<?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>0185-2698</journal-id>
<journal-title><![CDATA[Perfiles educativos]]></journal-title>
<abbrev-journal-title><![CDATA[Perfiles educativos]]></abbrev-journal-title>
<issn>0185-2698</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Investigaciones sobre la Universidad y la Educación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0185-26982020000100031</article-id>
<article-id pub-id-type="doi">10.22201/iisue.24486167e.2019.167.58890</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Relaciones entre área y perímetro: de la intuición inicial a la deducción operatoria. Estudio en niños de alto desempeño académico]]></article-title>
<article-title xml:lang="en"><![CDATA[Ratios of area to perimeter: from initial intuition to operative deduction. A study in children with high academic performance]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ávila]]></surname>
<given-names><![CDATA[Alicia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[Silvia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Pedagógica Nacional  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,sgp0615@yahoo.com.mx  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2020</year>
</pub-date>
<volume>42</volume>
<numero>167</numero>
<fpage>31</fpage>
<lpage>52</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0185-26982020000100031&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0185-26982020000100031&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0185-26982020000100031&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Este artículo deriva de una investigación cuyo objetivo fue analizar las intuiciones iniciales de niños de 9 a 12 años respecto de las relaciones entre área y perímetro y el proceso mediante el cual abandonan tales intuiciones. El estudio se llevó a cabo con 12 niños de alto desempeño escolar en matemáticas que en el momento de la investigación cursaban cuarto, quinto y sexto grado de educación primaria. Se analizan las intuiciones iniciales sobre las relaciones área-perímetro y su evolución hacia la deducción operatoria a partir de la resolución de seis problemas que las implican y el diálogo sobre las soluciones elaboradas. Con el apoyo del interrogatorio crítico propio de la teoría psicogenética se identifican también los recursos matemáticos que utilizan los niños en ese proceso. Se concluye que el trabajo sobre estas relaciones con un enfoque geométrico tiene grandes potencialidades para desarrollar el pensamiento matemático de los niños.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This article is the product of an investigation which sought to analyze the initial intuitions of children ages 9 to 12 regarding ratios of area to perimeter and the process whereby they abandon such intuitions. The study was conducted with 12 children with high scholastic performance in mathematics, who, at the time of the investigation, were in the fourth, fifth, and sixth years of elementary school. We analyze their initial intuitions on area-perimeter ratios and their evolution toward operative deduction based on solving six problems involving them and discussion of the solutions reached. With the aid of critical questioning rooted in psychogenetic theory, we also identify the mathematical resources the children used in that process. The study concludes that working on these ratios with a geometric approach has great potential to develop mathematical thinking in children.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Relaciones áreaperímetro]]></kwd>
<kwd lng="es"><![CDATA[Niños]]></kwd>
<kwd lng="es"><![CDATA[Alto desempeño académico]]></kwd>
<kwd lng="es"><![CDATA[Intuición]]></kwd>
<kwd lng="es"><![CDATA[Pensamiento matemático]]></kwd>
<kwd lng="es"><![CDATA[Deducción operatoria]]></kwd>
<kwd lng="en"><![CDATA[Area-perimeter ratios]]></kwd>
<kwd lng="en"><![CDATA[Children]]></kwd>
<kwd lng="en"><![CDATA[High performance]]></kwd>
<kwd lng="en"><![CDATA[Intuition]]></kwd>
<kwd lng="en"><![CDATA[Mathematical thinking]]></kwd>
<kwd lng="en"><![CDATA[Operative deduction]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bang]]></surname>
<given-names><![CDATA[Vinh]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Intuition géometrique et déduction opératoire]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Bang]]></surname>
<given-names><![CDATA[Vinh]]></given-names>
</name>
<name>
<surname><![CDATA[Lunzer]]></surname>
<given-names><![CDATA[Eric]]></given-names>
</name>
</person-group>
<source><![CDATA[Conservations spatiales]]></source>
<year>1965</year>
<page-range>1-37</page-range><publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[Presses Universitaires de France]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bang]]></surname>
<given-names><![CDATA[Vinh]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[De l&#8217;intuition Géometrique: Construction de la plus grande surface possible à`partir d&#8217;un périmetre constant]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Bang]]></surname>
<given-names><![CDATA[Vinh]]></given-names>
</name>
<name>
<surname><![CDATA[Lunzer]]></surname>
<given-names><![CDATA[Eric]]></given-names>
</name>
</person-group>
<source><![CDATA[Conservations spatiales]]></source>
<year>1965</year>
<page-range>39-58</page-range><publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[Presses Universitaires de France]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Corberán]]></surname>
<given-names><![CDATA[Rosa María]]></given-names>
</name>
</person-group>
<source><![CDATA[Análisis del concepto de área de superficies planas. Estudio de su comprensión por los estudiantes, desde primaria a la universidad]]></source>
<year>1996</year>
<publisher-loc><![CDATA[Valencia, España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Valencia]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[Bruno]]></given-names>
</name>
<name>
<surname><![CDATA[Fandiño]]></surname>
<given-names><![CDATA[Martha Isabel]]></given-names>
</name>
</person-group>
<source><![CDATA[Area e perimetro. Aspetti concettuali e didaticci]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Bolonia ]]></publisher-loc>
<publisher-name><![CDATA[Centro Studi Erickson]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[D&#8217;Amore]]></surname>
<given-names><![CDATA[Bruno]]></given-names>
</name>
<name>
<surname><![CDATA[Fandiño]]></surname>
<given-names><![CDATA[Martha Isabel]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Relaciones entre área y perímetro: convicciones de maestros y estudiantes]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa. RELIME]]></source>
<year>2007</year>
<volume>10</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>39-68</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Douady]]></surname>
<given-names><![CDATA[Régine]]></given-names>
</name>
<name>
<surname><![CDATA[Perrin]]></surname>
<given-names><![CDATA[MarieJeanne]]></given-names>
</name>
</person-group>
<source><![CDATA[Liason École-College. Mesure des longueurs et des aires]]></source>
<year>1983</year>
<publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[IREM de París/Universidad de París VII]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Perrin]]></surname>
<given-names><![CDATA[Marie-Jeanne]]></given-names>
</name>
<name>
<surname><![CDATA[Douady]]></surname>
<given-names><![CDATA[Régine]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conceptions del élèves à propos d&#8217;aires de surfaces planes]]></article-title>
<source><![CDATA[Actes du premier colloque franco-allemand de didactique des mathématiques et de l&#8217;informatique]]></source>
<year>1988</year>
<page-range>161-72</page-range><publisher-loc><![CDATA[Grénoble (Francia) ]]></publisher-loc>
<publisher-name><![CDATA[La Pensée Sauvage]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Trabajos del año 1960-1961 y sexto simposio del Centro Internacional de Epistemología Genética]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
<name>
<surname><![CDATA[Bang]]></surname>
<given-names><![CDATA[Vinh]]></given-names>
</name>
<name>
<surname><![CDATA[Gréco]]></surname>
<given-names><![CDATA[Pierre]]></given-names>
</name>
<name>
<surname><![CDATA[Grize]]></surname>
<given-names><![CDATA[Jean-Blaise]]></given-names>
</name>
<name>
<surname><![CDATA[Hatwell]]></surname>
<given-names><![CDATA[Yvette]]></given-names>
</name>
<name>
<surname><![CDATA[Seagrim]]></surname>
<given-names><![CDATA[Gavin Nott]]></given-names>
</name>
<name>
<surname><![CDATA[Vurpillot]]></surname>
<given-names><![CDATA[Eliane]]></given-names>
</name>
</person-group>
<source><![CDATA[La epistemología del espacio]]></source>
<year>1971</year>
<page-range>1-38</page-range><publisher-loc><![CDATA[Buenos Aires ]]></publisher-loc>
<publisher-name><![CDATA[El Ateneo]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
</person-group>
<source><![CDATA[La representación del mundo en el niño]]></source>
<year>1973</year>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Espasa-Calpe]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
<name>
<surname><![CDATA[Inhelder]]></surname>
<given-names><![CDATA[Barber]]></given-names>
</name>
<name>
<surname><![CDATA[Szeminska]]></surname>
<given-names><![CDATA[Alina]]></given-names>
</name>
</person-group>
<source><![CDATA[La géométrie spontanée de l&#8217;enfant]]></source>
<year>1973</year>
<publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[Presses Universitaries de France]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
<name>
<surname><![CDATA[Inhelder]]></surname>
<given-names><![CDATA[Barber]]></given-names>
</name>
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
</person-group>
<source><![CDATA[Mental Imagery in the Child]]></source>
<year>1997</year>
<volume>6</volume>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[Jean]]></given-names>
</name>
<name>
<surname><![CDATA[Bang]]></surname>
<given-names><![CDATA[Vinh]]></given-names>
</name>
<name>
<surname><![CDATA[Gréco]]></surname>
<given-names><![CDATA[Pierre]]></given-names>
</name>
<name>
<surname><![CDATA[Grize]]></surname>
<given-names><![CDATA[Jean-Blaise]]></given-names>
</name>
<name>
<surname><![CDATA[Hatwell]]></surname>
<given-names><![CDATA[Yvette]]></given-names>
</name>
<name>
<surname><![CDATA[Seagrim]]></surname>
<given-names><![CDATA[Gavin Nott]]></given-names>
</name>
<name>
<surname><![CDATA[Vurpillot]]></surname>
<given-names><![CDATA[Eliane]]></given-names>
</name>
</person-group>
<source><![CDATA[La epistemología del espacio]]></source>
<year>1971</year>
<publisher-loc><![CDATA[Buenos Aires ]]></publisher-loc>
<publisher-name><![CDATA[El Ateneo]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stavy]]></surname>
<given-names><![CDATA[Ruth]]></given-names>
</name>
<name>
<surname><![CDATA[Tirosh]]></surname>
<given-names><![CDATA[Dina]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Intuitive Rules in Science and Mathematics: The case of &#8216;more of A - more of B&#8217;]]></article-title>
<source><![CDATA[International Journal of Science Education]]></source>
<year>1996</year>
<volume>18</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>653-67</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stephanou]]></surname>
<given-names><![CDATA[Lambros]]></given-names>
</name>
<name>
<surname><![CDATA[Pitta-Pantazi]]></surname>
<given-names><![CDATA[Demetra]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Impact of the Intuitive Rule &#8216;if a then b, if not a then not b&#8217;, in Perimeter and Area Tasks]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Novotná]]></surname>
<given-names><![CDATA[Jarmila]]></given-names>
</name>
<name>
<surname><![CDATA[Moraová]]></surname>
<given-names><![CDATA[Hana]]></given-names>
</name>
<name>
<surname><![CDATA[Krátká]]></surname>
<given-names><![CDATA[Martina]]></given-names>
</name>
<name>
<surname><![CDATA[Stehlíková]]></surname>
<given-names><![CDATA[Nada]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education]]></source>
<year>2006</year>
<volume>5</volume>
<page-range>177-84</page-range><publisher-loc><![CDATA[Praga ]]></publisher-loc>
<publisher-name><![CDATA[PME]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thomas]]></surname>
<given-names><![CDATA[David]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A General Inductive Approach for Analyzing Qualitative Evaluation Data]]></article-title>
<source><![CDATA[American Journal of Evaluation]]></source>
<year>2006</year>
<volume>27</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>237-46</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tsamir]]></surname>
<given-names><![CDATA[Pessia]]></given-names>
</name>
<name>
<surname><![CDATA[Mandel]]></surname>
<given-names><![CDATA[Nurit]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Intuitive Rule Same A-Same B: The case of area and perimeter]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Nakahara]]></surname>
<given-names><![CDATA[Tadao]]></given-names>
</name>
<name>
<surname><![CDATA[Koyama]]></surname>
<given-names><![CDATA[Masataka]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the 24th PME International Conference]]></source>
<year>2000</year>
<volume>4</volume>
<page-range>225-32</page-range><publisher-loc><![CDATA[Hiroshima ]]></publisher-loc>
<publisher-name><![CDATA[PME]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
