<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1517-9702</journal-id>
<journal-title><![CDATA[Educação e Pesquisa]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. Pesqui.]]></abbrev-journal-title>
<issn>1517-9702</issn>
<publisher>
<publisher-name><![CDATA[Faculdade de Educação da Universidade de São Paulo]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1517-97022023000100669</article-id>
<article-id pub-id-type="doi">10.1590/s1678-4634202349261007</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Saber e ensinar frações: concepções e práticas de professores do ensino fundamental 					]]></article-title>
<article-title xml:lang="en"><![CDATA[Knowing and teaching fractions: conceptions and practices of elementary school teachers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cardoso]]></surname>
<given-names><![CDATA[Paula]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mamede]]></surname>
<given-names><![CDATA[Ema]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade do Minho  ]]></institution>
<addr-line><![CDATA[Braga ]]></addr-line>
<country>Portugal</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<volume>49</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S1517-97022023000100669&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S1517-97022023000100669&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S1517-97022023000100669&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O saber do professor determina a qualidade das suas práticas. Porém, nem sempre o professor consegue colocar em prática as suas ideias. No caso particular dos números racionais, reconhece-se que esse é um tópico importante, mas também difícil de ensinar. Mais vezes do que o desejado, assistimos a um desalinhamento entre as ideias dos professores sobre as frações e as suas ideias para o ensino desses números. Este artigo analisa as concepções e ideias sobre as práticas dos professores do 1º. ciclo do ensino básico (anos iniciais do ensino fundamental) relativamente às frações, procurando responder às seguintes questões: 1) Que ideias têm os professores sobre as frações? 2) Como entendem que deve ser o seu ensino? Para o efeito, foram entrevistados 31 professores do ensino público português, com diversos anos de experiência no ensino. Foi conduzida uma entrevista individual semiestruturada, que procurou explorar conceitos e propriedades dos números racionais, em particular das frações, e a resolução de problemas envolvendo esses números. Os resultados obtidos evidenciam fragilidades dos docentes no conhecimento matemático sobre o conceito de fração, nomeadamente no domínio dos diferentes significados de fração, e na tradução dos diferentes modos de representação de frações. Na resolução de problemas envolvendo frações para a sala de aula, identificaram-se dificuldades, particularmente em situações que envolviam quantidades discretas e na marcação de números fracionários na reta numérica. Esses resultados parecem apelar a um ideal de formação contínua de professores que possa ir apoiando e atualizando as suas práticas letivas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract A teacher&#8217;s knowledge determines the quality of his or her practices. However, a teacher is not always able to put her or his ideas into practice. Concerning rational numbers, it is recognized that this is an important topic, a difficult one to teach, though. Often, we see a misalignment between teachers&#8217; ideas about fractions and their ideas about how to teach this topic. This paper analyses elementary teachers&#8217; conceptions and ideas about practices regarding fractions, whose goal is to answer the following questions: 1) What ideas do teachers have about fractions? 2) How do they understand their teaching should be? For this purpose, thirty-one (31) Portuguese elementary teachers from public schools, with several years of teaching experience, were interviewed. An individual semi-structured interview was conducted, seeking to explore concepts and properties of fractions as well as problem-solving involving fractions. The results obtained revealed teachers&#8217; weaknesses in mathematical knowledge associated with the concept of fraction, namely, in the domain of the different meanings of fraction, as well as in the interpretation of the different ways of representing fractions. Regarding problem-solving related to fractions, teachers&#8217; weaknesses were also identified, particularly in situations involving discrete quantities and in marking fractional numbers on the number line. These results seem to appeal to an ideal of teacher training capable of continuously supporting and updating teaching practices.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Ensinar frações]]></kwd>
<kwd lng="pt"><![CDATA[Concepções dos professores]]></kwd>
<kwd lng="pt"><![CDATA[Conhecimento didático]]></kwd>
<kwd lng="pt"><![CDATA[Ensino fundamental]]></kwd>
<kwd lng="en"><![CDATA[Teaching fractions]]></kwd>
<kwd lng="en"><![CDATA[Teachers&#8217; conceptions]]></kwd>
<kwd lng="en"><![CDATA[Didactic knowledge]]></kwd>
<kwd lng="en"><![CDATA[Elementary school]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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