<?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>1983-1730</journal-id>
<journal-title><![CDATA[Ensino em Re-Vista]]></journal-title>
<abbrev-journal-title><![CDATA[Ensino em Re-Vista]]></abbrev-journal-title>
<issn>1983-1730</issn>
<publisher>
<publisher-name><![CDATA[Universidade Federal de Uberlândia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1983-17302023000100137</article-id>
<article-id pub-id-type="doi">10.14393/er-v30a2023-39</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[A contribuição da Engenharia Didática como aporte metodológico para o ensino de Probabilidade]]></article-title>
<article-title xml:lang="es"><![CDATA[El aporte de la Ingeniería Didáctica como aporte metodológico a la enseñanza de la Probabilidad]]></article-title>
<article-title xml:lang="en"><![CDATA[The contribution of Didactic Engineering as a methodological contribution to the teaching of Probability]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castilho]]></surname>
<given-names><![CDATA[Cristimara Rodrigues de]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Figueiredo]]></surname>
<given-names><![CDATA[Heloisa Almeida de]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodrigues]]></surname>
<given-names><![CDATA[Chang Kuo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade Federal de Juiz de Fora  ]]></institution>
<addr-line><![CDATA[Juiz de Fora MG]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade Federal do Rio de Janeiro  ]]></institution>
<addr-line><![CDATA[Niterói RJ]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidade Federal de Juiz de Fora  ]]></institution>
<addr-line><![CDATA[Juiz de Fora MG]]></addr-line>
<country>Brasil</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>30</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S1983-17302023000100137&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S1983-17302023000100137&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S1983-17302023000100137&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO Este artigo é parte de uma pesquisa realizada em uma escola da rede particular na cidade do Rio de Janeiro, com estudantes do sexto ano do ensino fundamental a partir da temática: experimentação por meio da probabilidade frequentista para verificação da probabilidade clássica. O objetivo desta pesquisa foi investigar as contribuições da abordagem metodológica qualitativa, subsidiada pela Engenharia Didática, para o ensino de probabilidade. Para tal, foi realizado com os estudantes, algumas experimentações, possibilitadas pelo uso de uma roleta tecnológica criada pelas autoras em um aplicativo que foi instalado nos celulares dos alunos previamente, que contava com espaços equiprováveis e não equiprováveis. Destaca-se que o trabalho com atividades experimentais que culminam a uma regularidade, pode trazer um movimento para a aprendizagem de probabilidades, além de manter o foco nas habilidades específicas da BNCC, potencializando o entendimento das ideias básicas de probabilidade, levando, assim, à compreensão que a abordagem metodológica qualitativa pode contribuir para o ensino desta temática.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Este articulo hace parte de una investigación realizada en una escuela de la red particular en la ciudad de Rio de Janeiro, con estudiantes de sexto año de escuela primaria a partir de la temática: experimentación por medio de la probabilidad frecuentista para la verificación de la probabilidad clásica. El objetivo de esta investigación fue poner en claro las contribuciones del enfoque cualitativo usando la ingeniera didáctica, para la enseñanza de la probabilidad. En este sentido, fue realizado con los estudiantes, algunas experimentaciones, posibilitadas por el uso de una ruleta tecnológica creada con un aplicativo para este estudio e instalada en sus celulares que contaba con espacios equiprobables y no equiprobables. Se destaca que el trabajo con actividades experimentales que culminan con regularidad, logrando traer un movimiento para el aprendizaje de la probabilidad, además de eso, mantener el foco en las habilidades especificas de la BNCC, potencializando el entendimiento de las ideas básicas de probabilidad, llevando así, a la comprensión que el enfoque cualitativo puede contribuir para la enseñanza de esta temática.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT This article is part of a research carried out in a private school in the city of Rio de Janeiro, with students in the sixth year of elementary school based on the theme: experimentation through frequentist probability to verify the classic probability. The objective of this research was to investigate the contributions of the qualitative methodological approach, subsidized by Didactic Engineering, for teaching probability. To this end, some experiments were carried out with the students, made possible by the use of a technological roulette wheel created in an application for this study and installed on their cell phones, which had equiprobable and non-equiprobable spaces. It is noteworthy that working with experimental activities that culminate in regularity can bring about a movement towards learning probabilities, in addition to keeping the focus on the specific skills of the BNCC, enhancing the understanding of the basic ideas of probability, thus leading to the understanding that the qualitative methodological approach can contribute to the teaching of this theme.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Educação Matemática]]></kwd>
<kwd lng="pt"><![CDATA[Educação Estatística]]></kwd>
<kwd lng="pt"><![CDATA[Probabilidade]]></kwd>
<kwd lng="pt"><![CDATA[Engenharia Didática]]></kwd>
<kwd lng="es"><![CDATA[Educación Matemática]]></kwd>
<kwd lng="es"><![CDATA[Educación Estadística]]></kwd>
<kwd lng="es"><![CDATA[Probabilidad]]></kwd>
<kwd lng="es"><![CDATA[Ingeniería Didáctica]]></kwd>
<kwd lng="en"><![CDATA[Mathematics Education]]></kwd>
<kwd lng="en"><![CDATA[Statistical Education]]></kwd>
<kwd lng="en"><![CDATA[Probability]]></kwd>
<kwd lng="en"><![CDATA[Didactic Engineering]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ALMOULOUD]]></surname>
<given-names><![CDATA[S. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Fundamentos da Didática da matemática]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Curitiba ]]></publisher-loc>
<publisher-name><![CDATA[UFPR]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ANDRÉ]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pesquisa em educação: buscando rigor e qualidade]]></article-title>
<source><![CDATA[Cadernos de pesquisa]]></source>
<year>2001</year>
<page-range>51-64</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ARAÚJO]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
<name>
<surname><![CDATA[BORBA]]></surname>
<given-names><![CDATA[M. C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Construindo pesquisas coletivamente em Educação Matemática]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[BORBA]]></surname>
<given-names><![CDATA[M. de C]]></given-names>
</name>
</person-group>
<source><![CDATA[Pesquisa qualitativa em educação matemática]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Belo Horizonte ]]></publisher-loc>
<publisher-name><![CDATA[Autêntica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ARTIGUE]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ingènierie Didactique]]></article-title>
<source><![CDATA[Recherches em Didactique dês athématiques]]></source>
<year>1988</year>
<volume>9</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>281-308</page-range><publisher-loc><![CDATA[Grenoble ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BITTAR]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[ABE]]></surname>
<given-names><![CDATA[S. T]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ensino de Probabilidades: a Articulação entre as visões clássica, frequentista e geométrica]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[COUTINHO]]></surname>
<given-names><![CDATA[C. de Q. S]]></given-names>
</name>
</person-group>
<source><![CDATA[Discussões sobre o ensino e a aprendizagem da probabilidade e da estatística na escola básica]]></source>
<year>2013</year>
<page-range>99-120</page-range><publisher-loc><![CDATA[Campinas, SP ]]></publisher-loc>
<publisher-name><![CDATA[Mercado das Letras]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<collab>BRASIL. Ministério da Educação</collab>
<source><![CDATA[Base Nacional Comum Curricular]]></source>
<year>2018</year>
<publisher-loc><![CDATA[Brasília ]]></publisher-loc>
<publisher-name><![CDATA[MEC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BRYANT]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[NUNES]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
</person-group>
<source><![CDATA[Children&#8217;s understanding of probability: a literature review]]></source>
<year>2012</year>
<publisher-name><![CDATA[Nuffield Foundation]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BÔAS]]></surname>
<given-names><![CDATA[S. G. V.]]></given-names>
</name>
<name>
<surname><![CDATA[KONTI]]></surname>
<given-names><![CDATA[K. C]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Base Nacional Comum Curricular: um olhar para Estatística e Probabilidade nos Anos Iniciais do Ensino Fundamental]]></article-title>
<source><![CDATA[Ensino em Re-Vista]]></source>
<year>2018</year>
<volume>25</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>984-1003</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BOGDAN]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[BIKLEN]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigação qualitativa em educação: uma introdução à teoria e aos métodos]]></source>
<year>1994</year>
<publisher-loc><![CDATA[Portugal ]]></publisher-loc>
<publisher-name><![CDATA[Porto editora]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[COUTINHO]]></surname>
<given-names><![CDATA[C. de Q]]></given-names>
</name>
</person-group>
<source><![CDATA[Introdução ao conceito de probabilidade por uma visão frequentista: Estudo Epistemológico e Didático]]></source>
<year>1996</year>
<publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
<publisher-name><![CDATA[EDUC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[COUTINHO]]></surname>
<given-names><![CDATA[C. de Q]]></given-names>
</name>
</person-group>
<source><![CDATA[Probabilidade Geométrica: Um contexto para a modelização e a simulação em situações aleatórias com Cabri]]></source>
<year>2002</year>
<conf-name><![CDATA[ Anais... ANPED]]></conf-name>
<conf-date>2002</conf-date>
<conf-loc>Caxambu, MG </conf-loc>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[COUTINHO]]></surname>
<given-names><![CDATA[C. de Q]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conceitos probabilísticos: quais contextos a história nos aponta?]]></article-title>
<source><![CDATA[REVEMAT - Revista Eletrônica de Educação Matemática]]></source>
<year>2007</year>
<volume>2</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>50-67</page-range><publisher-loc><![CDATA[Florianópolis ]]></publisher-loc>
<publisher-name><![CDATA[UFSC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FREIRE]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<source><![CDATA[Pedagogia da autonomia: saberes necessários à prática educativa]]></source>
<year>2005</year>
<publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
<publisher-name><![CDATA[Paz e Terra]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[GAL]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Towards &#8220;probability literacy" for all citizens: Building blocks and instructional dilemmas]]></article-title>
<source><![CDATA[Exploring probability in school]]></source>
<year>2005</year>
<page-range>39-63</page-range><publisher-loc><![CDATA[Boston, MA ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[LOPES]]></surname>
<given-names><![CDATA[C. E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[O ensino da estatística e da probabilidade na educação básica e a formação dos professores]]></article-title>
<source><![CDATA[Cadernos Cedes]]></source>
<year>2008</year>
<volume>28</volume>
<numero>74</numero>
<issue>74</issue>
<page-range>57-73</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[MACHADO]]></surname>
<given-names><![CDATA[S. D. A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Engenharia Didática]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[MACHADO]]></surname>
<given-names><![CDATA[S. D. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Educação Matemática: Uma introdução]]></source>
<year>2002</year>
<edition>2</edition>
<page-range>197-208</page-range><publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
<publisher-name><![CDATA[Educ]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[NETO]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<source><![CDATA[Cálculo de Probabilidades I]]></source>
<year>2016</year>
<publisher-loc><![CDATA[Juiz de Fora ]]></publisher-loc>
<publisher-name><![CDATA[UFJF]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[PONTE]]></surname>
<given-names><![CDATA[J. P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Tarefas no ensino e na aprendizagem da Matemática]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[PONTE]]></surname>
<given-names><![CDATA[J. P]]></given-names>
</name>
</person-group>
<source><![CDATA[Práticas Profissionais dos Professores de Matemática]]></source>
<year>2014</year>
<edition>1</edition>
<publisher-name><![CDATA[Instituto de Educação da Universidade de Lisboa]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[PONTES]]></surname>
<given-names><![CDATA[M. M]]></given-names>
</name>
<name>
<surname><![CDATA[LIMA]]></surname>
<given-names><![CDATA[D. S. S. M]]></given-names>
</name>
<name>
<surname><![CDATA[VASCONCELOS]]></surname>
<given-names><![CDATA[F. V]]></given-names>
</name>
<name>
<surname><![CDATA[VASCONCELOS]]></surname>
<given-names><![CDATA[A. K. P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A temática &#8216;Probabilidade e Estatística&#8217; nos anos iniciais do Ensino Fundamental a partir da promulgação da BNCC: percepções pedagógicas]]></article-title>
<source><![CDATA[Revista de Estudos e Pesquisas sobre Ensino Tecnológico (EDUCITEC)]]></source>
<year>2019</year>
<volume>5</volume>
<numero>12</numero>
<issue>12</issue>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[SAVIANI]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[GALVÃO]]></surname>
<given-names><![CDATA[A. C]]></given-names>
</name>
</person-group>
<source><![CDATA[Educação na Pandemia: a falácia do ensino remoto]]></source>
<year>2021</year>
<volume>XXXI</volume>
<publisher-name><![CDATA[Universidade e Sociedade ANDES-SN]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[SILVA]]></surname>
<given-names><![CDATA[I. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Probabilidades: a visão laplaciana e a visão frequentista na introdução do conceito]]></source>
<year>2002</year>
<publisher-loc><![CDATA[São Paulo ]]></publisher-loc>
<publisher-name><![CDATA[Pontifícia Universidade Católica de São Paulo]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
