<?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>2177-6059</journal-id>
<journal-title><![CDATA[Roteiro]]></journal-title>
<abbrev-journal-title><![CDATA[Roteiro]]></abbrev-journal-title>
<issn>2177-6059</issn>
<publisher>
<publisher-name><![CDATA[Universidade do Oeste de Santa Catarina]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2177-60592018000401001</article-id>
<article-id pub-id-type="doi">10.18593/r.v43i3.16083</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Como ensinar frações? Práticas que (in)formam o professor que ensina matemática]]></article-title>
<article-title xml:lang="en"><![CDATA[How to teach fractions? Practices that (in)form teachers teaching mathematics]]></article-title>
<article-title xml:lang="es"><![CDATA[¿Cómo enseñar fracciones? Prácticas que (in)forman el profesor que enseña matemática]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pozzobon]]></surname>
<given-names><![CDATA[Marta Cristina Cezar]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Oliveira]]></surname>
<given-names><![CDATA[Cláudio José de]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Federal do Pampa (Unipampa) Curso de Pedagogia Programa de Pós-Graduação em Educação,]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade de Santa Cruz do Sul Programa de Pós-Graduação em Educação ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>09</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>09</month>
<year>2018</year>
</pub-date>
<volume>43</volume>
<numero>3</numero>
<fpage>1001</fpage>
<lpage>1026</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S2177-60592018000401001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S2177-60592018000401001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S2177-60592018000401001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo:  Neste artigo discute-se sobre a forma&#231;&#227;o do professor que ensina matem&#225;tica nos anos iniciais, em especial no que se refere ao ensino de fra&#231;&#245;es. O corpus de an&#225;lise selecionado para este texto se constitui do caderno de matem&#225;tica de um programa de forma&#231;&#227;o continuada de professores dos anos iniciais do Ensino Fundamental, de uma entrevista com uma professora de Did&#225;tica da Matem&#225;tica que atuou na forma&#231;&#227;o de professores na d&#233;cada de 1970 e de seu caderno de planejamento. Para realizar as an&#225;lises, adotamos uma perspectiva te&#243;rica p&#243;s-cr&#237;tica associada aos estudos de Ludwig Wittgenstein. O que defendemos &#233; que os conceitos s&#227;o produzidos a partir dos usos, em conformidade com suas regras gramaticais, e que os significados de uma palavra e os significados das proposi&#231;&#245;es matem&#225;ticas s&#227;o produzidos nos diferentes jogos de linguagem. Das an&#225;lises empreendidas no material, foram organizados dois enunciados: a) Ensinar fra&#231;&#245;es: &#8220;trazer um bolo&#8221; e &#8220;fazer um desenho&#8221; e b) &#8220;Lembrar seu significado&#8221; para ensinar o conceito de fra&#231;&#245;es. A partir desses enunciados, problematizamos que os conceitos matem&#225;ticos s&#227;o normas que independem do cotidiano e de aspectos emp&#237;ricos, intuitivos ou indutivos. Desse modo, sugerimos que o professor tenha conhecimento da natureza das proposi&#231;&#245;es matem&#225;ticas e se responsabilize pelo ensino de suas regras, n&#227;o trazendo a utilidade dos conceitos, mas as conven&#231;&#245;es produzidas pela linguagem matem&#225;tica.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract:  This article discusses the formation of the teacher who teaches mathematics in the initial years, especially in what concerns the teaching of fractions. The corpus of analysis selected for this text consists of the mathematics notebook of the continuing education program for teachers of the early years of Elementary School, an interview and a planning notebook of a Mathematics Didactics teacher who acted in the formation of teachers during the 1970s. In order to carry out the analyzes, we adopted a post-critical theoretical perspective associated with the studies of Ludwig Wittgenstein. What we defend is that concepts are produced from the uses, in accordance with their grammatical rules, and that the meanings of a word and the meanings of the mathematical propositions are produced in the different language games. From the analyzes undertaken in the material, two statements were organized: a) Teach fractions: "bring a cake" and "make a drawing" and b) "Remember its meaning" to teach the concept of fractions. From these statements, we problematize that the mathematical concepts are norms that are independent of the quotidian and of empirical, intuitive or inductive aspects. In this way, we suggest that the teacher be aware of the nature of mathematical propositions and be responsible for the teaching of their rules, not bringing the usefulness of the concepts, but the conventions produced by the mathematical language.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen:  Este art&#237;culo discute la formaci&#243;n del profesor que ense&#241;a matem&#225;ticas en los a&#241;os iniciales, en especial, en lo que se refiere a la ense&#241;anza de fracciones. El corpus de an&#225;lisis seleccionado para este texto se constituye del cuaderno de matem&#225;ticas del programa de formaci&#243;n continuada de profesores de los a&#241;os iniciales de la Ense&#241;anza Fundamental, de una entrevista y de un cuaderno de planificaci&#243;n de una profesora de Did&#225;ctica de la Matem&#225;tica, que actu&#243; en la formaci&#243;n de profesores en la d&#233;cada de 1970. Para realizar los an&#225;lisis, adoptamos una perspectiva te&#243;rica post-cr&#237;tica asociada a los estudios de Ludwig Wittgenstein. Lo que defendemos es que los conceptos son producidos a partir de los usos, de acuerdo con sus reglas gramaticales, y que los significados de una palabra y los significados de las proposiciones matem&#225;ticas son producidos en los diferentes juegos de lenguaje. De los an&#225;lisis emprendidos en el material se organizaron dos enunciados: a) Ense&#241;ar fracciones: "traer un pastel" y "hacer un dibujo" y b) "Recordar su significado" para ense&#241;ar el concepto de fracciones. A partir de estos enunciados, problematizamos que los conceptos matem&#225;ticos son normas que independen de lo cotidiano y de aspectos emp&#237;ricos, intuitivos o inductivos. De este modo, sugerimos que el profesor tenga conocimiento de la naturaleza de las proposiciones matem&#225;ticas y se responsabilice por la ense&#241;anza de sus reglas, no trayendo la utilidad de los conceptos, sino las convenciones producidas por el lenguaje matem&#225;tico.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Ensino de frações]]></kwd>
<kwd lng="pt"><![CDATA[Anos iniciais]]></kwd>
<kwd lng="pt"><![CDATA[Educação Matemática]]></kwd>
<kwd lng="pt"><![CDATA[Práticas.]]></kwd>
<kwd lng="en"><![CDATA[Teaching of fractions]]></kwd>
<kwd lng="en"><![CDATA[Early years]]></kwd>
<kwd lng="en"><![CDATA[Mathematical education]]></kwd>
<kwd lng="en"><![CDATA[Practices.]]></kwd>
<kwd lng="es"><![CDATA[Enseñanza de fracciones]]></kwd>
<kwd lng="es"><![CDATA[Años iniciales]]></kwd>
<kwd lng="es"><![CDATA[Educaciones Matemáticas]]></kwd>
<kwd lng="es"><![CDATA[Prácticas.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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