<?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>S1665-24362015000300329</article-id>
<article-id pub-id-type="doi">10.12802/relime.13.1832</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[El obstáculo epistemológico del infinito actual: Persistencia, resistencia y categorías de análisis]]></article-title>
<article-title xml:lang="en"><![CDATA[The epistemological obstacle of the actual infinity: Persistence, resistence and categories of analysis]]></article-title>
</title-group>
<contrib-group>
<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[Mena-Lorca]]></surname>
<given-names><![CDATA[Jaime]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montoya-Delgadillo]]></surname>
<given-names><![CDATA[Elizabeth]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Morales]]></surname>
<given-names><![CDATA[Astrid]]></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[,Pontificia Universidad Católica de Valparaíso Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>11</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>11</month>
<year>2015</year>
</pub-date>
<volume>18</volume>
<numero>3</numero>
<fpage>329</fpage>
<lpage>358</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362015000300329&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362015000300329&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362015000300329&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Los obstáculos epistemológicos suelen tener raíces profundas en la propia Matemática, que pueden pesquisarse en la historia de la disciplina, y se caracterizan a la vez por la persistencia con la cual reaparecen en diversas situaciones y lo determinante que son para el logro de los aprendizajes. Estos obstáculos con frecuencia no son advertidos por el docente, bien sea porque ha reemplazado oportunamente sus propias concepciones (semánticas) por otras de carácter teórico -superando así el obstáculo, sin reparar explícitamente en ello-, o porque no ha logrado aun hacer esa substitución. En este trabajo presentamos una ilustración particularmente relevante de lo anterior, que se refiere a la persistencia de un obstáculo ligado al concepto de infinito en personas en distinto estadio de formación. Luego mostramos una característica adicional del obstáculo que llamamos resistencia. Posteriormente, utilizamos diversas perspectivas teóricas propiamente didácticas para adentrarnos en la cuestión. Finalmente, proponemos algunas reflexiones que se pueden derivar de nuestro estudio.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Epistemological obstacles often have deep roots in Mathematics itself; those roots can be explored in the history of the discipline, and are characterized both by the persistence with which they reappear in various situations and the determining role that they play for the achievement of learning. These obstacles often remain unnoticed by the instructor, either because he/ she has replaced in time his/her own (semantic) conceptions by others of a theoretical nature - overcoming thus the obstacle, but not being aware of it - or else because he/she has not yet made that substitution. In this paper, we present a particularly relevant illustration of the above, which refers to the persistence of an obstacle related to the concept of infinity in different stages of learning. Then we show an additional characteristic of the obstacle, that we call resistance. Subsequently, we use various theoretical approaches, properly didactic, to go into the question. Lastly, we put forward some reflections that can be derived from our study.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo: Os obstáculos epistemológicos muitas vezes têm raízes profundas na própria matemática, que podem-se indagar na história da disciplina, e caracterizam-se ao mesmo tempo pela persistência com que reaparecem em diferentes situações e o decisivas que são para o secesso da aprendizagem. Estes obstáculos muitas vezes não são notados pelo professor, ou porque ele substituiu no momento oportuno suas próprias concepções (semânticas) por outras de carácter teórico - superando assim o obstáculo sem reparar explicitamente em isso -, ou porque não fez ainda essa substituição. Neste artigo apresentamos uma ilustração particularmente relevante do anterior, que refere-se à persistência do obstáculo ligados ao conceito de infinito em pessoas em diferentes estágios de formação. Após, nos mostramos um recurso adicional que nomeamos de resistência. Posteriormente, utilizamos diversas perspectivas teóricas de ensino proprias da didática, para entrar na questão. Finalmente, nos propomos algumas reflexões que podem-se derivadar de nosso estudo.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé: Les obstacles épistémologiques ont des racines profondes dans la Mathématique, racines qu'on peut reconnaître dans l'histoire de la discipline ; elles se caractérisent tant par sa persistance, réapparaissant en des diverses situations, et parce qu'elles son déterminantes pour l'acquisition des connaissances. Néanmoins, ces obstacles demeurent souvent inaperçus par l'enseignant, parfois parce qu'il a remplacé ses propres conceptions (sémantiques) par d'autres, théoriques, ou bien justement parce qu'il n'a pas encore fait cette substitution. Dans ce travail nous présentons une illustration particulièrement remarquable de ce qui précède, qui se rapporte à la persistance d'un obstacle lié au concept d'infini chez des sujets possédant des niveaux de formation différents. Ensuite nous exhibons une caractéristique additionnelle de l'obstacle que nous appelons résistance. Après, nous utilisons diverses approches théoriques, proprement didactiques, pour aborder la question. Finalement, nous présentons quelques réflexions qui découlent de notre étude.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Infinito potencial]]></kwd>
<kwd lng="es"><![CDATA[Infinito actual]]></kwd>
<kwd lng="es"><![CDATA[Epistemología]]></kwd>
<kwd lng="es"><![CDATA[Obstáculo epistemológico]]></kwd>
<kwd lng="en"><![CDATA[Potential infinity]]></kwd>
<kwd lng="en"><![CDATA[Actual infinity]]></kwd>
<kwd lng="en"><![CDATA[Epistemology]]></kwd>
<kwd lng="en"><![CDATA[Epistemological obstacle]]></kwd>
<kwd lng="pt"><![CDATA[Infinito potencial]]></kwd>
<kwd lng="pt"><![CDATA[Infinito atual]]></kwd>
<kwd lng="pt"><![CDATA[Epistemologia]]></kwd>
<kwd lng="pt"><![CDATA[Obstáculo epistemológico]]></kwd>
<kwd lng="fr"><![CDATA[L'infini potentiel]]></kwd>
<kwd lng="fr"><![CDATA[L'infini actuel]]></kwd>
<kwd lng="fr"><![CDATA[L'épistémologie]]></kwd>
<kwd lng="fr"><![CDATA[Obstacle épistémologique]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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