<?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>S2448-80892019000300039</article-id>
<article-id pub-id-type="doi">10.24844/em3103.02</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[La negación: Un aporte a la construcción de definiciones en el aula escolar de geometría]]></article-title>
<article-title xml:lang="en"><![CDATA[Negation: A contribution to the construction of definitions in a geometry classroom]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Samper]]></surname>
<given-names><![CDATA[Carmen]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Vargas]]></surname>
<given-names><![CDATA[Claudia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Pedagógica Nacional Facultad de Ciencia y Tecnología Departamento de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Pedagógica Nacional Facultad de Ciencia y Tecnología Departamento de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2019</year>
</pub-date>
<volume>31</volume>
<numero>3</numero>
<fpage>39</fpage>
<lpage>60</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892019000300039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892019000300039&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892019000300039&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En este artículo presentamos el análisis de los argumentos de siete estudiantes de grado décimo (14 a16 años) en los que usan la negación de proposiciones, cuando intentan definir una figura geométrica, desconocida para ellos, y justificar su decisión. El objetivo del estudio fue encontrar las características del uso de la negación, para determinar si se cumple lo que muchos investigadores en educación matemática han encontrado: el uso de la negación acarrea muchas dificultades. La estrategia metodológica utilizada es el estudio de caso, dado que los datos empleados fueron las transcripciones de los registros en audio y video del trabajo realizado por los estudiantes. Concluimos que el tipo de tareas propuestas a las estudiantes, diseñadas para favorecer los procesos matemáticos definir y argumentar y el uso de un software de geometría dinámica, propiciaron el uso espontáneo de la negación. Identificamos bajo qué circunstancias los estudiantes recurrieron al uso de la negación para justificar sus aserciones.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In this article, we present an analysis of the arguments of seven tenth grade students (14 to 16 years old) when they try to define a geometric figure unknown to them, and justify their decision, for which they use the negation of propositions. The objective of our study was to find the characteristics of the use of negations, to determine whether what many researchers in mathematics education have found is true: the use of negations in arguments entails difficulties. The research strategy used was case study method, because our data were the transcriptions of the video and audio registers of the student's work. We conclude that the type of tasks proposed to the students, designed to favor the mathematical processes defining and justifying and the use of a dynamic geometry software, promotes spontaneous use of negations. We identify under what circumstances the students recurred to the use of negations to justify their assertions.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[argumento]]></kwd>
<kwd lng="es"><![CDATA[negación]]></kwd>
<kwd lng="es"><![CDATA[definir]]></kwd>
<kwd lng="es"><![CDATA[argumentar]]></kwd>
<kwd lng="es"><![CDATA[geometría dinámica]]></kwd>
<kwd lng="en"><![CDATA[argument]]></kwd>
<kwd lng="en"><![CDATA[negation]]></kwd>
<kwd lng="en"><![CDATA[defining]]></kwd>
<kwd lng="en"><![CDATA[justifying]]></kwd>
<kwd lng="en"><![CDATA[dynamic geometry]]></kwd>
</kwd-group>
</article-meta>
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<given-names><![CDATA[Y. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cognitive Development of Proof]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Hanna]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[de Villiers]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proof and Proving in Mathematics Education: The 19th ICMI Study]]></source>
<year>2012</year>
<volume>15</volume>
<page-range>13-49</page-range><publisher-loc><![CDATA[Dordrecht, Netherlands ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
