<?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>S1517-97022022000100752</article-id>
<article-id pub-id-type="doi">10.1590/s1678-4634202248236913por</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[O pensamento conceitual de fração: o modo de organização do ensino davydoviano]]></article-title>
<article-title xml:lang="en"><![CDATA[Conceptual thinking of fractions: the Davydovian mode of teaching organization]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Freitas]]></surname>
<given-names><![CDATA[Daiane de]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Damazio]]></surname>
<given-names><![CDATA[Ademir]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade do Extremo Sul Catarinense  ]]></institution>
<addr-line><![CDATA[Criciúma SC]]></addr-line>
<country>Brasil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<volume>48</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S1517-97022022000100752&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S1517-97022022000100752&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S1517-97022022000100752&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Este artigo se apresenta no contexto de organização do ensino numa perspectiva materialista histórica e dialética. Mais especificamente, sua referência é o ensino desenvolvimental, proposto por Davýdov e seus colaboradores. A delimitação se expressa na seguinte questão de pesquisa: quais as manifestações do movimento do pensamento conceitual de fração nas tarefas particulares do livro didático e de orientação ao professor, quando a referência é o modo davydoviano de organização do ensino? Nesta pesquisa bibliográfica, os dados de análise tomam como amostra cinco tarefas particulares extraídas do livro didático do 5º ano, baseadas na proposição de Davýdov, acompanhadas pelo livro de orientação ao professor. As três primeiras tarefas explicitam o movimento de redução do concreto ao abstrato; as demais revelam o movimento do pensamento de ascensão do abstrato ao concreto. O estudo revela que os processos de redução e ascensão direcionam o pensamento para a apropriação das relações essenciais que constituem o conceito de fração. A essência se manifesta no problema de medição, gerador da necessidade de subdivisão da unidade de medida, que constituirá a unidade intermediária. Os dois movimentos se caracterizam por processos mediados que levam o pensamento à abstração e à generalização das conexões internas constituintes da lei e da causa do conceito.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This article was produced in the context of teaching organization from a historical and dialectic perspective. More specifically, its main reference is the developmental teaching proposed by Davýdov and his collaborators. The specification can be expressed in the following research question: what are the manifestations of the movement of conceptual thinking of fractions in the particular tasks in textbooks and teacher&#8217;s guides, when their reference is the Davydovian mode of teaching organization? In this bibliographical research, the analyzed data represents a sample of five particular tasks taken from the 5th Year textbook, based on Davýdov&#8217;s proposal and accompanied by the teacher&#8217;s guide. The first three tasks reveal the movement of reduction from the concrete to the abstract; the remaining tasks reveal the movement of thought as an ascension from the abstract to the concrete. This study reveals that the processes of reduction and ascension direct thinking towards the acquisition of the essential relations constituting the concept of fractions. Essence manifests in the measurement problem which creates the need for a division of the unit of measurement that will establish an intermediary unit. Both movements are characterized by mediated processes leading thinking into the abstraction and generalization of the inner connections constituting the law and cause of the concept.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Fração]]></kwd>
<kwd lng="pt"><![CDATA[Proposição davydoviana]]></kwd>
<kwd lng="pt"><![CDATA[Movimentos do pensamento]]></kwd>
<kwd lng="en"><![CDATA[Fraction &#8211; Davydovian proposal &#8211; Thought movements]]></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[ALEKSANDROV]]></surname>
<given-names><![CDATA[Aleksandr Danilovich]]></given-names>
</name>
<name>
<surname><![CDATA[KOLMOGOROV]]></surname>
<given-names><![CDATA[Andrey]]></given-names>
</name>
<name>
<surname><![CDATA[LAVRENTYEV]]></surname>
<given-names><![CDATA[Mikhail Alekseevich]]></given-names>
</name>
</person-group>
<source><![CDATA[La matemática: su contenido, métodos y significado]]></source>
<year>1973</year>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Alianza Universidad]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[AMORIM]]></surname>
<given-names><![CDATA[Marlene Pires]]></given-names>
</name>
</person-group>
<source><![CDATA[Apropriação de significações do conceito de números racionais: um enfoque histórico-cultural. 2007]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Criciúma ]]></publisher-loc>
<publisher-name><![CDATA[Universidade do Extremo Sul Catarinense]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[DAVÍDOV]]></surname>
<given-names><![CDATA[Vasili]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Análisis de los principios didácticos de la escuela tradicional y posibles principios de enseñanza en el futuro próximo]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[SHUARE]]></surname>
<given-names><![CDATA[Marta]]></given-names>
</name>
</person-group>
<source><![CDATA[La psicología evolutiva y pedagógica en la URSS]]></source>
<year>1987</year>
<page-range>143-55</page-range><publisher-loc><![CDATA[Moscú ]]></publisher-loc>
<publisher-name><![CDATA[Progreso]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[DAVÍDOV]]></surname>
<given-names><![CDATA[Vasili]]></given-names>
</name>
</person-group>
<source><![CDATA[La enseñanza escolar y el desarrollo psíquico: investigación psicológica teórica y experimental]]></source>
<year>1988</year>
<publisher-loc><![CDATA[Moscú ]]></publisher-loc>
<publisher-name><![CDATA[Progreso]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[DAVÍDOV]]></surname>
<given-names><![CDATA[Vasili]]></given-names>
</name>
<name>
<surname><![CDATA[MÁRKOVA]]></surname>
<given-names><![CDATA[Aelita]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La concepción de la actividad de estudio de los escolares]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[SHUARE]]></surname>
<given-names><![CDATA[Marta]]></given-names>
</name>
</person-group>
<source><![CDATA[La psicología evolutiva y pedagógica en la URSS]]></source>
<year>1987</year>
<page-range>316-37</page-range><publisher-loc><![CDATA[Moscú ]]></publisher-loc>
<publisher-name><![CDATA[Progreso]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[DAVÝDOV]]></surname>
<given-names><![CDATA[Vasily Vasilyevich]]></given-names>
</name>
</person-group>
<source><![CDATA[Tipos de generalización en la enseñanza]]></source>
<year>1982</year>
<edition>3</edition>
<publisher-loc><![CDATA[Habana ]]></publisher-loc>
<publisher-name><![CDATA[Pueblo y Educación]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[FREITAS]]></surname>
<given-names><![CDATA[Daiane de]]></given-names>
</name>
</person-group>
<source><![CDATA[O movimento do pensamento expresso nas tarefas particulares propostas por Davýdov e colaboradores para apropriação do sistema conceitual de fração. 2016]]></source>
<year>2016</year>
<publisher-loc><![CDATA[Criciúma ]]></publisher-loc>
<publisher-name><![CDATA[Universidade do Extremo Sul Catarinense]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[&#1043;&#1054;&#1056;&#1041;&#1054;&#1042;]]></surname>
<given-names><![CDATA[&#1057;&#1077;&#1088;&#1075;&#1077;&#1081; &#1060;&#1077;&#1076;&#1086;&#1088;&#1086;&#1074;&#1080;&#1095;]]></given-names>
</name>
</person-group>
<source><![CDATA[&#1054;&#1073;&#1091;&#1095;&#1077;&#1085;&#1080;&#1077; &#1084;&#1072;&#1090;&#1077;&#1084;&#1072;&#1090;&#1080;&#1082;&#1072;: 5 &#1082;&#1083;&#1072;&#1089;&#1089;&#1072;. &#1087;&#1086;&#1089;&#1086;&#1073;&#1080;&#1077; &#1076;&#1083;&#1103; &#1091;&#1095;&#1080;&#1090;&#1077;&#1083;&#1103; (&#1089;&#1080;&#1089;&#1090;&#1077;&#1084;&#1072; &#1076;. &#1098;. &#1101;&#1083;&#1100;&#1082;&#1086;&#1085;&#1080;&#1085;&#1072; - &#1074;.&#1074;. &#1076;&#1072;&#1074;&#1099;&#1076;&#1086;&#1074;&#1072;)]]></source>
<year>2006</year>
<publisher-loc><![CDATA[&#1052;&#1086;&#1089;&#1082;&#1074;&#1072; ]]></publisher-loc>
<publisher-name><![CDATA[&#1042;&#1048;&#1058;&#1040;-&#1055;&#1056;&#1045;&#1057;&#1057;]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[&#1043;&#1054;&#1056;&#1041;&#1054;&#1042;]]></surname>
<given-names><![CDATA[&#1057;&#1077;&#1088;&#1075;&#1077;&#1081; &#1060;&#1077;&#1076;&#1086;&#1088;&#1086;&#1074;&#1080;&#1095;]]></given-names>
</name>
</person-group>
<source><![CDATA[&#1084;&#1072;&#1090;&#1077;&#1084;&#1072;&#1090;&#1080;&#1082;&#1072;: &#1091;&#1095;&#1077;&#1073;&#1085;&#1080;&#1082; &#1090;&#1077;&#1090;&#1088;&#1072;&#1076;&#1100; &#1076;&#1083;&#1103; 5 &#1082;&#1083;&#1072;&#1089;&#1089;&#1072;&#1086;&#1073;&#1097;&#1077;&#1086;&#1073;&#1088;&#1072;&#1079;&#1086;&#1074;&#1072;&#1090;. &#1091;&#1095;&#1088;&#1077;&#1078;&#1076;. (&#1089;&#1080;&#1089;&#1090;&#1077;&#1084;&#1072; &#1076;. &#1098;. &#1101;&#1083;&#1100;&#1082;&#1086;&#1085;&#1080;&#1085;&#1072; - &#1074;.&#1074;. &#1076;&#1072;&#1074;&#1099;&#1076;&#1086;&#1074;&#1072;). &#1074; 3 - &#1093; &#1095;&#1072;&#1089;&#1090;&#1103;&#1093;]]></source>
<year>2011</year>
<publisher-loc><![CDATA[&#1052;&#1086;&#1089;&#1082;&#1074;&#1072; ]]></publisher-loc>
<publisher-name><![CDATA[&#1042;&#1048;&#1058;&#1040;-&#1055;&#1056;&#1045;&#1057;&#1057;]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ISIDORO]]></surname>
<given-names><![CDATA[Luciane Corrêa do Nascimento]]></given-names>
</name>
</person-group>
<source><![CDATA[Modo de organização do ensino desenvolvimental de fração: o conhecimento revelado por acadêmicas de pedagogia. 2019]]></source>
<year>2019</year>
<publisher-loc><![CDATA[Tubarão ]]></publisher-loc>
<publisher-name><![CDATA[Universidade do Sul de Santa Catarina]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[KOPNIN]]></surname>
<given-names><![CDATA[Pavel Vasilyevich]]></given-names>
</name>
</person-group>
<source><![CDATA[A dialética como lógica e teoria do conhecimento]]></source>
<year>1978</year>
<publisher-loc><![CDATA[Rio de Janeiro ]]></publisher-loc>
<publisher-name><![CDATA[Civilização Brasileira]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[KOPNIN]]></surname>
<given-names><![CDATA[Pavel Vasilyevich]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Lo abstrato y lo concreto]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[ROSENTAL]]></surname>
<given-names><![CDATA[Mark Moisevich]]></given-names>
</name>
<name>
<surname><![CDATA[STRAKS]]></surname>
<given-names><![CDATA[Grigori Markovich]]></given-names>
</name>
</person-group>
<source><![CDATA[Categorias del materialismo dialectico]]></source>
<year>1958</year>
<page-range>299-320</page-range><publisher-loc><![CDATA[México, DF ]]></publisher-loc>
<publisher-name><![CDATA[Grijalbo]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[LIBÂNEO]]></surname>
<given-names><![CDATA[José Carlos]]></given-names>
</name>
<name>
<surname><![CDATA[FREITAS]]></surname>
<given-names><![CDATA[Raquel Aparecida Marra de Madeira]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Vasily Vasilyevich Davydov: a escola e a formação do pensamento teórico-científico]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[LONGAREZI]]></surname>
<given-names><![CDATA[Andréa Maturano]]></given-names>
</name>
<name>
<surname><![CDATA[PUENTES]]></surname>
<given-names><![CDATA[Roberto Valdés]]></given-names>
</name>
</person-group>
<source><![CDATA[Ensino desenvolvimental: vida, pensamento e obra dos principais representantes russos]]></source>
<year>2013</year>
<page-range>315-50</page-range><publisher-loc><![CDATA[Uberlândia ]]></publisher-loc>
<publisher-name><![CDATA[UFU]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[MADEIRA]]></surname>
<given-names><![CDATA[Silvana Citadin]]></given-names>
</name>
</person-group>
<source><![CDATA[&#8220;Prática&#8221;: uma leitura histórico-crítica e proposições davydovianas para o conceito de multiplicação. 2012]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Criciúma ]]></publisher-loc>
<publisher-name><![CDATA[Universidade do Extremo Sul Catarinense]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ROMEIRO]]></surname>
<given-names><![CDATA[Iraji de Oliveira]]></given-names>
</name>
</person-group>
<source><![CDATA[O movimento do pensamento teórico de professores sobre o conceito de fração e o sentido atribuído aos materiais didáticos na atividade de ensino. 2017]]></source>
<year>2017</year>
<publisher-loc><![CDATA[Guarulhos ]]></publisher-loc>
<publisher-name><![CDATA[Universidade Federal de São Paulo]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ROSA]]></surname>
<given-names><![CDATA[Josélia Euzébio da]]></given-names>
</name>
</person-group>
<source><![CDATA[Proposições de Davydov para o ensino de matemática no primeiro ano escolar: inter-relações dos sistemas de significações numéricas. 2012]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Curitiba ]]></publisher-loc>
<publisher-name><![CDATA[Universidade Federal do Paraná]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ROSENTAL]]></surname>
<given-names><![CDATA[Mark Moisevich]]></given-names>
</name>
</person-group>
<source><![CDATA[Da teoria marxista do conhecimento]]></source>
<year>1956</year>
<publisher-loc><![CDATA[Rio de Janeiro ]]></publisher-loc>
<publisher-name><![CDATA[Vitória]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ROSENTAL]]></surname>
<given-names><![CDATA[Mark Moisevich]]></given-names>
</name>
<name>
<surname><![CDATA[Boget]]></surname>
<given-names><![CDATA[Augusto Vidal]]></given-names>
</name>
</person-group>
<source><![CDATA[Princípios de lógica dialéctica]]></source>
<year>1962</year>
<publisher-loc><![CDATA[Montevideo ]]></publisher-loc>
<publisher-name><![CDATA[Pueblos Unidos]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[SANTOS]]></surname>
<given-names><![CDATA[Cleber de Oliveira dos]]></given-names>
</name>
</person-group>
<source><![CDATA[O movimento conceitual de fração a partir dos fundamentos da lógica dialética para o modo de organização do ensino. 2017]]></source>
<year>2017</year>
<publisher-loc><![CDATA[Tubarão ]]></publisher-loc>
<publisher-name><![CDATA[Universidade do Sul de Santa Catarina]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[SCHMITTAU]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The role of theoretical analysis in developing algebraic thinking: a vygotskian perspective]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[CAI]]></surname>
<given-names><![CDATA[Jinfa]]></given-names>
</name>
<name>
<surname><![CDATA[KNUTH]]></surname>
<given-names><![CDATA[Eric]]></given-names>
</name>
</person-group>
<source><![CDATA[Early algebraization: avanços na educação matemática]]></source>
<year>2011</year>
<page-range>71-85</page-range><publisher-loc><![CDATA[Berlin ]]></publisher-loc>
<publisher-name><![CDATA[Heidelberg]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[ZUCKERMAN]]></surname>
<given-names><![CDATA[Galina]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Introducing basic concepts: in search of the missing scaffolds]]></article-title>
<source><![CDATA[Cultural-Historical Psychology]]></source>
<year>2017</year>
<volume>13</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>4-14</page-range><publisher-loc><![CDATA[Moscow ]]></publisher-loc>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
