<?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>S2448-80892016000300145</article-id>
<article-id pub-id-type="doi">10.24844/em2803.06</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[¿Cuán abundantes son los conjuntos de números? Estudiantes comparando infinitos]]></article-title>
<article-title xml:lang="en"><![CDATA[How Abundant are the Sets of Numbers? Students Comparing Infinite Sets of Numbers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montoro]]></surname>
<given-names><![CDATA[Virginia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Scheuer]]></surname>
<given-names><![CDATA[Nora]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez Echeverría]]></surname>
<given-names><![CDATA[Ma. del Puy]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional del Comahue Departamento de Matemática Centro Regional Universitario Bariloche]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional del Comahue Centro Regional Universitario Bariloche ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Autónoma de Madrid Facultad de Psicología Departamento de Psicología Básica]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</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>3</numero>
<fpage>145</fpage>
<lpage>174</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892016000300145&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892016000300145&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892016000300145&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Estudiamos las concepciones sobre la cardinalidad infinita de conjuntos numéricos, de estudiantes con distinta formación matemática. Se analizó una tarea de comparación de conjuntos infinitos de números, resuelta por estudiantes de educación secundaria y estudiantes universitarios con distinto grado de formación matemática. Se clasificó a los estudiantes según sus ideas sobre el infinito y se realizó un Análisis Factorial de Correspondencia relacionando éstas clases con el nivel de estudios de los estudiantes. Encontramos un gradiente de profundidad de estas ideas que comienzan desde de lo que hemos denominado horror infiniti, con las variantes de evitar el infinito o considerarlo como indefinido, presente principalmente en los estudiantes con menor nivel de estudios de matemática. En una zona intermedia se ubica la concepción más frecuente, la concepción finitista, ya sea tácita, explícita, o se base en los enteros como modelo de inclusión. La concepción más compleja, la infinitista, sólo fue explicitada por estudiantes universitarios, según dos enfoques: pensar la cardinalidad de los conjuntos infinitos como una única cantidad infinita, o concebir distintos cardinales infinitos, este último expresado sólo por estudiantes avanzados de matemática.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: We studied how students with different mathematical background conceive infinite cardinality of number sets. We analyzed a task in which high school and college students were requested to compare infinite number sets. Students were classified according to their ideas on infinity. Using this classification together with the students' level of math education, we performed a correspondence factorial analysis. A gradient was found in the depth of students' ideas. At one end we found what we called horror infiniti, based students propensity avoid infinity and instead construe it as something undefined. These views were associated with students with less mathematical education. In an intermediate zone, the finitist conception was placed. It was the most frequent way of thinking among the participants of the study, with three versions: tacitly infinitist, explicitly finitist, or taking the integers as model of inclusion. At the other end, the infinitist conception was placed. It was present among students with college mathematical education, according to two types: thinking of the cardinality of number sets as a unique infinite quantity; or conceiving different infinite cardinals. The latter was found only in advanced mathematics students.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[conjuntos numéricos]]></kwd>
<kwd lng="es"><![CDATA[infinito cardinal]]></kwd>
<kwd lng="es"><![CDATA[educación secundaria]]></kwd>
<kwd lng="es"><![CDATA[estudiantes universitarios]]></kwd>
<kwd lng="en"><![CDATA[comparison]]></kwd>
<kwd lng="en"><![CDATA[number sets]]></kwd>
<kwd lng="en"><![CDATA[cardinal infinity]]></kwd>
<kwd lng="en"><![CDATA[mathematics education]]></kwd>
</kwd-group>
</article-meta>
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