<?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>1665-2436</journal-id>
<journal-title><![CDATA[Revista latinoamericana de investigación en matemática educativa]]></journal-title>
<abbrev-journal-title><![CDATA[Relime]]></abbrev-journal-title>
<issn>1665-2436</issn>
<publisher>
<publisher-name><![CDATA[Comité Latinoamericano de Matemática Educativa A.C.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1665-24362023000300295</article-id>
<article-id pub-id-type="doi">10.12802/relime.23.2632</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Espiral da conceituação: um estudo sobre o campo conceitual das funções afim e a programação de computadores]]></article-title>
<article-title xml:lang="en"><![CDATA[Spiral of conceptualization: a study on the conceptual field of affine functions and computer programming]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lessa]]></surname>
<given-names><![CDATA[Valéria Espíndola]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Teixeira]]></surname>
<given-names><![CDATA[Adriano Canabarro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Federal do Rio Grande do Sul  ]]></institution>
<addr-line><![CDATA[Erechim ]]></addr-line>
<country>Brasil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidade de Passo Fundo  ]]></institution>
<addr-line><![CDATA[Passo Fundo ]]></addr-line>
<country>Brazil</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>26</volume>
<numero>3</numero>
<fpage>295</fpage>
<lpage>326</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362023000300295&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362023000300295&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362023000300295&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo: Neste artigo apresentamos um estudo que objetivou investigar os processos de representação e de compreensão de invariantes operatórios do Campo Conceitual das Funções Afim de dois estudantes do Curso Técnico em Informática do IFRS, Campus Erechim, por meio da programação de computadores. O referencial teórico foi embasado na Teoria dos Campos Conceituais de Gérard Vergnaud e na Teoria Construcionista de Seymour Papert e colaboradores. Os dados da pesquisa foram produzidos mediante a realização, pelos estudantes, de situações sobre Funções Afim com o ambiente Scratch, associado ao método da observação interativa. Como resultados, a pesquisa apontou para a concretização e dinamização do conceito de taxa de variação constante, além de possibilitar a elaboração da Espiral da Conceituação.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En este artigo presentamos un estudio que ha objetivado averiguar los procesos de representaciones y la comprensión de invariables operatorias del Campo Conceptual de las Funciones Afines de dos estudiantes de la Carrera Técnica en Informática del IFRS, Campus Erechim, por medio de la programación de computadoras. Los refenciales teóricos están puestos en la Teoría de los Campos Conceptuales de Gérard Vergnaud y en la Teoría Construccionista de Seymour Papert y sus aportadores. Los datos de esta investigación han sido producidos a través de la realización, por los estudiantes, de situaciones sobre Funciones Afines con el ambiente Scratch, junto al método de observación interactiva. Como resultados, la investigación ha apuntado hacia la concretización y dinamización del concepto de la tasa de variación constante, además de aportar en la elaboración de la Espiral Conceptual.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In this article we present a study that aimed to investigate the processes of representation and understanding of operative invariants of the Conceptual Field of Affine Functions of two students of the Technical Course in Informatics of IFRS, Campus Erechim, through computer programming. The theoretical framework was based on the Conceptual Fields Theory of Gérard Vergnaud and the Constructionist Theory of Seymour Papert and collaborators. The research data were produced through the realization, by the students, of situations about Affine Functions with the Scratch environment, associated with the interactive observation method. As results, the research pointed to the concretization and dynamization of the concept of constant rate of change, besides enabling the elaboration of the Spiral of Conceptualization.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé: Dans cet article nous présentons une étude qui avait pour but d'investiguer les processus de représentation et de compréhension des invariants opératoires du Champ Conceptuel des Fonctions Affines de deux étudiants du Cours Technique d'Informatique de l'IFRS, Campus Erechim, à travers la programmation informatique. Le cadre théorique était basé sur la Théorie des Champs Conceptuels de Gérard Vergnaud et la Théorie Constructiviste de Seymour Papert et collaborateurs. Les données de recherche ont été produites par la réalisation, par les élèves, de situations sur les fonctions affines avec l'environnement Scratch, associé à la méthode d'observation interactive. Comme résultats, la recherche a indiqué la concrétisation et la dynamisation du concept de taux constant de changement, en plus de permettre l'élaboration de la Spirale de Conceptualisation.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Funções Afim]]></kwd>
<kwd lng="pt"><![CDATA[Programação de computadores]]></kwd>
<kwd lng="pt"><![CDATA[Invariantes operatórios]]></kwd>
<kwd lng="pt"><![CDATA[Representações]]></kwd>
<kwd lng="pt"><![CDATA[Compreensões]]></kwd>
<kwd lng="es"><![CDATA[Funciones Afines]]></kwd>
<kwd lng="es"><![CDATA[Programación de computadoras]]></kwd>
<kwd lng="es"><![CDATA[Invariables operatorias]]></kwd>
<kwd lng="es"><![CDATA[Representaciones]]></kwd>
<kwd lng="es"><![CDATA[Comprensiones]]></kwd>
<kwd lng="en"><![CDATA[Affine functions]]></kwd>
<kwd lng="en"><![CDATA[Computer programming]]></kwd>
<kwd lng="en"><![CDATA[Operative invariants]]></kwd>
<kwd lng="en"><![CDATA[Representations]]></kwd>
<kwd lng="en"><![CDATA[Comprehensions]]></kwd>
<kwd lng="fr"><![CDATA[Fonctions affines]]></kwd>
<kwd lng="fr"><![CDATA[Programmation informatique]]></kwd>
<kwd lng="fr"><![CDATA[Invariants opératoires]]></kwd>
<kwd lng="fr"><![CDATA[Représentations]]></kwd>
<kwd lng="fr"><![CDATA[Compréhensions]]></kwd>
</kwd-group>
</article-meta>
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