<?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>S2448-80892016000200119</article-id>
<article-id pub-id-type="doi">10.24844/em2802.05</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Procesos iterativos infinitos y objetos trascendentes: un modelo de construcción del infinito matemático desde la teoría APOE]]></article-title>
<article-title xml:lang="en"><![CDATA[Infinite iterative processes and transcendent objects: A model of construction of mathematical infinity from the APOS Theory]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Villabona Millán]]></surname>
<given-names><![CDATA[Diana Paola]]></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-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Industrial de Santander Escuela de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2016</year>
</pub-date>
<volume>28</volume>
<numero>2</numero>
<fpage>119</fpage>
<lpage>150</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892016000200119&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892016000200119&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892016000200119&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En este estudio se analizan las estructuras mentales que un individuo puede desarrollar al construir el concepto de infinito en dos contextos particulares: la paradoja de Aquiles y la tortuga y el triángulo de Sierpi&#324;ski. Con base en la descomposición genética genérica del infinito, planteada por Roa-Fuentes y Oktaç (2014), se estudian las características particulares de las estructuras y los mecanismos que cada contexto genera. El análisis de los datos a partir del trabajo llevado a cabo por estudiantes de posgrado en Matemáticas y Educación Matemática, muestra cómo se da paso de un proceso iterativo infinito (infinito potencial) a un objeto trascendente (infinito actual). Además se muestra la importancia del mecanismo de coordinación para la construcción de procesos iterativos infinitos.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The present study aims to examine the mental structures that a person can develop to construct the mathematical concept of infinity in two particular contexts: "the paradox of Achilles and the tortoise" and the "Sierpi&#324;ski triangle". Based on the genetic generic decomposition of the infinite, proposed by Roa-Fuentes and Oktaç (2014), this investigation focuses on the study of the particular characteristics, mechanisms and structures produced by each context. The analysis of data from work done by postgraduate students (in Mathematics and Mathematics Education) shows how from the infinite iterative process (potential infinity) advances towards to a transcend object (actual infinity). Furthermore, the results reflect the importance of the coordination mechanism in the construction of infinite iterative process.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Teoría APOE]]></kwd>
<kwd lng="es"><![CDATA[paradojas]]></kwd>
<kwd lng="es"><![CDATA[triángulo de Sierpi&#324;ski]]></kwd>
<kwd lng="es"><![CDATA[procesos iterativos infinitos]]></kwd>
<kwd lng="es"><![CDATA[objetos trascendentes]]></kwd>
<kwd lng="en"><![CDATA[APOS theory]]></kwd>
<kwd lng="en"><![CDATA[paradoxes]]></kwd>
<kwd lng="en"><![CDATA[Sierpi&#324;ski triangle, infinite iterative processes]]></kwd>
<kwd lng="en"><![CDATA[transcendent objects]]></kwd>
</kwd-group>
</article-meta>
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