<?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>S1665-24362018000100057</article-id>
<article-id pub-id-type="doi">10.12802/relime.18.2113</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Construcción cognitiva del espacio vectorial R 2]]></article-title>
<article-title xml:lang="en"><![CDATA[Cognitive construction of vector spaceR 2]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez Jara]]></surname>
<given-names><![CDATA[Miguel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<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[Trigueros Gaisman]]></surname>
<given-names><![CDATA[María]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Playa Ancha  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Instituto Tecnológico Autónomo de México  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2018</year>
</pub-date>
<volume>21</volume>
<numero>1</numero>
<fpage>57</fpage>
<lpage>86</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362018000100057&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362018000100057&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362018000100057&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN Presentamos antecedentes sobre la validación de un modelo cognitivo para el aprendizaje del espacio vectorial R 2. Como hallazgo, destacamos el papel que desempeña asociar un par de números reales a una ecuación lineal homogénea (de dos incógnitas) para inducir estructura algebraica a su conjunto solución. Además, se entrega evidencia de cómo el uso de un parámetro, para escribir una solución de una ecuación lineal homogénea, es un factor importante que pone de relieve a la ponderación de una solución por un escalar como una operación que se asocia al conjunto solución de una ecuación lineal homogénea. Todo lo anterior en estrecha relación con la construcción del espacio vectorial R 2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT We present background information on the validation of a cognitive model for the learning of the vector space R 2. As a result, we highlight the role played by the association of a pair of real numbers to a homogeneous linear equation (with two unknowns) to induce an algebraic structure to the solution set. Furthermore, we present evidence of how the use of a parameter to write a solution of a homogeneous linear equation, is an important factor that highlights the product of a solution by a scalar as an operation that is associated with the solution set of a homogeneous linear equation. All of this has a close connection with the construction of the vector space R 2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[RESUME Nous présentons les antécédents d&#8217;un modèle cognitif pour l&#8217;apprentissage de l&#8217;espace vectorielR 2 et sa validation. En tant que contribution, il faut remarquer le rôle joué par l&#8217;association d&#8217;une paire de nombres réels à une équation linéaire homogène (avec deux inconnues) pour induire une solution algébrique à son ensemble solution. Nous présentons aussi d&#8217;une part, des évidences sur l&#8217;utilisation d&#8217;un paramètre, comme un facteur important, qui souligne la pondération d&#8217;une solution par un nombre réel en tant qu&#8217;opération associée à l&#8217;ensemble de la solution d&#8217;une équation linéaire homogène, pour écrire une solution d&#8217;une équation linéaire homogène. Ces résultats ont une étroite relation avec la construction de l&#8217;espace vectoriel R 2.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[RESUMO Apresentamos antecedentes sobre a validação dum modelo cognitivo para a aprendizagem do espaço vetorial R 2. Destacamos o papel que desempenha a associação dum par de números reais com uma equação lineal homogénea (de duas incógnitas) para induzir estrutura algébrica a seu conjunto solução. Ademais amostramos evidencia de como o uso dum parâmetro para escrever uma solução duma equação lineal homogénea, é um fator importante que destaca a ponderação duma solução por um escalar como uma operação que se associa ao conjunto solução duma equação lineal homogénea. Tudo o anterior em estreita relação com a construção do espaço vetorial R 2.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Modelo cognitivo]]></kwd>
<kwd lng="es"><![CDATA[Espacio vectorial R2]]></kwd>
<kwd lng="es"><![CDATA[Ecuación lineal homogénea]]></kwd>
<kwd lng="es"><![CDATA[Conjunto solución]]></kwd>
<kwd lng="es"><![CDATA[Teoría APOE]]></kwd>
<kwd lng="en"><![CDATA[Cognitive model]]></kwd>
<kwd lng="en"><![CDATA[Vector space R2]]></kwd>
<kwd lng="en"><![CDATA[Homogeneous linear equation]]></kwd>
<kwd lng="en"><![CDATA[Solution set]]></kwd>
<kwd lng="en"><![CDATA[APOS theory]]></kwd>
<kwd lng="fr"><![CDATA[Modèle cognitif]]></kwd>
<kwd lng="fr"><![CDATA[Espace vectoriel R2]]></kwd>
<kwd lng="fr"><![CDATA[Équation linéaire homogène]]></kwd>
<kwd lng="fr"><![CDATA[Ensemble solution]]></kwd>
<kwd lng="fr"><![CDATA[Théorie APOS]]></kwd>
<kwd lng="pt"><![CDATA[Modelo cognitivo]]></kwd>
<kwd lng="pt"><![CDATA[Espaço vetorial R2]]></kwd>
<kwd lng="pt"><![CDATA[Equação linear homogénea]]></kwd>
<kwd lng="pt"><![CDATA[Conjunto solução]]></kwd>
<kwd lng="pt"><![CDATA[Teoria APOS]]></kwd>
</kwd-group>
</article-meta>
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