<?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>S2448-80892021000100098</article-id>
<article-id pub-id-type="doi">10.24844/em3301.04</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una lección sobre el teorema de Thales, vista desde el conocimiento especializado del profesor]]></article-title>
<article-title xml:lang="en"><![CDATA[A lesson on Thales&#8217; theorem viewed from the specialized teacher&#8217;s knowledge]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Climent]]></surname>
<given-names><![CDATA[Nuria]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Espinoza-Vásquez]]></surname>
<given-names><![CDATA[Gonzalo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Carrillo]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Henríquez-Rivas]]></surname>
<given-names><![CDATA[Carolina]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ponce]]></surname>
<given-names><![CDATA[Rodrigo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Huelva Didáctica de la Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</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[,Universidad de Huelva  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Talca Facultad de Ciencias de la Educación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Universidad de Talca Instituto de Matemática y Física ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2021</year>
</pub-date>
<volume>33</volume>
<numero>1</numero>
<fpage>98</fpage>
<lpage>124</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892021000100098&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892021000100098&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892021000100098&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Este artículo, partiendo de la observación de una lección de un profesor chileno de Educación Secundaria en la que se introduce el teorema de Thales, aborda la interpretación de dicha lección desde el conocimiento del profesor, utilizando el modelo Mathematics Teacher&#8217;s Specialised Knowledge (MTSK). Se consideran aspectos del conocimiento especializado en relación, por un lado, con el teorema de Thales como objeto de aprendizaje y enseñanza, y, por otro, con la práctica matemática de demostrar. Teniendo como referente las propuestas del currículo chileno para la enseñanza de dicho contenido, extraemos una imagen de elementos relacionados del conocimiento del profesor que nos permiten explicar qué se enfatiza en la lección. Los resultados muestran que la finalidad de aplicación que el profesor atribuye al aprendizaje del teorema, junto con su visión de este como una consecuencia de la semejanza y el énfasis en su tratamiento numérico, se muestran relacionados con el conocimiento de registros, las conexiones que establece con otros contenidos, el uso de recursos, el tipo de tareas que propone y el conocimiento de la práctica matemática que evidencia.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstrac: This paper presents the analysis of an observed lesson on Thales&#8217;s Theorem in a Chilean secondary school, using the Mathematics Teacher&#8217;s Spe-cialised Knowledge (MTSK) model. We consider various aspects of the teacher&#8217;s specialised knowledge with respect to Thales&#8217;s Theorem itself, as an element of teaching and learning, and to demonstrations, as a mathematical practice, in general. From this analysis, and guided by the Chilean syllabus requirement for this topic, we construct a snapshot of the interrelated elements of knowledge deployed by the teacher, which enables us to account for how he brings par-ticular aspects into focus. The findings show that the utility which he attaches to the theorem, that of being able to apply it, alongside his view of it as a result of similarity and his emphasis on a numerical approach, is closely linked to his knowledge of registers, the interconnections he makes with other content items, his use of resources, the kind of tasks he sets up, and the knowledge of math-ematical practices he makes evident.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Teorema de Thales]]></kwd>
<kwd lng="es"><![CDATA[Semejanza.]]></kwd>
<kwd lng="es"><![CDATA[Conocimiento del profesor]]></kwd>
<kwd lng="es"><![CDATA[Práctica del profesor de matemáticas]]></kwd>
<kwd lng="es"><![CDATA[Educación Secundaria.]]></kwd>
<kwd lng="en"><![CDATA[Thales&#8217;s Theorem]]></kwd>
<kwd lng="en"><![CDATA[Similarity]]></kwd>
<kwd lng="en"><![CDATA[Teacher knowledge]]></kwd>
<kwd lng="en"><![CDATA[Mathematics teaching practices]]></kwd>
<kwd lng="en"><![CDATA[Secondary education.]]></kwd>
</kwd-group>
</article-meta>
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