<?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>S1665-24362020000300271</article-id>
<article-id pub-id-type="doi">10.12802/relime.20.2331</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una secuencia didáctica para la enseñanza de la transformación lineal: unificación de métodos y problemas, modelización y explicitación del aprendizaje]]></article-title>
<article-title xml:lang="en"><![CDATA[A Didactic Sequence in the Teaching of Linear Transformation: Unification of Methods and Problems, Modeling and Explanation of Learning]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pascual Pizarro]]></surname>
<given-names><![CDATA[Sara]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Bío-Bío  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2020</year>
</pub-date>
<volume>23</volume>
<numero>3</numero>
<fpage>271</fpage>
<lpage>310</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362020000300271&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362020000300271&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362020000300271&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Este trabajo contribuye, por un lado, a determinar las implicaciones didácticas de un análisis epistemológico sobre la generalidad de métodos económicos y análogos en la resolución de problemas de carácter lineal y, por otro lado, a construir y evaluar una secuencia didáctica que haga entender mejor por los estudiantes el significado de un concepto unificador y ayudar a la movilización espontánea de sus propiedades por la exposición a una serie de problemas que recurren a diferentes marcos matemáticos (numérico, geométrico, físico y analítico). La articulación teórica concierne a la Modelización y la Dualidad proceso/objeto en la formación del concepto. Nos inspiramos en una ingeniería didáctica para presentar una parte de los resultados de nuestra investigación. Estos resultados se refieren a los niveles de explicitación y a las competencias desarrolladas en el uso de las habilidades técnicas y métodos matemáticos que ayudan a explicitar el proceso de formación de la noción.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT This work contributes, on the one hand, to determine the didactic implications of an epistemological analysis on the generality of economic and analogous methods in the resolution of problems of linear carácter. On the other hand, to construct and to evaluate a didactic sequence that makes the students understand better the meaning of a unifying concept and to help to the spontaneous mobilization of its properties by the exposure to a series of problems that resort to different mathematical frameworks (numerical, geometric, physical and analytical). The theoretical articulation concerns the Modelling and process/object duality in the formation of the concept. We are inspire by a didactic engineering to present a part of the results of our research. These results refer to the levels of explicitness and to the competences developed in the use of technical skills and mathematical methods that help to make explicit the process of formation of the notion.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO Este trabalho contribui, por um lado, para determinar as implicações didácticas de uma análise epistemológica sobre a generalidade dos métodos económicos e análogos na resolução de problemas de carácter linear e, por outro lado, para construir e avaliar uma sequência didáctica que faça compreender melhor pelos estudantes o significado de um conceito unificador e ajuda a mobilização espontânea das suas propriedades através da exposição a uma série de problemas que recorrem a diferentes quadros matemáticos (numérico, geométrico, físico e analítico). A articulação teórica concerne à Modelização e à Dualidade de processo/ objeto na formação do conceito. Somos inspirados por uma engenharia didáctica para apresentar uma parte dos resultados da nossa investigação. Estes resultados se referem aos níveis de explicitação e às competências desenvolvidas na utilização de habilidades técnicas e métodos matemáticos que ajudam a tornar explícito o processo de formação da noção.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[RÉSUMÉ Ce travail contribue, d&#8217;une part, à déterminer les implications didactiques d&#8217;une analyse épistémologique sur la généralité des méthodes économiques et analogues dans la résolution de problèmes de caractère linéaire et, d&#8217;autre part, à construire et à évaluer une séquence didactique qui fait mieux comprendre aux élèves la signification d&#8217;un concept unificateur et aide à la mobilisation spontanée de ses propriétés par l&#8217;exposition à une série de problèmes qui font appel à différents cadres mathématiques (numérique, géométrique, physique et analytique). L&#8217;articulation théorique concerne la modélisation et la dualité processus/objet dans la formation du concept. Nous nous inspirons d&#8217;une ingénierie didactique pour présenter une partie des résultats de nos recherches. Ces résultats font référence aux niveaux d&#8217;explicitation et aux compétences développées dans l&#8217;utilisation des aptitudes techniques et des méthodes mathématiques qui contribuent à rendre explicite le processus de formation de la notion.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Ingeniería didáctica]]></kwd>
<kwd lng="es"><![CDATA[Secuencia didáctica]]></kwd>
<kwd lng="es"><![CDATA[Modelo unificador]]></kwd>
<kwd lng="es"><![CDATA[Competencias de modelización]]></kwd>
<kwd lng="es"><![CDATA[Niveles de explicitación]]></kwd>
<kwd lng="en"><![CDATA[Didactical engineering]]></kwd>
<kwd lng="en"><![CDATA[Didactic sequence]]></kwd>
<kwd lng="en"><![CDATA[Unifying model]]></kwd>
<kwd lng="en"><![CDATA[Competencies in modeling]]></kwd>
<kwd lng="en"><![CDATA[Levels of communication]]></kwd>
<kwd lng="pt"><![CDATA[Engenharia didática]]></kwd>
<kwd lng="pt"><![CDATA[Sequência didática]]></kwd>
<kwd lng="pt"><![CDATA[Modelo unificador]]></kwd>
<kwd lng="pt"><![CDATA[Competências de modelização]]></kwd>
<kwd lng="pt"><![CDATA[Níveis de explicitação]]></kwd>
<kwd lng="fr"><![CDATA[Ingénierie didactique]]></kwd>
<kwd lng="fr"><![CDATA[Séquence didactique]]></kwd>
<kwd lng="fr"><![CDATA[Modèle unificateur]]></kwd>
<kwd lng="fr"><![CDATA[Compétences de modélisation]]></kwd>
<kwd lng="fr"><![CDATA[Niveaux d&#8217;explicitation]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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