<?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>2448-8089</journal-id>
<journal-title><![CDATA[Educación matemática]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. mat.]]></abbrev-journal-title>
<issn>2448-8089</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Investigación y Divulgación de la Educación Matemática A.C.; Universidad de Guadalajara]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2448-80892022000300163</article-id>
<article-id pub-id-type="doi">10.24844/em3403.06</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Comprensión del conjunto solución de un sistema de ecuaciones lineales de dos incógnitas: un estudio de casos]]></article-title>
<article-title xml:lang="en"><![CDATA[Understanding the solution set of a system of linear equations of two unknowns: a case study]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[Miguel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mena-Lorca]]></surname>
<given-names><![CDATA[Arturo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gregori]]></surname>
<given-names><![CDATA[Pablo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Vásquez]]></surname>
<given-names><![CDATA[Patricia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[del Valle]]></surname>
<given-names><![CDATA[María]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Parraguez]]></surname>
<given-names><![CDATA[Marcela]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Playa Ancha Facultad de Educación Departamento de Ciencias de la Educación]]></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[,Universitat Jaume I Instituto de Matemáticas y Aplicaciones de Castellón Departamento de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad de Concepción Facultad de Ecuación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af6">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</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>34</volume>
<numero>3</numero>
<fpage>163</fpage>
<lpage>193</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892022000300163&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892022000300163&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892022000300163&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En este artículo se reporta cómo estudiantes chilenos, de secundaria y universitarios, comprenden el Conjunto Solución de un Sistema de Ecuaciones Lineales de tres ecuaciones y dos incógnitas (CSSEL3x2). El estudio se sustenta en la teoría Modos de Pensamiento, con una metodología de Estudio de Caso, y el uso de la Estadística Implicativa. Como estrategia, se utilizaron ecuaciones equivalentes, para indagar en la influencia del concepto de dependencia lineal en el tránsito de las distintas maneras de concebir su conjunto solución. Se destaca en las respuestas de los estudiantes el uso del concepto de pendiente y la idea de combinación lineal como mecanismos para transitar entre los modos sintético-geométrico y analíticos asociados al CSSEL3x2. Se constató una desarticulación entre los distintos modos de pensar el conjunto solución cuando se incorporan parámetros a los coeficientes de las ecuaciones, lo que es particularmente notorio para el caso conformado por estudiantes que habían cursado Álgebra Lineal. Por otra parte, se aprecia que el concepto de dependencia lineal que se pone en juego en el análisis se restringe al caso de múltiplo escalar.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: This article reports the Chilean high school and university students&#8217; understanding of the Solution Set of a System of Linear Equations of Three Equations and Two Unknowns (CSSEL 3x2). The study is based on the theory of Modes of Thought, with a Case Study methodology and the use of Implicative Statistics. As a strategy, equivalent equations were used to investigate the influence of the concept of linear dependence on the path to the different ways of conceiving its set of solutions. The use of the concept of slope and the idea of linear combination as mechanisms to transit between the synthetic-geometric and analytical modes associated with the CSSEL3x2 stand out in the students&#8217; responses. A disarticulation between the different ways of thinking the whole solution when parameters are incorporated to the coefficients of the equations was observed, which is particularly noticeable for students who had studied Linear Algebra. On the other hand, we show that the concept of linear dependence that is brought into play in the analysis is restricted to the case of scalar multiples.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Modos de pensamiento]]></kwd>
<kwd lng="es"><![CDATA[Sistemas de ecuaciones lineales]]></kwd>
<kwd lng="es"><![CDATA[Con-junto solución]]></kwd>
<kwd lng="es"><![CDATA[Estadística implicativa]]></kwd>
<kwd lng="en"><![CDATA[Modes of thought]]></kwd>
<kwd lng="en"><![CDATA[Systems of Linear Equations]]></kwd>
<kwd lng="en"><![CDATA[Solution Set]]></kwd>
<kwd lng="en"><![CDATA[Impli-cative Statistics.]]></kwd>
</kwd-group>
</article-meta>
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