{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T08:39:44Z","timestamp":1771922384219,"version":"3.50.1"},"reference-count":39,"publisher":"FapUNIFESP (SciELO)","license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"am","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Educ. Pesqui."],"abstract":"<jats:p>Resumo O saber do professor determina a qualidade das suas pr\u00e1ticas. Por\u00e9m, nem sempre o professor consegue colocar em pr\u00e1tica as suas ideias. No caso particular dos n\u00fameros racionais, reconhece-se que esse \u00e9 um t\u00f3pico importante, mas tamb\u00e9m dif\u00edcil de ensinar. Mais vezes do que o desejado, assistimos a um desalinhamento entre as ideias dos professores sobre as fra\u00e7\u00f5es e as suas ideias para o ensino desses n\u00fameros. Este artigo analisa as concep\u00e7\u00f5es e ideias sobre as pr\u00e1ticas dos professores do 1\u00ba. ciclo do ensino b\u00e1sico (anos iniciais do ensino fundamental) relativamente \u00e0s fra\u00e7\u00f5es, procurando responder \u00e0s seguintes quest\u00f5es: 1) Que ideias t\u00eam os professores sobre as fra\u00e7\u00f5es? 2) Como entendem que deve ser o seu ensino? Para o efeito, foram entrevistados 31 professores do ensino p\u00fablico portugu\u00eas, com diversos anos de experi\u00eancia no ensino. Foi conduzida uma entrevista individual semiestruturada, que procurou explorar conceitos e propriedades dos n\u00fameros racionais, em particular das fra\u00e7\u00f5es, e a resolu\u00e7\u00e3o de problemas envolvendo esses n\u00fameros. Os resultados obtidos evidenciam fragilidades dos docentes no conhecimento matem\u00e1tico sobre o conceito de fra\u00e7\u00e3o, nomeadamente no dom\u00ednio dos diferentes significados de fra\u00e7\u00e3o, e na tradu\u00e7\u00e3o dos diferentes modos de representa\u00e7\u00e3o de fra\u00e7\u00f5es. Na resolu\u00e7\u00e3o de problemas envolvendo fra\u00e7\u00f5es para a sala de aula, identificaram-se dificuldades, particularmente em situa\u00e7\u00f5es que envolviam quantidades discretas e na marca\u00e7\u00e3o de n\u00fameros fracion\u00e1rios na reta num\u00e9rica. Esses resultados parecem apelar a um ideal de forma\u00e7\u00e3o cont\u00ednua de professores que possa ir apoiando e atualizando as suas pr\u00e1ticas letivas.<\/jats:p>","DOI":"10.1590\/s1678-4634202349261007","type":"journal-article","created":{"date-parts":[[2023,7,10]],"date-time":"2023-07-10T16:41:14Z","timestamp":1689007274000},"source":"Crossref","is-referenced-by-count":2,"title":["Saber e ensinar fra\u00e7\u00f5es: concep\u00e7\u00f5es e pr\u00e1ticas de professores do ensino fundamental"],"prefix":"10.1590","volume":"49","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5798-7107","authenticated-orcid":false,"given":"Paula","family":"Cardoso","sequence":"first","affiliation":[{"name":"Universidade do Minho,  Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1623-8406","authenticated-orcid":false,"given":"Ema","family":"Mamede","sequence":"additional","affiliation":[{"name":"Universidade do Minho,  Portugal"}]}],"member":"530","published-online":{"date-parts":[[2023]]},"reference":[{"issue":"3","key":"ref1","first-page":"14","article-title":"Knowing mathematics for teaching. Who knows mathematics well enough to teach third grade, and how can we decide?","volume":"29","author":"Ball Deborah","year":"2005","journal-title":"American Educator"},{"key":"ref2","series-title":"Handbook of research on teaching","first-page":"433","volume-title":"Research on teaching mathematics: the unsolved problem of teachers\u2019 mathematical knowledge","author":"Ball Deborah","year":"2001"},{"issue":"5","key":"ref3","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1177\/0022487108324554","article-title":"Content knowledge for teaching: what makes it special?","volume":"59","author":"Ball Deborah","year":"2008","journal-title":"Journal of Teacher Education"},{"key":"ref4","series-title":"Handbook of research on mathematics teaching and learning","first-page":"296","volume-title":"Rational number, ratio, and proportion","author":"Behr Merlyn","year":"1992"},{"key":"ref5","series-title":"Acquisition of mathematics concepts and processes","first-page":"92","volume-title":"Rational-number concepts","author":"Behr Merlyn","year":"1983"},{"key":"ref6","series-title":"Investiga\u00e7\u00e3o qualitativa em educa\u00e7\u00e3o: uma introdu\u00e7\u00e3o \u00e0 teoria e aos m\u00e9todos","author":"Bogdan Robert","year":"2010"},{"key":"ref7","article-title":"Profissionalismo docente e estrat\u00e9gias para o seu fortalecimento: entrevista com Lee Shulman","volume":"45","author":"BORN B\u00e1rbara","year":"2019","journal-title":"Educa\u00e7\u00e3o e Pesquisa"},{"key":"ref8","series-title":"Ensinar fra\u00e7\u00f5es: um olhar sobre o conhecimento de professores do 1\u00ba. ciclo do ensino b\u00e1sico","author":"CARDOSO Paula","year":"2017"},{"key":"ref9","first-page":"452","author":"CARDOSO Paula","year":"2009"},{"key":"ref10","series-title":"Contributos para o desenvolvimento do sentido de n\u00famero racional","first-page":"247","volume-title":"Ensinar fra\u00e7\u00f5es nos primeiros anos de escolaridade","author":"CARDOSO Paula","year":"2021"},{"key":"ref11","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s10649-021-10033-4","article-title":"Teachers\u2019 conceptual understanding of fraction operations: results from a national sample of elementary school teachers","volume":"107","author":"COPUR-GENCTURK Yasemin","year":"2021","journal-title":"Educational Studies in Mathematics"},{"key":"ref12","series-title":"Programa de matem\u00e1tica do ensino b\u00e1sico","year":"2013"},{"key":"ref13","series-title":"Aprendizagens essenciais","year":"2018"},{"key":"ref14","series-title":"Handbook of research on teaching","first-page":"119","volume-title":"Qualitative methods in research on teaching","author":"ERICKSON Frederick","year":"1986","edition":"3"},{"key":"ref15","series-title":"Handbook of qualitative research","first-page":"105","volume-title":"Competing paradigms in qualitative research","author":"GUBA Egon","year":"1994"},{"key":"ref16","series-title":"Children\u2019s understanding of mathematics: 11-16","first-page":"66","volume-title":"Fractions","author":"Hart Kathleen","year":"1981"},{"key":"ref17","series-title":"Rational numbers: An integration of research","first-page":"49","volume-title":"Fractional Numbers: from quotient fields to recursive understanding","author":"Kieren Thomas","year":"1993"},{"key":"ref18","series-title":"Number and measurement: paper from a research workshop","first-page":"101","volume-title":"On the mathematical, cognitive and instructional foundations of rational numbers","author":"Kieren Thomas","year":"1976"},{"key":"ref19","series-title":"Second handbook of research and learning","first-page":"629","volume-title":"Rational numbers and proportional reasoning toward a theoretical framework for research","author":"LAMON Susan","year":"2007"},{"key":"ref20","series-title":"Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers","author":"LAMON Susan","year":"2006","edition":"2"},{"key":"ref21","first-page":"226","author":"Li Yeping","year":"2021"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"267","DOI":"10.2307\/749828","article-title":"Building on informal knowledge through instruction in a complex content domain: partitioning, units, and understanding multiplication of fractions","volume":"32","author":"Mack Nancy","year":"2001","journal-title":"Journal for Research in Mathematics Education"},{"key":"ref23","series-title":"The effects of situations on children\u2019s understanding of fractions","author":"MAMEDE Ema","year":"2007"},{"key":"ref24","series-title":"Quaderni de Ricerca In Didattica - 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