perceber o pensamento algébrico de crianças do jardim de infância. Acta Scientiae, Canoas, v. 23, n. 6, p. 30–59, 2021. https://doi.org/10.17648/acta.scientiae.6302
CRESWELL, John W. Qualitative Inquary and Research Design: Choosing among five approaches. [S. l.]: Sage, 2013.
DINDYAL, Jaguthsing; SCHACK, Edna O.; CHOY, Ban Heng; SHERIN, Miriam Gamoran. Exploring the terrains of mathematics teacher noticing. ZDM, [s. l.], v. 53, n. 1, 1 Apr. 2021. https://doi.org/10.1007/s11858-021-01249-y
ERICKSON, Frederick. Qualitative research methods for science education. In: FRASER, B. J. (ed.). Second International Handbook of Science Education. [S. l.]: Springer, 2012. p. 1451–1469. https://doi.org/10.1007/978-1-4020-9041-7_93
FERNÁNDEZ, Ceneida; MORENO, Mar; SÁNCHEZ-MATAMOROS, Gloria. Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development. ZDM, [s. l.], 2024. https://doi.org/10.1007/s11858-024-01573-z
FISHER, Molly H.; THOMAS, Jonathan; SCHACK, Edna O.; JONG, Cindy; TASSELL, Janet. Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, [s. l.], v. 30, n. 2, p. 209–232, 1 Jun. 2018. https://doi.org/10.1007/s13394-017-0228-0
FUJITA, Taro. Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, [s. l.], v. 31, n. 1, p. 60–72, Mar. 2012. https://doi.org/10.1016/j.jmathb.2011.08.003
GROSSMAN, Pam; COMPTON, Christa; IGRA, Danielle; RONFELDT, Matthew; SHAHAN, Emily; WILLIAMSON, Peter W. Teaching Practice: A Cross-Professional Perspective. Teachers College Record, [s. l.], v. 111, n. 9, p. 2055–2100, 2009.
GÜNER, Pınar; BOZKUŞ, Figen; GÜLER, Mustafa. To notice, but what? An investigation on pre-service teachers’ noticing of strengths and deficits in student thinking. Teaching and Teacher Education, [s. l.], v. 160, 1 Jul. 2025. https://doi.org/10.1016/j.tate.2025.105035
HAJ YAHYA, Aehsan; MAHAMEED, Areej; ARISHA HAJ YAHYA, Hussam. Does the Use of Concept Maps Affect the Defining and the Understanding of Inclusion Relationships? Mathematical Thinking and Learning, [s. l.], 2024. https://doi.org/10.1080/10986065.2024.2310038
HERSHKOWITZ, Rina. Psychological Aspects of Learning Geometry. In: NESHER, Pearla; KILPATRICK, Jeremy (eds.). Mathematics and cognition: A research synthesis by the International group for the psychology of mathematics education. Cambridge: Cambridge University Press, 1990. p. 70–95. https://doi.org/10.1017/cbo9781139013499.006
IVARS, Pedro; FERNÁNDEZ, Ceneida; LLINARES, Salvador. A Learning Trajectory as a Scaffold for Pre-service Teachers’ Noticing of Students’ Mathematical Understanding. International Journal of Science and Mathematics Education, [s. l.], v. 18, n. 3, p. 529–548, Mar. 2020. https://doi.org/10.1007/s10763-019-09973-4
JACOBS, Victoria R.; EMPSON, Susan B.; JESSUP, Naomi A.; DUNNING, Amy; PYNES, D’Anna A.; KRAUSE, Gladys; FRANKE, Todd M. Profiles of teachers’ expertise in professional noticing of children’s mathematical thinking. Journal of Mathematics Teacher Education, [s. l.], 2022. https://doi.org/10.1007/s10857-022-09558-z
JACOBS, Victoria R; LAMB, Lisa L C; PHILIPP, Randolph A. Professional Noticing of Children’s Mathematical Thinking. Journal for Research in Mathematics Education, [s. l.], v. 41, n. 2, p. 169–202, 2010. https://doi.org/10.5951/jresematheduc.41.2.0169
KÖNIG, Johannes; SANTAGATA, Rossella; SCHEINER, Thorsten; ADLEFF, Ann Kristin; YANG, Xinrong; KAISER, Gabriele. Teacher noticing: A systematic literature review of conceptualizations, research designs, and findings on learning to notice. Educational Research Review, [s. l.], v. 36, 1 Jun. 2022. https://doi.org/10.1016/j.edurev.2022.100453
LEE, Hea Jin; KIM, Hee Jeong; CHO, Hyungmi. Investigating preservice teachers’ feedback to students’ mathematical solutions. Journal of Education for Teaching, [s. l.], 2024. https://doi.org/10.1080/02607476.2024.2326508
MAGIERA, Marta T.; ZAMBAK, Vecihi S. Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records. International Journal of STEM Education, [s. l.], v. 8, n. 1, 1 Dec. 2021. https://doi.org/10.1186/s40594-020-00263-y
RODRIGUES, Renata Viviane Raffa; CYRINO, Márcia Cristina de Costa Trindade; OLIVEIRA, Hélia. Percepção profissional de futuros professores sobre o pensamento algébrico dos alunos na exploração de um caso multimídia. Quadrante, [s. l.], v. XXVIII, n. 1, p. 100–123, 2019.
RUTTEN, Logan; BUTVILLE, Danielle; WOLKENHAUER, Rachel; DVIR, Boaz. Noticing, interpreting, deciding: How elementary teachers address unplanned difficult-topics moments in educational practice. Teaching and Teacher Education, [s. l.], v. 161, 1 Jul. 2025. https://doi.org/10.1016/j.tate.2025.105017
SCHEINER, Thorsten. Shifting the ways prospective teachers frame and notice student mathematical thinking: from deficits to strengths. Educational Studies in Mathematics, [s. l.], v. 114, n. 1, p. 35–61, 1 Sep. 2023. https://doi.org/10.1007/s10649-023-10235-y
STOCKERO, Shari L. Transferability of teacher noticing. ZDM, [s. l.], v. 53, n. 1, p. 73–84, 1 Apr. 2021. https://doi.org/10.1007/s11858-020-01198-y
SUPERFINE, Alison Castro; FISHER, Amanda; BRAGELMAN, John; AMADOR, Julie. Shifting perspectives on preservice teachers’ noticing of children’s mathematical thinking. In: SCHACK, Edna O.; FISHER, Molly H.; WILHELM, Jennifer A. (eds.). Teacher noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks. [S. l.]: Springer, 2017. p. 409–426. https://doi.org/10.1007/978-3-319-46753-5
ULUSOY, Fadime; ÇAKIROĞLU, Erdinç. Exploring prospective teachers’ noticing of students’ understanding through micro-case videos. Journal of Mathematics Teacher Education, [s. l.], v. 24, n. 3, p. 253–282, 1 Jun. 2021. https://doi.org/10.1007/s10857-020-09457-1
VILLIERS, Michael de. The Role and Function of a Hierarchical Classification of Quadrilaterals. For the Learning of Mathematics, [s. l.], v. 1, n. 14, p. 11–18, Feb. 1994.
VILLIERS, Michael de; GOVENDER, Rajendran; PATTERSON, Nikita. Defining in Geometry. In: CRAINE, T. V.; RUBINSTEIN, R. (eds.). Understanding Geometry for a Changing World. [S. l.]: NCTM, 2009. p. 189–203.
BALDINGER, Erin E. Reasoning about student written work through self-comparison: how pre-service secondary teachers use their own solutions to analyze student work. Mathematical Thinking and Learning, [s. l.], v. 22, n. 1, p. 56–78, 2 Jan. 2019. https://doi.org/10.1080/10986065.2019.1624930
CABRAL, Joana; OLIVEIRA, Hélia; MENDES, Fátima. O conhecimento matemático de futuras educadoras e professoras sobre sequências repetitivas e a capacidade de perceber o pensamento algébrico de crianças do jardim de infância. Acta Scientiae, Canoas, v. 23, n. 6, p. 30–59, 2021. https://doi.org/10.17648/acta.scientiae.6302
CRESWELL, John W. Qualitative Inquary and Research Design: Choosing among five approaches. [S. l.]: Sage, 2013.
DINDYAL, Jaguthsing; SCHACK, Edna O.; CHOY, Ban Heng; SHERIN, Miriam Gamoran. Exploring the terrains of mathematics teacher noticing. ZDM, [s. l.], v. 53, n. 1, 1 Apr. 2021. https://doi.org/10.1007/s11858-021-01249-y
ERICKSON, Frederick. Qualitative research methods for science education. In: FRASER, B. J. (ed.). Second International Handbook of Science Education. [S. l.]: Springer, 2012. p. 1451–1469. https://doi.org/10.1007/978-1-4020-9041-7_93
FERNÁNDEZ, Ceneida; MORENO, Mar; SÁNCHEZ-MATAMOROS, Gloria. Prospective secondary teachers’ noticing of students’ thinking about the limit concept: pathways of development. ZDM, [s. l.], 2024. https://doi.org/10.1007/s11858-024-01573-z
FISHER, Molly H.; THOMAS, Jonathan; SCHACK, Edna O.; JONG, Cindy; TASSELL, Janet. Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, [s. l.], v. 30, n. 2, p. 209–232, 1 Jun. 2018. https://doi.org/10.1007/s13394-017-0228-0
FUJITA, Taro. Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, [s. l.], v. 31, n. 1, p. 60–72, Mar. 2012. https://doi.org/10.1016/j.jmathb.2011.08.003
GROSSMAN, Pam; COMPTON, Christa; IGRA, Danielle; RONFELDT, Matthew; SHAHAN, Emily; WILLIAMSON, Peter W. Teaching Practice: A Cross-Professional Perspective. Teachers College Record, [s. l.], v. 111, n. 9, p. 2055–2100, 2009.
GÜNER, Pınar; BOZKUŞ, Figen; GÜLER, Mustafa. To notice, but what? An investigation on pre-service teachers’ noticing of strengths and deficits in student thinking. Teaching and Teacher Education, [s. l.], v. 160, 1 Jul. 2025. https://doi.org/10.1016/j.tate.2025.105035
HAJ YAHYA, Aehsan; MAHAMEED, Areej; ARISHA HAJ YAHYA, Hussam. Does the Use of Concept Maps Affect the Defining and the Understanding of Inclusion Relationships? Mathematical Thinking and Learning, [s. l.], 2024. https://doi.org/10.1080/10986065.2024.2310038
HERSHKOWITZ, Rina. Psychological Aspects of Learning Geometry. In: NESHER, Pearla; KILPATRICK, Jeremy (eds.). Mathematics and cognition: A research synthesis by the International group for the psychology of mathematics education. Cambridge: Cambridge University Press, 1990. p. 70–95. https://doi.org/10.1017/cbo9781139013499.006
IVARS, Pedro; FERNÁNDEZ, Ceneida; LLINARES, Salvador. A Learning Trajectory as a Scaffold for Pre-service Teachers’ Noticing of Students’ Mathematical Understanding. International Journal of Science and Mathematics Education, [s. l.], v. 18, n. 3, p. 529–548, Mar. 2020. https://doi.org/10.1007/s10763-019-09973-4
JACOBS, Victoria R.; EMPSON, Susan B.; JESSUP, Naomi A.; DUNNING, Amy; PYNES, D’Anna A.; KRAUSE, Gladys; FRANKE, Todd M. Profiles of teachers’ expertise in professional noticing of children’s mathematical thinking. Journal of Mathematics Teacher Education, [s. l.], 2022. https://doi.org/10.1007/s10857-022-09558-z
JACOBS, Victoria R; LAMB, Lisa L C; PHILIPP, Randolph A. Professional Noticing of Children’s Mathematical Thinking. Journal for Research in Mathematics Education, [s. l.], v. 41, n. 2, p. 169–202, 2010. https://doi.org/10.5951/jresematheduc.41.2.0169
KÖNIG, Johannes; SANTAGATA, Rossella; SCHEINER, Thorsten; ADLEFF, Ann Kristin; YANG, Xinrong; KAISER, Gabriele. Teacher noticing: A systematic literature review of conceptualizations, research designs, and findings on learning to notice. Educational Research Review, [s. l.], v. 36, 1 Jun. 2022. https://doi.org/10.1016/j.edurev.2022.100453
LEE, Hea Jin; KIM, Hee Jeong; CHO, Hyungmi. Investigating preservice teachers’ feedback to students’ mathematical solutions. Journal of Education for Teaching, [s. l.], 2024. https://doi.org/10.1080/02607476.2024.2326508
MAGIERA, Marta T.; ZAMBAK, Vecihi S. Prospective K-8 teachers’ noticing of student justifications and generalizations in the context of analyzing written artifacts and video-records. International Journal of STEM Education, [s. l.], v. 8, n. 1, 1 Dec. 2021. https://doi.org/10.1186/s40594-020-00263-y
RODRIGUES, Renata Viviane Raffa; CYRINO, Márcia Cristina de Costa Trindade; OLIVEIRA, Hélia. Percepção profissional de futuros professores sobre o pensamento algébrico dos alunos na exploração de um caso multimídia. Quadrante, [s. l.], v. XXVIII, n. 1, p. 100–123, 2019.
RUTTEN, Logan; BUTVILLE, Danielle; WOLKENHAUER, Rachel; DVIR, Boaz. Noticing, interpreting, deciding: How elementary teachers address unplanned difficult-topics moments in educational practice. Teaching and Teacher Education, [s. l.], v. 161, 1 Jul. 2025. https://doi.org/10.1016/j.tate.2025.105017
SCHEINER, Thorsten. Shifting the ways prospective teachers frame and notice student mathematical thinking: from deficits to strengths. Educational Studies in Mathematics, [s. l.], v. 114, n. 1, p. 35–61, 1 Sep. 2023. https://doi.org/10.1007/s10649-023-10235-y
STOCKERO, Shari L. Transferability of teacher noticing. ZDM, [s. l.], v. 53, n. 1, p. 73–84, 1 Apr. 2021. https://doi.org/10.1007/s11858-020-01198-y
SUPERFINE, Alison Castro; FISHER, Amanda; BRAGELMAN, John; AMADOR, Julie. Shifting perspectives on preservice teachers’ noticing of children’s mathematical thinking. In: SCHACK, Edna O.; FISHER, Molly H.; WILHELM, Jennifer A. (eds.). Teacher noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks. [S. l.]: Springer, 2017. p. 409–426. https://doi.org/10.1007/978-3-319-46753-5
ULUSOY, Fadime; ÇAKIROĞLU, Erdinç. Exploring prospective teachers’ noticing of students’ understanding through micro-case videos. Journal of Mathematics Teacher Education, [s. l.], v. 24, n. 3, p. 253–282, 1 Jun. 2021. https://doi.org/10.1007/s10857-020-09457-1
VILLIERS, Michael de. The Role and Function of a Hierarchical Classification of Quadrilaterals. For the Learning of Mathematics, [s. l.], v. 1, n. 14, p. 11–18, Feb. 1994.
VILLIERS, Michael de; GOVENDER, Rajendran; PATTERSON, Nikita. Defining in Geometry. In: CRAINE, T. V.; RUBINSTEIN, R. (eds.). Understanding Geometry for a Changing World. [S. l.]: NCTM, 2009. p. 189–203.
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2026-04-14
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Formação de Professores que Ensinam Matemática: diversos contextos e modalidades
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Copyright (c) 2026 Perspectivas da Educação Matemática
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CYBULSKI, Fernanda; OLIVEIRA, Hélia; DE COSTA TRINDADE CYRINO, Márcia Cristina. Noticing de futuros professores de Matemática no contexto da classificação hierárquica de quadriláteros. Perspectivas da Educação Matemática, [S. l.], v. 19, n. 52, 2026. DOI: 10.46312/1zzefr59. Disponível em: https://periodicos.ufms.br/index.php/pedmat/article/view/23680. Acesso em: 16 abr. 2026.
