Noticing of preservice mathematics teachers in the context of hierarchical classification of quadrilaterals
DOI:
https://doi.org/10.46312/1zzefr59Keywords:
Professional Teacher Noticing, Preservice Mathematics Teacher Education, Hierarchical Classification of QuadrilateralsAbstract
This article discusses the noticing of preservice mathematics teachers (PMT) about a middle school student’s thinking regarding a hierarchical classification of quadrilaterals. The investigation involved engaging PMT in discussions on theoretical aspects of geometry learning, followed by the analysis of written work produced by a middle school student during a quadrilateral classification task. Based on a qualitative and interpretative analysis, the results indicated that the PMT attended errors and difficulties presented by the student; interpreted these difficulties considering the prototype phenomenon, partitive classification, and limitations related to geometric definitions; and proposed questions, visual resources, and diverse examples as strategies to overcome the errors and difficulties that were attended to. The noticing focused on relevant aspects of the hierarchical structure of quadrilateral classification, highlighting the importance of teacher education actions that integrate theoretical frameworks and the analysis of school practices to enhance the development of professional teacher noticing.
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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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CYBULSKI, Fernanda; OLIVEIRA, Hélia; DE COSTA TRINDADE CYRINO, Márcia Cristina. Noticing of preservice mathematics teachers in the context of hierarchical classification of quadrilaterals. 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 apr. 2026.
