<?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>0102-7735</journal-id>
<journal-title><![CDATA[Revista Educação em Questão]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Educ. Questão]]></abbrev-journal-title>
<issn>0102-7735</issn>
<publisher>
<publisher-name><![CDATA[Universidade Federal do Rio Grande do Norte]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0102-77352020000300012</article-id>
<article-id pub-id-type="doi">10.21680/1981-1802.2020v58n57id20024</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Raciocínio proporcional na matemática escolar]]></article-title>
<article-title xml:lang="en"><![CDATA[Proportional reasoning in school mathematic]]></article-title>
<article-title xml:lang="es"><![CDATA[Razonamiento proporcional en matemática escolar]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Faria]]></surname>
<given-names><![CDATA[Rejane Waiandt Schuwartz de Carvalho]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Maltempi]]></surname>
<given-names><![CDATA[Marcus Vinicius]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Federal de Viçosa (Brasil) Departamento de Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade Estadual Paulista (Brasil) Instituto de Geociências e Ciências Exatas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brasil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>07</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>07</month>
<year>2020</year>
</pub-date>
<volume>58</volume>
<numero>57</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S0102-77352020000300012&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S0102-77352020000300012&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S0102-77352020000300012&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Este artigo objetiva discutir a relevância do raciocínio na matemática escolar e os elementos necessários a uma atividade que privilegie o raciocínio proporcional. Para tanto, discutimos o lugar de destaque da sequência &#8220;definição &#8594; exemplos &#8594; exercícios&#8221; na matemática escolar. Historicamente, a memorização tem sido valorizada no cenário educacional brasileiro e tem roubado do raciocínio o papel de protagonista. Abordamos a relevância do raciocínio proporcional na matemática escolar, direcionando a discussão para o processo de elaboração de uma atividade que o estimule, com base nos pressupostos da metodologia qualitativa de pesquisa. As conclusões indicam que os elementos necessários para estimular o raciocínio proporcional são: formular atividades intencionais, com foco no raciocínio qualitativo; elaborar questões pautadas na estrutura multiplicativa; privilegiar situações relativas ao cotidiano, com caráter transdisciplinar; propor uma visão abrangente e integrada das vertentes da matemática utilizando tecnologias digitais em uma perspectiva intradisciplinar.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This article aims to discuss the relevance of reasoning in school mathematics and the required elements for an activity that privileges proportional reasoning. To this end, we discuss the prominent place of sequence &#8220;definition &#8594; examples &#8594; exercises&#8221; in school mathematics. Historically, memorization has been valued in the Brazilian educational scenario and has stolen the protagonist role from reasoning. We address the relevance of proportional reasoning in school mathematics, directing the discussion to the process of elaborating an activity that stimulates it, based on the assumptions of the qualitative research methodology. The conclusions indicate that the necessary elements to stimulate proportional reasoning are: to formulate intentional activities, focusing on qualitative reasoning; elaborate questions based on the multiplicative structure; to privilege situations related to daily life, with transdisciplinary character; to propose a comprehensive and integrated view of the aspects of mathematic using digital technologies from an intradisciplinary perspective.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Este artículo tiene como objetivo discutir la relevancia del razonamiento en la matemática escolar y los elementos necesarios para una actividad que privilegie el razonamiento proporcional. Con este fin, discutimos el lugar prominente de la secuencia &#8221;definición &#8594; ejemplos &#8594; ejercicios&#8221; en las matemáticas escolares. Históricamente, la memorización ha sido valorada en la escena educativa brasileña y ha robado el papel de protagonista al razonamiento. Abordamos la relevancia del razonamiento proporcional en la matemática escolar, dirigiendo la discusión al proceso de elaboración de una actividad que lo estimule, basado en los supuestos de la metodología de investigación cualitativa. Las conclusiones indican que los elementos necesarios para estimular el razonamiento proporcional son: formular actividades intencionales, enfocándose en el razonamiento cualitativo; elaborar preguntas basadas en la estructura multiplicativa; privilegiar las situaciones relacionadas con la vida cotidiana, con carácter transdisciplinario; proponer una visión integral e integrada de los aspectos de la matemática utilizando tecnologías digitales desde una perspectiva intradisciplinaria.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Memorização na matemática]]></kwd>
<kwd lng="pt"><![CDATA[Anos finais do ensino fundamental]]></kwd>
<kwd lng="pt"><![CDATA[Ensino de matemática]]></kwd>
<kwd lng="pt"><![CDATA[Educação matemática]]></kwd>
<kwd lng="en"><![CDATA[Memorization in mathematics]]></kwd>
<kwd lng="en"><![CDATA[Final years of elementary school]]></kwd>
<kwd lng="en"><![CDATA[Mathematic teaching]]></kwd>
<kwd lng="en"><![CDATA[Mathematic education]]></kwd>
<kwd lng="es"><![CDATA[Memorización en matemáticas]]></kwd>
<kwd lng="es"><![CDATA[Años finales de la escuela primaria]]></kwd>
<kwd lng="es"><![CDATA[Enseñanza de la matemática]]></kwd>
<kwd lng="es"><![CDATA[Educación matemática]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BENNEMANN]]></surname>
<given-names><![CDATA[Marcio]]></given-names>
</name>
<name>
<surname><![CDATA[ALLEVATO]]></surname>
<given-names><![CDATA[Norma Suely Gomes]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Educação matemática crítica]]></article-title>
<source><![CDATA[Revista de Produção Discente em Educação Matemática]]></source>
<year>2012</year>
<volume>1</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>103-12</page-range><publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BOAVIDA]]></surname>
<given-names><![CDATA[Ana Maria]]></given-names>
</name>
<name>
<surname><![CDATA[PAIVA]]></surname>
<given-names><![CDATA[Ana Luísa]]></given-names>
</name>
<name>
<surname><![CDATA[CEBOLA]]></surname>
<given-names><![CDATA[Graça]]></given-names>
</name>
<name>
<surname><![CDATA[VALE]]></surname>
<given-names><![CDATA[Isabel]]></given-names>
</name>
<name>
<surname><![CDATA[PIMENTEL]]></surname>
<given-names><![CDATA[Teresa]]></given-names>
</name>
</person-group>
<source><![CDATA[A experiência matemática no ensino básico]]></source>
<year>2008</year>
<publisher-loc><![CDATA[Lisboa ]]></publisher-loc>
<publisher-name><![CDATA[DGIDC-ME]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;AMBROSIO]]></surname>
<given-names><![CDATA[Beatriz Silva]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Como ensinar matemática hoje? Temas e debates]]></article-title>
<source><![CDATA[ISBEM]]></source>
<year>1989</year>
<volume>2</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>15-9</page-range><publisher-loc><![CDATA[Brasília ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;AMBROSIO]]></surname>
<given-names><![CDATA[Ubiratan]]></given-names>
</name>
</person-group>
<source><![CDATA[Etnomatemática: elo entre as tradições e a modernidade]]></source>
<year>2005</year>
<publisher-loc><![CDATA[Belo Horizonte ]]></publisher-loc>
<publisher-name><![CDATA[Autêntica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;AMBROSIO]]></surname>
<given-names><![CDATA[Ubiratan]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Transdisciplinaridade como uma resposta à sustentabilidade]]></article-title>
<source><![CDATA[Revista Terceiro Incluído: Transdisciplinaridade e Educação Ambiental]]></source>
<year>2011</year>
<volume>1</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-13</page-range><publisher-loc><![CDATA[Goiânia ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FARIA]]></surname>
<given-names><![CDATA[Rejane Waiandt Schuwartz de Carvalho]]></given-names>
</name>
</person-group>
<source><![CDATA[Raciocínio proporcional: integrando aritmética, geometria e álgebra com o GeoGebra]]></source>
<year>2016</year>
<page-range>280</page-range><publisher-loc><![CDATA[Rio Claro ]]></publisher-loc>
<publisher-name><![CDATA[Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista Júlio de Mesquita Filho]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FARIA]]></surname>
<given-names><![CDATA[Rejane Waiandt Schuwartz de Carvalho]]></given-names>
</name>
<name>
<surname><![CDATA[MALTEMPI]]></surname>
<given-names><![CDATA[Marcus Vinicius]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Intradisciplinaridade Matemática com GeoGebra na Matemática Escolar]]></article-title>
<source><![CDATA[Bolema]]></source>
<year>2018</year>
<volume>32</volume>
<numero>62</numero>
<issue>62</issue>
<page-range>348-67</page-range><publisher-loc><![CDATA[Rio Claro ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FERNÁNDEZ]]></surname>
<given-names><![CDATA[Ceneida]]></given-names>
</name>
<name>
<surname><![CDATA[LLINARES]]></surname>
<given-names><![CDATA[Salvador]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Relaciones implicativas entre las estrategias empleadas en la resolución de situaciones lineales y no lineales]]></article-title>
<source><![CDATA[Relime]]></source>
<year>2012</year>
<volume>15</volume>
<page-range>277-310</page-range><publisher-loc><![CDATA[Cidade do México ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FREIRE]]></surname>
<given-names><![CDATA[Paulo]]></given-names>
</name>
</person-group>
<source><![CDATA[Pedagogia do compromisso: América Latina e educação popular]]></source>
<year>2018</year>
<publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
<publisher-name><![CDATA[Paz e Terra]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FREIRE]]></surname>
<given-names><![CDATA[Paulo]]></given-names>
</name>
</person-group>
<source><![CDATA[Pedagogia do oprimido]]></source>
<year>1981</year>
<edition>9</edition>
<publisher-loc><![CDATA[Rio de Janeiro ]]></publisher-loc>
<publisher-name><![CDATA[Paz e Terra]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[LAMON]]></surname>
<given-names><![CDATA[Susan]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers]]></source>
<year>2005</year>
<edition>2</edition>
<publisher-loc><![CDATA[Mahwah, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[MALTEMPI]]></surname>
<given-names><![CDATA[Marcus Vinicius]]></given-names>
</name>
<name>
<surname><![CDATA[MENDES]]></surname>
<given-names><![CDATA[Ricardo de Oliveira]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[TECNOLOGIAS DIGITAIS NA SALA DE AULA: Por que não]]></article-title>
<source><![CDATA[Anais [...]]]></source>
<year>2016</year>
<conf-name><![CDATA[ CONGRESSO INTERNACIONAL DE TIC NA EDUCAÇÃO]]></conf-name>
<conf-date>4, 2016</conf-date>
<conf-loc>Lisboa </conf-loc>
<publisher-loc><![CDATA[Lisboa ]]></publisher-loc>
<publisher-name><![CDATA[Instituto de Educação da Universidade de Lisboa]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[MATA-PEREIRA]]></surname>
<given-names><![CDATA[Joana]]></given-names>
</name>
<name>
<surname><![CDATA[PONTE]]></surname>
<given-names><![CDATA[João Pedro da]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Promover o raciocínio matemático dos alunos: uma investigação baseada em design]]></article-title>
<source><![CDATA[Bolema]]></source>
<year>2018</year>
<volume>32</volume>
<numero>62</numero>
<issue>62</issue>
<page-range>781-801</page-range><publisher-loc><![CDATA[Rio Claro ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[NACARATO]]></surname>
<given-names><![CDATA[Adair Mendes]]></given-names>
</name>
<name>
<surname><![CDATA[MENGALI]]></surname>
<given-names><![CDATA[Brenda Leme Da Silva]]></given-names>
</name>
<name>
<surname><![CDATA[PASSOS]]></surname>
<given-names><![CDATA[Cármen Lúcia Brancaglion]]></given-names>
</name>
</person-group>
<source><![CDATA[A matemática nos anos Iniciais do ensino fundamental: tecendo fios do ensinar e do aprender]]></source>
<year>2009</year>
<publisher-loc><![CDATA[Belo Horizonte ]]></publisher-loc>
<publisher-name><![CDATA[Autêntica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[OLIVEIRA]]></surname>
<given-names><![CDATA[Ana Maria Rocha]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A contribuição da prática reflexiva para uma docência com profissionalidade]]></article-title>
<source><![CDATA[Boletim Técnico do Senac]]></source>
<year>2007</year>
<volume>33</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>46-61</page-range><publisher-loc><![CDATA[Rio de Janeiro ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[PONTE]]></surname>
<given-names><![CDATA[João Pedro da]]></given-names>
</name>
<name>
<surname><![CDATA[OLIVEIRA]]></surname>
<given-names><![CDATA[Hélía]]></given-names>
</name>
<name>
<surname><![CDATA[VARANDAS]]></surname>
<given-names><![CDATA[José Manuel]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[O contributo das tecnologias de informação e comunicação para o desenvolvimento do conhecimento e da identidade profissional]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[FIORENTINI]]></surname>
<given-names><![CDATA[Dario]]></given-names>
</name>
</person-group>
<source><![CDATA[Formação de professores de matemática: explorando novos caminhos com outros olhares]]></source>
<year>2008</year>
<publisher-loc><![CDATA[Campinas ]]></publisher-loc>
<publisher-name><![CDATA[Mercado de Letras]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[SOUZA]]></surname>
<given-names><![CDATA[Maria Cecilia Cortez Christiano]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Decorar, lembrar e repetir: o significado das práticas escolares na escola brasileira do final do século XIX]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[SOUSA]]></surname>
<given-names><![CDATA[Cynthia Pereira de]]></given-names>
</name>
</person-group>
<source><![CDATA[História da educação: processos, práticas e saberes]]></source>
<year>1998</year>
<publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
<publisher-name><![CDATA[Escrituras]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[VALENTE]]></surname>
<given-names><![CDATA[Wagner Rodrigues]]></given-names>
</name>
<name>
<surname><![CDATA[PINHEIRO]]></surname>
<given-names><![CDATA[Nara Vilma Lima]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Chega de decorar a Tabuada! As Cartas de Parker e a Árvore do Cálculo na ruptura de uma tradição]]></article-title>
<source><![CDATA[Educação Matemática em Revista]]></source>
<year>2015</year>
<volume>1</volume>
<numero>16</numero>
<issue>16</issue>
<page-range>22-37</page-range><publisher-loc><![CDATA[Brasília ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[VALENTE]]></surname>
<given-names><![CDATA[Wagner Rodrigues]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Os movimentos da matemática na Escola: do ensino de matemática para a educação matemática; da educação matemática para o ensino de matemática; do ensino de matemática para a Educação Matemática; da Educação Matemática para o Ensino de Matemática]]></article-title>
<source><![CDATA[Pensar a Educação em Revista]]></source>
<year>2016</year>
<volume>2</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>3-23</page-range><publisher-loc><![CDATA[Curitiba ]]></publisher-loc>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
