<?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>0100-3143</journal-id>
<journal-title><![CDATA[Educação e Realidade]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. Real.]]></abbrev-journal-title>
<issn>0100-3143</issn>
<publisher>
<publisher-name><![CDATA[Universidade Federal do Rio Grande do Sul - Faculdade de Educação]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0100-31432018000100293</article-id>
<article-id pub-id-type="doi">10.1590/2175-623664750</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[A Resolução de Problemas de Produto Cartesiano por Alunos do Ensino Fundamental]]></article-title>
<article-title xml:lang="en"><![CDATA[Problems of Cartesian Product Solved by Elementary School Students]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Magina]]></surname>
<given-names><![CDATA[Sandra Maria Pinto]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Spinillo]]></surname>
<given-names><![CDATA[Alina Galvão]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Melo]]></surname>
<given-names><![CDATA[Lianny Milenna de Sá]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Estadual de Santa Cruz  ]]></institution>
<addr-line><![CDATA[Ilhéus BA]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade Federal de Pernambuco  ]]></institution>
<addr-line><![CDATA[Recife PE]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Centro de Referência de Assistência Social de Ipojuca  ]]></institution>
<addr-line><![CDATA[Ipojuca PE]]></addr-line>
<country>Brazil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2018</year>
</pub-date>
<volume>43</volume>
<numero>1</numero>
<fpage>293</fpage>
<lpage>311</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S0100-31432018000100293&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S0100-31432018000100293&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S0100-31432018000100293&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo:  O estudo investigou a resolu&#231;&#227;o de problemas de produto cartesiano diretos (requer a multiplica&#231;&#227;o para sua resolu&#231;&#227;o) e inverso (requer a divis&#227;o para sua resolu&#231;&#227;o) por alunos do Ensino Fundamental, examinando o n&#237;vel de complexidade deles e os procedimentos adotados por esses alunos em fun&#231;&#227;o do tipo de problema. Solicitou-se que 269 alunos do 3&#186; ao 5&#186; ano, entre 8 e 10 anos, resolvessem um problema de produto cartesiano direto e outro inverso. Como esperado, o problema inverso foi o mais dif&#237;cil. As estrat&#233;gias mostraram que os n&#237;veis de racioc&#237;nio combinat&#243;rio variavam em fun&#231;&#227;o do tipo de problema. Observou-se uma progress&#227;o no processo de resolu&#231;&#227;o de problemas de produto cartesiano diretos, mas n&#227;o nos inversos. ]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The study investigated the solution of direct (which requires multiplication for its resolution) and inverse (which requires division for its resolution) Cartesian product problems by elementary education students, examining the level of problem complexity and the children procedures according to the type of problem. A total of 269 8 and 10 year-old students attending from 3rd to 5th grade, were asked 8 and 10 years to solve direct and inverse Cartesian product problems. As expected, the inverse problem was the most difficult one. The strategies showed that levels of combinatorial reasoning vary according to the type of problem. It was also found a progression in the solution of direct Cartesian product problems, but not in relation to the solution of inverse problems. ]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Resolução de Problemas]]></kwd>
<kwd lng="pt"><![CDATA[Produto Cartesiano]]></kwd>
<kwd lng="pt"><![CDATA[Ensino Fundamental]]></kwd>
<kwd lng="en"><![CDATA[Problem Solving]]></kwd>
<kwd lng="en"><![CDATA[Cartesian Product Problems]]></kwd>
<kwd lng="en"><![CDATA[Elementary Education]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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