<?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>S2448-80892023000100035</article-id>
<article-id pub-id-type="doi">10.24844/em3501.02</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Similitudes y diferencias entre la educación de la mirada en geometría elemental y en arte figurativo]]></article-title>
<article-title xml:lang="en"><![CDATA[Similarities and differences between gaze education in elementary geometry and figurative art]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[Bruno]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[Raymond]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Distrital Francisco José de Caldas Departamento de Matematica ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Université du Littoral Côte d&#8217;Opale  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>France</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<volume>35</volume>
<numero>1</numero>
<fpage>35</fpage>
<lpage>58</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892023000100035&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892023000100035&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892023000100035&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Un acto espontaneo y aparentemente inmediato y simple, como la mirada, que se usa para observar las figuras en geometría o las pinturas en el arte figurativo, revela por el contrario una complejidad notable no esperada en el aprendizaje de la geometría. En este estudio se sugieren modalidades didácticas para ayudar a educar esta mirada. Se proponen analogías entre el &#8220;ver&#8221; figuras geométricas y el &#8220;ver&#8221; obras del arte figurativo. Se analiza el fenómeno del reconocimiento de las figuras así llamadas imposibles y se proponen algunos ejemplos de obras de arte para la interpretación de las cuales no es suficiente la mirada, sino que es necesario un análisis de tipo semiótico]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. An apparently immediate and simple spontaneous act, as the sight, that we use to look at figures in geometry and at pictures in figurative art, reveals on the contrary unexpected complexities with remarkable consequences on the learning of geometry. In this study we suggest didactical ways to educate it. We suggest several analogies between &#8220;seeing&#8221; geometrical figures and &#8220;seeing&#8221; in figurative art. We analyse the recognition of the so-called impossible figures and we provide some examples of works of art for whose interpretation sight is not enough, but it requires a semiotic analysis (suggested by the author).]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[geometría elemental]]></kwd>
<kwd lng="es"><![CDATA[didáctica de la geometría]]></kwd>
<kwd lng="es"><![CDATA[mirada]]></kwd>
<kwd lng="es"><![CDATA[ver en geometría - ver en el arte figurativo]]></kwd>
<kwd lng="en"><![CDATA[elementary geometry]]></kwd>
<kwd lng="en"><![CDATA[geometry education]]></kwd>
<kwd lng="en"><![CDATA[sight]]></kwd>
<kwd lng="en"><![CDATA[to see in geometry - to see in figurative art]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Asenova]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Vedere geometricamente: La percezione non iconica nella scuola primaria]]></article-title>
<source><![CDATA[La matematica e la sua didattica]]></source>
<year>2018</year>
<volume>26</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>173-210</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Oscar Reutersvärd]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Bonfiglioli]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Valentini]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Matematica, arte e tecnologia: da Escher alla computer graphics]]></source>
<year>2000</year>
<page-range>xix-xi</page-range><publisher-name><![CDATA[Aspasia]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[L&#8217;opera di Oscar Reutersvärd]]></article-title>
<source><![CDATA[La matematica e la sua didattica]]></source>
<year>2002</year>
<volume>16</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>240-5</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Oscar Reutersvärd]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2005</year>
<volume>8</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>379-82</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Figurative arts and mathematics: Pipes, horses and meanings]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Capecchi]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Buscema]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Contucci]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Applications of Mathematics in Models, Artificial Neural Networks and Arts: Mathematics and Society]]></source>
<year>2010</year>
<page-range>491-504</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B]]></given-names>
</name>
</person-group>
<source><![CDATA[Arte e matematica: Metafore, analogie, rappresentazioni, identità tra due mondi possibili]]></source>
<year>2015</year>
<publisher-name><![CDATA[Edizioni Dedalo]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bernar Venet: Elogio del processo razionale]]></article-title>
<source><![CDATA[Nuova Meta]]></source>
<year>2015</year>
<volume>37</volume>
<page-range>30-41</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[L&#8217;educazione dello sguardo in geometria elementare e in arte figurativa. Quali variabili cognitive e didattiche sono coinvolte? Come si rappresenta in arte l&#8217;impossibilità? Quali elementi semiotici possono essere coinvolti nell&#8217;arte? The education of the gaze in elementary geometry and in figurative art. What are the cognitive and educational variables involved? How does art represent impossibility? What semiotic elements can we take into account be in art?]]></article-title>
<source><![CDATA[La matemática e la sua didattica]]></source>
<year>2019</year>
<volume>27</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>47-67</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Menna]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[De mathematica]]></source>
<year>1974</year>
<publisher-name><![CDATA[Galleria dell&#8217;Obelisco]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Di Genova]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[Storia dell&#8217;arte italiana del &#8217;900]]></source>
<year>1993</year>
<publisher-name><![CDATA[Bora]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Les conditions cognitives de l&#8217;apprentissage de la géométrie: Développement de la visualisation, différenciation des raisonnements et coordination de leurs fonctionnements]]></article-title>
<source><![CDATA[Annales de Didactique et de Sciences Cognitives]]></source>
<year>2005</year>
<volume>10</volume>
<page-range>5-53</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Eight problems for a semiotic approach in mathematics education]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Radford]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Schubring]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Seeger]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Semiotics in Mathematics Education: Epistemology, History, Classroom and Culture]]></source>
<year>2008</year>
<page-range>39-61</page-range><publisher-name><![CDATA[Sense Publishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Figures et visualisation géométrique: «voir» en géométrie]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Baillé]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Du mot au concept: Figure]]></source>
<year>2015</year>
<page-range>147-82</page-range><publisher-name><![CDATA[Presses Universitaires]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Per l&#8217;educazione allo sguardo in geometria elementare e in pittura]]></article-title>
<source><![CDATA[La matematica e la sua didattica]]></source>
<year>2018</year>
<volume>26</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>211-45</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Eco]]></surname>
<given-names><![CDATA[U.]]></given-names>
</name>
</person-group>
<source><![CDATA[Trattato di semiotica generale]]></source>
<year>1975</year>
<publisher-name><![CDATA[Bompiani]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Frege]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Über Sinn und Bedeutung]]></article-title>
<source><![CDATA[Zeitschrift für Philosophie und philosophische Kritik]]></source>
<year>1892</year>
<volume>100</volume>
<page-range>25-50</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lageira]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Magritte: Mots et images]]></source>
<year>2003</year>
<publisher-name><![CDATA[Gallimard]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Magritte]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Les mots et les images]]></article-title>
<source><![CDATA[La Révolution surréaliste]]></source>
<year>1929</year>
<volume>5</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>32-3</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Menna]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[La linea analitica dell&#8217;arte moderna]]></source>
<year>1975</year>
<publisher-name><![CDATA[Einaudi]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Penrose]]></surname>
<given-names><![CDATA[L. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Penrose]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Impossible objects: A special type of visual illusion]]></article-title>
<source><![CDATA[British Journal of Psychology]]></source>
<year>1958</year>
<volume>49</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>31-3</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
