<?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>S1665-24362022000100063</article-id>
<article-id pub-id-type="doi">10.12802/relime.22.2513</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estructuras y mecanismos mentales que desde una perspectiva geométrica modelan y articulan el aprendizaje de valor y vector propio en &#8477;2]]></article-title>
<article-title xml:lang="en"><![CDATA[Mental structures and mechanisms that from a geometric perspective model and articulate the learning of eigenvalue and eigenvector in &#8477;2]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Parraguez González]]></surname>
<given-names><![CDATA[Marcela]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Roa-Fuentes]]></surname>
<given-names><![CDATA[Solange]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jiménez Alarcón]]></surname>
<given-names><![CDATA[Raúl]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Betancur Sánchez]]></surname>
<given-names><![CDATA[Alexander]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Católica del Norte  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</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>25</volume>
<numero>1</numero>
<fpage>63</fpage>
<lpage>92</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362022000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362022000100063&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362022000100063&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Se proponen dos descomposiciones genéticas (DG&#8217;s) refinadas, como resultado de la aplicación del Ciclo de investigación de APOE, que describen estructuras y mecanismos mentales para el concepto de valor y vector propio en dos casos de estudio. La primera DG0 modela los conocimientos previos que estudiantes de secundaria (14 - 16 años) deben lograr para construir en la universidad dicho concepto en    R  2, -este modelo se sustenta en la rotación de vectores y el concepto de múltiplo escalar-. La segunda DG1 modela en    R  2 la construcción de valor y vector propio en estudiantes universitarios de primer año y muestra cómo apoyarse en tópicos de secundaria para estructurar dicho concepto a partir de relaciones entre la transformación lineal y el vector múltiplo escalar como generador de una recta. El análisis de datos permite validar las DG&#8217;s y bosquejar un camino cognitivo para el aprendizaje del concepto de valor y vector propio en    R  2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Two refined genetic decompositions (DGs) are proposed, as a result of the application of the APOS Research Cycle, which describe mental structures and mechanisms for the concept of value and eigenvector in two case studies. The first DG0 models the prior knowledge that high school students (14 - 16 years old) must achieve in    R  2 order to build this concept in the university -this model is based on vector rotation and the concept of scalar multiple-. The second DG1 models in    R  2 the construction of eigenvalue and eigenvector in first-year university students and shows how to rely on secondary education to structure that concept from relationships between the linear transformation and the scalar multiple vector as a generator of a line. The data analysis allows to validate the DG's and outline a cognitive path for learning the concept of eigenvalue and eigenvector in    R  2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Duas decomposições genéticas refinadas (DGs) são propostas, como resultado da aplicação do Ciclo de Pesquisa APOS, que descrevem estruturas mentais e mecanismos para o conceito de valor e autovetor em dois estudos de caso. O primeiro DG0 modela o conhecimento prévio que os alunos do ensino médio (14 - 16 anos) devem adquirir para construir esse conceito na universidade em    R  2 -este modelo é baseado na rotação vetorial e no conceito de múltiplo escalar-. O segundo DG1 modela a    R  2 construção de autovalor e autovetor em estudantes universitários do primeiro ano e mostra como contar com o ensino médio para estruturar esse conceito a partir das relações entre a transformação linear e o vetor múltiplo escalar como gerador de uma linha. A análise dos dados permite validar os GD's e traçar um caminho cognitivo para a aprendizagem do conceito de autovalor e autovetor em    R  2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé Deux décompositions génétiques raffinées (DG) sont proposées, à la suite de l'application du cycle de recherche APOS, qui décrit les structures mentales et les mécanismes du concept de valeur et de vecteur propre dans deux études de cas. Le premier DG0 modélise les connaissances préalables que les lycéens (14 - 16 ans) doivent acquérir pour construiré en    R  2 ce concept à l'université -ce modèle est basé sur la rotation vectorielle et le concept de multiple scalaire-. Le deuxième DG1 modélise en    R  2la construction de valeur et de vecteur propre chez les étudiants de première année d'université et montre comment utiliser le soutien de l'enseignement secondaire pour structurer ledit concept en fonction des relations entre la transformation linéaire et le vecteur multiple scalaire en tant que générateur d'une ligne. L'analyse des données permet de valider les DG&#8217;s et de tracer un chemin cognitif pour apprendre le concept de valeur et de vecteur propre en    R  2.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Valor propio]]></kwd>
<kwd lng="es"><![CDATA[Vector propio]]></kwd>
<kwd lng="es"><![CDATA[Rotación]]></kwd>
<kwd lng="es"><![CDATA[Múltiplo escalar]]></kwd>
<kwd lng="es"><![CDATA[Teoría APOE]]></kwd>
<kwd lng="en"><![CDATA[Eigenvalue]]></kwd>
<kwd lng="en"><![CDATA[Eigenvector]]></kwd>
<kwd lng="en"><![CDATA[Rotation]]></kwd>
<kwd lng="en"><![CDATA[Scalar Product]]></kwd>
<kwd lng="en"><![CDATA[APOS Theory]]></kwd>
<kwd lng="pt"><![CDATA[Autovalue]]></kwd>
<kwd lng="pt"><![CDATA[Autovetor]]></kwd>
<kwd lng="pt"><![CDATA[Rotação]]></kwd>
<kwd lng="pt"><![CDATA[Produto Escalar]]></kwd>
<kwd lng="pt"><![CDATA[Teoria APOS]]></kwd>
<kwd lng="fr"><![CDATA[Valeur propre]]></kwd>
<kwd lng="fr"><![CDATA[vecteur propre]]></kwd>
<kwd lng="fr"><![CDATA[rotation]]></kwd>
<kwd lng="fr"><![CDATA[produit scalaire]]></kwd>
<kwd lng="fr"><![CDATA[théorie APOS]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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