<?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>S1983-17302025000100106</article-id>
<article-id pub-id-type="doi">10.14393/er-v32e2025-08</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[O Movimento Lógico-Histórico da Progressão Aritmética: uma contribuição para o ensino de Matemática]]></article-title>
<article-title xml:lang="es"><![CDATA[El movimiento lógico-histórico de la progresión aritmética: una contribución a la enseñanza de las matemáticas]]></article-title>
<article-title xml:lang="en"><![CDATA[The Logical-Historical Movement of Arithmetic Progression: a contribution to math teaching]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pereira]]></surname>
<given-names><![CDATA[Elton José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Resende]]></surname>
<given-names><![CDATA[Marilene Ribeiro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidade de Uberaba  ]]></institution>
<addr-line><![CDATA[Uberaba MG]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade de Uberaba  ]]></institution>
<addr-line><![CDATA[Uberaba MG]]></addr-line>
<country>Brasil</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<volume>32</volume>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_arttext&amp;pid=S1983-17302025000100106&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_abstract&amp;pid=S1983-17302025000100106&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://educa.fcc.org.br/scielo.php?script=sci_pdf&amp;pid=S1983-17302025000100106&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO Este artigo descreve aspectos do movimento lógico-histórico do conceito de Progressão Aritmética (PA), identificando nexos conceituais (internos e externos) de Álgebra, trabalhada no Ensino Médio. A metodologia é a revisão bibliográfica de fontes brasileiras em língua portuguesa e em espanhol. A análise dos resultados aponta que o movimento lógico-histórico de PA, didaticamente, possibilita aos alunos, pelo acesso aos nexos conceituais, desenvolverem ações mentais ligadas ao pensamento teórico. Assim, o ensino de PA não é apenas uma técnica operatória, mas uma oportunidade de desenvolver um conceito como instrumento cognitivo, desenvolvido a partir das necessidades humanas. Alguns nexos internos do conceito de PA são comuns aos de outros conceitos algébricos, como fluência, grandeza, variável, campo de variação e interdependência, podendo ser acrescidos nexos próprios, como a ordem (posição), cujo campo de variação é o conjunto dos números naturais, e a existência de uma variação constante (diferença) entre os termos da sequência.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Este artículo describe aspectos del movimiento lógico-histórico del concepto de Progresión Aritmética (PA), identificando vínculos conceptuales (internos y externos) con el Álgebra, que se enseña en la enseñanza media. La metodología es una revisión bibliográfica de fuentes brasileñas en portugués y español. El análisis de los resultados muestra que el movimiento lógico-histórico del PA, didácticamente, permite a los alumnos desarrollar acciones mentales vinculadas al pensamiento teórico a través del acceso a los vínculos conceptuales. Así, la enseñanza del PA no es sólo una técnica operativa, sino una oportunidad para desarrollar un concepto como herramienta cognitiva, desarrollada a partir de necesidades humanas. Algunos de los enlaces internos del concepto de PA son comunes a los de otros conceptos algebraicos, como fluencia, magnitud, variable, campo de variación e interdependencia, pero podemos añadir enlaces propios, como orden (posición), cuyo campo de variación es el conjunto de los números naturales, y la existencia de una variación constante (diferencia) entre los términos de la sucesión.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT This article describes aspects of the logical-historical movement of the concept of Arithmetic Progression (AP), identifying conceptual links (internal and external) with Algebra, which is taught in secondary school. The methodology is a bibliographical review of Brazilian sources in Portuguese and Spanish. The analysis of the results shows that the logical-historical movement of AP, didactically, enables students to develop mental actions linked to theoretical thinking through access to conceptual links. Thus, the teaching of AP is not just an operative technique, but an opportunity to develop a concept as a cognitive tool, developed from human needs. Some of the internal links in the concept of AP are common to other algebraic concepts, such as fluency, magnitude, variable, field of variation and interdependence, but we can add our own links, such as order (position), whose field of variation is the set of natural numbers, and the existence of a constant variation (difference) between the terms of the sequence.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Pensamento Teórico]]></kwd>
<kwd lng="pt"><![CDATA[Ensino de Matemática]]></kwd>
<kwd lng="pt"><![CDATA[Ensino Médio]]></kwd>
<kwd lng="pt"><![CDATA[Progressão Aritmética.]]></kwd>
<kwd lng="es"><![CDATA[Pensamiento teórico]]></kwd>
<kwd lng="es"><![CDATA[Enseñanza de Matemáticas]]></kwd>
<kwd lng="es"><![CDATA[Escuela secundaria]]></kwd>
<kwd lng="es"><![CDATA[Progresión aritmética.]]></kwd>
<kwd lng="en"><![CDATA[Theoretical Thinking]]></kwd>
<kwd lng="en"><![CDATA[Teaching Mathematics]]></kwd>
<kwd lng="en"><![CDATA[High School]]></kwd>
<kwd lng="en"><![CDATA[Arithmetic Progression.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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