{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T19:03:32Z","timestamp":1771959812845,"version":"3.50.1"},"reference-count":54,"publisher":"Universidade Federal de Grande Dourados","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/br\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["TANGRAM"],"abstract":"<jats:p>Este estudo centra-se no conhecimento revelado por professores de matem\u00e1tica num curso de forma\u00e7\u00e3o sobre fra\u00e7\u00f5es. Os professores resolveram uma tarefa focando estimativa, dificuldades dos alunos e recursos no contexto da divis\u00e3o de fra\u00e7\u00f5es. Os resultados sugerem que os professores enfrentam alguns desafios, como: estimar o resultado de divis\u00e3o de fra\u00e7\u00f5es e elencar poss\u00edveis dificuldades conceituais dos alunos, conhecimento a respeito de recursos e como utiliz\u00e1-los para o ensino da divis\u00e3o de fra\u00e7\u00f5es. Esta pesquisa se faz relevante, pois alunos e professores apresentam dificuldades em rela\u00e7\u00e3o \u00e0 divis\u00e3o de fra\u00e7\u00f5es, principalmente no que se refere ao sentido de n\u00famero fracion\u00e1rio, representa\u00e7\u00e3o e unidade de refer\u00eancia.<\/jats:p>","DOI":"10.30612\/tangram.v9i1.19232","type":"journal-article","created":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:06:29Z","timestamp":1771956389000},"source":"Crossref","is-referenced-by-count":0,"title":["O Conhecimento Especializado do Professor de Matem\u00e1tica no contexto da Divis\u00e3o de Fra\u00e7\u00f5es em uma Tarefa para a Forma\u00e7\u00e3o"],"prefix":"10.30612","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5202-7852","authenticated-orcid":false,"given":"Gabriela","family":"Gibim","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1579-8073","authenticated-orcid":false,"given":"Laura","family":"Rifo","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0064-1452","authenticated-orcid":false,"given":"Nuria","family":"Climent","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3505-4431","authenticated-orcid":false,"given":"Miguel","family":"Ribeiro","sequence":"additional","affiliation":[]}],"member":"12060","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"340916","unstructured":"Andr\u00e9s de Zaragoza, Juan (1515). Sumario breve de la pr\u00e1ctica de la arithm\u00e9tica y todo el curso de larte mercantinol bien declarado: el qual se llama maestro de cuento. Impresor Juan Joffre."},{"key":"340917","unstructured":"Ara\u00fajo, W. A. D. (2013). O uso do FRAC-SOMA 235 no processo de ensino e aprendizagem de fra\u00e7\u00f5es para o ensino fundamental. In Anais do 11\u00ba Encontro Nacional de Educa\u00e7\u00e3o Matem\u00e1tica (ENEM) (pp. 1\u201310). Curitiba, PR."},{"key":"340918","unstructured":"http:\/\/sbem.bruc.com.br\/XIENEM\/pdf\/72_1718_ID.pdf"},{"key":"340919","doi-asserted-by":"crossref","unstructured":"Ball, D. L. (1990). Prospective elementary and secondary teachers\u2019 understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.","DOI":"10.5951\/jresematheduc.21.2.0132"},{"key":"340920","unstructured":"Bayound, J. M. (2011). A comparison of pre-service and experienced elementary teachers\u2019 pedagogical content knowledge (PCK) of common error patterns in fractions. [Doctoral Thesis]. American University of Beirut, Beirut, L\u00edbano."},{"key":"340921","doi-asserted-by":"crossref","unstructured":"Buys, K. (2008). Mental Arithmetic. In M. Huevel- Panhuizen, K. Buys, & A. Treffers (Eds.), Children Learning Mathematics: A Learning-Teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school (pp. 173-2020. Sense publishers.","DOI":"10.1163\/9789087903954_014"},{"key":"340922","unstructured":"Brasil (2018). Base Nacional Comum Curricular. Bras\u00edlia-DF: Minist\u00e9rio da Educa\u00e7\u00e3o."},{"key":"340923","unstructured":"Brocardo, J., Di, L., & Kraemer, J. (2003). Algoritmos e sentido do n\u00famero. Educa\u00e7\u00e3o Matem\u00e1tica, 75, 11-15."},{"key":"340924","unstructured":"Bulgar, S. (2003). Using Research to Inform Practice: Children Make Sense of Division of Fractions. International Group for the Psychology of Mathematics Education, 2, 157-164."},{"key":"340925","unstructured":"Carrapi\u00e7o, R. (2015). C\u00e1lculo mental com n\u00fameros racionais: Um estudo com alunos do 6. ano de escolaridade [Tese de doutorado]. Instituto de Educa\u00e7\u00e3o da Universidade de Lisboa, Lisboa."},{"key":"340926","doi-asserted-by":"crossref","unstructured":"Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-\u00c1vila, D., & Mu\u00f1oz-Catal\u00e1n, M. C. (2018). The mathematics teacher\u2019s Specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253.","DOI":"10.1080\/14794802.2018.1479981"},{"key":"340927","unstructured":"Climent, N. (2002). El desarrollo profesional del maestro de primaria respecto de la ense\u00f1anza de la matem\u00e1tica. [Tese de Doutorado]. Universidad de Huelva."},{"key":"340928","unstructured":"Contreras, M. (2012). Problemas multiplicativos relacionados con la divisi\u00f3n de fracciones: un estudio sobre su ense\u00f1anza y aprendizaje. [Tese de doutorado]. Universidad de Valencia, Valencia."},{"key":"340929","doi-asserted-by":"crossref","unstructured":"Cooney, T. J. (1994). Research on teacher education. In search of common ground. Journal for Research in Mathematics Education, 25(3), 355-376.","DOI":"10.2307\/749575"},{"key":"340930","unstructured":"Figueiredo, H. A., & dos Santos Soares, F. (2016). Utilizando Problemas de Fermi para Estimar. Encontro Nacional de Educa\u00e7\u00e3o Matem\u00e1tica, Bras\u00edlia."},{"key":"340931","unstructured":"Fontanive, N. S., Klein, R., & Rodrigues, S. S. (2012). Boas pr\u00e1ticas docentes no ensino da Matem\u00e1tica. Estudos & Pesquisas Educacionais, 3, 195-277."},{"key":"340932","unstructured":"Flores, P. (2013). \u00bfPor qu\u00e9 multiplicar en cruz? Curso de formaci\u00f3n inicial de profesores de matem\u00e1ticas en la Universidad. [Artigo]. 7\u00ba Congreso Iberoamericano de Educaci\u00f3n Matem\u00e1tica, Montevideo, Uruguay."},{"key":"340933","unstructured":"Garc\u00eda, A. I. M. (2013). Conocimiento profesional de un grupo de profesores sobre la divisi\u00f3n de fracciones. [Disserta\u00e7\u00e3o de Mestrado]. Universidad de Granada, Granada."},{"key":"340934","unstructured":"Giongo, I. M., Quartieri, M. T., & Rehfeldt, M. J. H. (2013). Problematizando o uso da Estimativa em aulas de Matem\u00e1tica da escola b\u00e1sica. [Artigo]. 11\u00ba Encontro Nacional de Educa\u00e7\u00e3o Matem\u00e1tica, Curitiba, Paran\u00e1."},{"key":"340935","unstructured":"Godino, J.D., Batanero, C. Font, V., Contreras, A., & Wilhelmi, M. R. (2016). The theory of didactical suitability: Networking a system of didactics principles for mathematics education form different theoretical perspectives. [Article]. 13th International Congress on Mathematical Education, Hamburg, Germany."},{"key":"340936","unstructured":"Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, G. Martin, & D. Schifter (Eds.), A research companion to Principles and Standards for School Mathematics (pp. 5\u201326). Reston, VA: National Council of Teachers of Mathematics."},{"key":"340937","unstructured":"Huinker D. (2002). Examining dimensions of fraction operation sense. In B. Litwiller (Ed.) Making sense of fractions, ratios, and proportions. National Council of Teachers of Mathematics."},{"key":"340938","doi-asserted-by":"crossref","unstructured":"Kelly, C. (2006). Using manipulatives in mathematical problem solving: A performance-based analysis. The Mathematics Enthusiast, 3. https:\/\/doi.org\/10.54870\/1551-3440.1049.","DOI":"10.54870\/1551-3440.1049"},{"key":"340939","unstructured":"Kieren, T. E. (1980). Five Faces of Mathematical Knowledge Building. Department of Secondary Education, University of Alberta."},{"key":"340940","doi-asserted-by":"crossref","unstructured":"Lampert, M. (1988). What can research on teacher education tell us about improving quality in mathematics education? Teaching and Teacher Education, 4(2), 157-170.","DOI":"10.1016\/0742-051X(88)90015-7"},{"key":"340941","doi-asserted-by":"crossref","unstructured":"Li, Y.; Kulm, G. (2008). Knowledge and confidence of pre-service mathematics teachers: the case of fraction division. ZDM, 40(5), 833-843.","DOI":"10.1007\/s11858-008-0148-2"},{"key":"340942","doi-asserted-by":"crossref","unstructured":"Lo, J. J., & Luo, F. (2012). Prospective elementary teachers\u2019 knowledge of fraction division. Journal of Mathematics Teacher Education, 15(6), 481-500 https:\/\/link.springer.com\/journal\/10857","DOI":"10.1007\/s10857-012-9221-4"},{"key":"340943","unstructured":"Lopes, A. J. (2008). O que nossos alunos podem estar deixando de aprender sobre fra\u00e7\u00f5es, quando tentamos lhes ensinar fra\u00e7\u00f5es. Bolema, 21(31) 1-22."},{"key":"340944","doi-asserted-by":"crossref","unstructured":"Lubinski, C. A.; Fox, T.; Thomason, R. (1998). Learning to make sense of division of fractions: One K-8 preservice teacher\u2019s perspective. School Science and Mathematics, 98(5), 247-251. https:\/\/www.semanticscholar.org\/paper\/Learning-to-Make-Sense-of-Division-of-Fractions%3A-Lubinski-Fox\/241a78189841638524ae1776410ce0dd95216795.","DOI":"10.1111\/j.1949-8594.1998.tb17298.x"},{"key":"340945","doi-asserted-by":"crossref","unstructured":"Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers\u2019 understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum.","DOI":"10.4324\/9781410602589"},{"key":"340946","unstructured":"Menezes; Ribeiro (2023). Pensar e fazer pesquisa na forma\u00e7\u00e3o de professor com foco no Conhecimento Interpretativo e Especializado do professor. Campinas: Cognoscere."},{"key":"340947","doi-asserted-by":"crossref","unstructured":"Monger, W., Sander, G. P., & Tortora, E. (2021). Estudo sobre o uso da estimativa na resolu\u00e7\u00e3o de tarefas matem\u00e1ticas por alunos do quinto ano do Ensino Fundamental. Revista De Educa\u00e7\u00e3o Matem\u00e1tica, 18, e021027.","DOI":"10.37001\/remat25269062v18id548"},{"key":"340948","unstructured":"Moreira, I. M. B. (2013). O ensino das opera\u00e7\u00f5es com fra\u00e7\u00f5es envolvendo calculadora. In Anais do VII Congreso Iberoamericano de Educaci\u00f3n Matem\u00e1tica (CIBEM) (pp. 2996\u20133005). Montevideo, Uruguai. http:\/\/www.cibem7.semur.edu.uy\/7\/actas\/pdfs\/1231.pdf"},{"key":"340949","unstructured":"Moriel Junior, J. G. (2014). Conhecimento especializado para ensinar divis\u00e3o de fra\u00e7\u00f5es (Tese de doutorado, Universidade Federal de Mato Grosso)."},{"key":"340950","unstructured":"Monteiro, C., & Pinto, H. (2005). A aprendizagem dos n\u00fameros racionais. Quadrante, 14(1), 89-107."},{"key":"340951","unstructured":"Mcintosh, A., Reys, B., & Reys, R. E. (1992). Uma proposta de quadro de refer\u00eancia para examinar o sentido b\u00e1sico de n\u00famero. For the Learning of Mathematics, 1(3), 1-17."},{"key":"340952","doi-asserted-by":"crossref","unstructured":"Newton, K. J. (2008). An Extensive Analysis of Preservice Elementary Teachers\u2019 Knowledge of Fractions. American Educational Research Journal, 45(4), 1080-1110.","DOI":"10.3102\/0002831208320851"},{"key":"340953","doi-asserted-by":"crossref","unstructured":"\u00d6zel, S. (2013). An Analysis of In-service Teachers\u2019 Pedagogical Content Knowledge of Division of Fractions. Anthropologist, 16(1-2), 1-5.","DOI":"10.1080\/09720073.2013.11891330"},{"key":"340954","unstructured":"Parra, C. (1996). C\u00e1lculo Mental na escola prim\u00e1ria. In C. Parra, I. Saiz, I. (Orgs.) Did\u00e1tica da Matem\u00e1tica. Artmed."},{"key":"340955","unstructured":"Perez, B. F. (2009). Materiales para la ense\u00f1anza de las fracciones. Revista Digital Innovaci\u00f3n y Experiencias Educativas, 24, 1-8."},{"key":"340956","unstructured":"Pinto, H., & Ribeiro, M. (2013). Conhecimento e forma\u00e7\u00e3o de futuros professores dos primeiros anos \u2013 o sentido de n\u00famero racional. Da Investiga\u00e7\u00e3o \u00e0s Pr\u00e1ticas, 33(1), 77\u201396."},{"key":"340957","unstructured":"Redmond, A. (2009). Prospective elementary teachers\u2019 division of fractions understanding: A mixed methods study (Doctoral thesis, University of Phoenix)."},{"key":"340958","unstructured":"Ribeiro, M. (2018). Das generalidades \u00e0s especificidades do conhecimento do professor que ensina matem\u00e1tica: Metodologias na conceitualiza\u00e7\u00e3o (entender e desenvolver) do conhecimento interpretativo. In Abordagens te\u00f3ricas e metodol\u00f3gicas nas pesquisas em educa\u00e7\u00e3o matem\u00e1tica (Vol. 13, pp. 167\u2013185). Biblioteca do Educador \/ SBEM."},{"key":"340959","doi-asserted-by":"crossref","unstructured":"Ribeiro, M., Almeida, A., & Mellone, M. (2021). Conceitualizando tarefas formativas para desenvolver as especificidades do conhecimento interpretativo e especializado do professor. Perspectivas da Educa\u00e7\u00e3o Matem\u00e1tica, 14(35), 1\u201332.","DOI":"10.46312\/pem.v14i35.13263"},{"key":"340960","unstructured":"Rizvi, N. F., & Lawson, M. J. (2007). Prospective teachers\u2019 knowledge: Concept of division. International Education Journal, 8(2), 377\u2013392. https:\/\/files.eric.ed.gov\/fulltext\/EJ834275.pdf"},{"key":"340961","unstructured":"Segovia, I., Castro, E., Castro, E. y Rico, L. (1989). Estimaci\u00f3n en c\u00e1lculo y medida. Madrid: S\u00edntesis."},{"key":"340962","unstructured":"Segovia, I., & Castro, E. (2009). La estimaci\u00f3n en el c\u00e1lculo y en la medida. Electronic Journal of Research in Educational Psychology, 17(1), 449-536."},{"key":"340963","unstructured":"Serrazina, L., & Rodrigues, M. (2018). Forma\u00e7\u00e3o de professores e desenvolvimento do sentido do n\u00famero. In R. F. Carneiro, A. C. Souza, & L. F. Bertini (Orgs.), A matem\u00e1tica nos anos iniciais do ensino fundamental: Pr\u00e1ticas de sala de aula e de forma\u00e7\u00e3o de professores (pp. 138-162). Sociedade Brasileira de Educa\u00e7\u00e3o Matem\u00e1tica."},{"key":"340964","unstructured":"Sharp, J.; Garofalo, J.; Adams, B. (2002). Children\u2019s development of meaningful fraction algorithms: a kid\u2019s cookies and a puppy\u2019s pill. In B. Litwiller, G. Bright (Orgs.), Making sense of fractions, ratios, and proportions: Yearbook (pp.18-28). NCTM."},{"key":"340965","unstructured":"Sharon, V. V., Swarthout, M. B. (2014, 27 February - 01 March). Evaluating instruction for developing conceptual understanding of fraction division. [Artigo]. 41th Annual Meeting of the Research Council on Mathematics Learning. San Antonio, Texas."},{"key":"340966","doi-asserted-by":"crossref","unstructured":"Siegler, R. S., & Lortie-Forgues, H. (2017). Hard lessons: Why rational number arithmetic is so difficult for so many people. Current Directions in Psychological Science, 26(4), 346\u2013351. https:\/\/doi.org\/10.1177\/0963721417700129","DOI":"10.1177\/0963721417700129"},{"key":"340967","doi-asserted-by":"crossref","unstructured":"Simon, M. A. (1993). Prospective Elementary Teachers\u2019 Knowledge of Division. Journal for Research in Mathematics Education, 24(3), 233-254.","DOI":"10.2307\/749346"},{"key":"340968","doi-asserted-by":"crossref","unstructured":"Sosa, L., Guzm\u00e1n, M. V., & Ribeiro, M. (2019). Conhecimento do professor sobre dificuldades de aprendizagem no t\u00f3pico adi\u00e7\u00e3o de express\u00f5es alg\u00e9bricas no Ensino M\u00e9dio. Educa\u00e7\u00e3o Matem\u00e1tica Pesquisa, 21(3), 369-397.","DOI":"10.23925\/1983-3156.2019vol21i3p369-397"},{"key":"340969","doi-asserted-by":"crossref","unstructured":"Tirosh, D. (2000). Enhancing prospective teachers\u2019 knowledge of children\u2019s conceptions: The case of division of fractions. Journal for Research of Mathematics Education, 31(1) 5-25.","DOI":"10.2307\/749817"}],"container-title":["TANGRAM - Revista de Educa\u00e7\u00e3o Matem\u00e1tica"],"original-title":[],"link":[{"URL":"https:\/\/ojs.ufgd.edu.br\/tangram\/article\/download\/19232\/11623","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/ojs.ufgd.edu.br\/tangram\/article\/download\/19232\/11623","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T18:06:51Z","timestamp":1771956411000},"score":1,"resource":{"primary":{"URL":"https:\/\/ojs.ufgd.edu.br\/tangram\/article\/view\/19232"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"references-count":54,"URL":"https:\/\/doi.org\/10.30612\/tangram.v9i1.19232","relation":{},"ISSN":["2595-0967"],"issn-type":[{"value":"2595-0967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,27]]}}}