<?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>S2448-80892021000200115</article-id>
<article-id pub-id-type="doi">10.24844/em3302.05</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[&#8220;Los saltos de las ranas&#8221;. Estudio de una secuencia didáctica de proporcionalidad, con problemas de comparación de razones, en quinto grado de primaria]]></article-title>
<article-title xml:lang="en"><![CDATA[&#8220;The jumps of the frogs.&#8221; Study of a didactic sequence on proportionality, with ratio comparison tasks, in fifth grade of primary school]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Block Sevilla]]></surname>
<given-names><![CDATA[David]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Politécnico Nacional Centro de Investigaciones y Estudios Avanzados ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</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>2</numero>
<fpage>115</fpage>
<lpage>146</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892021000200115&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892021000200115&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892021000200115&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Se presenta un estudio de didáctica de la proporcionalidad, centra-do en la comparación de razones en quinto grado de primaria. Se diseñó y aplicó una secuencia de situaciones en el contexto de unas ranas que, al dar cierto número de saltos, avanzan cierto número de metros; se trata de averiguar qué rana da los saltos más grandes. La medida de un salto no es un número entero, pero no es necesario explicitarlo, las comparaciones se hacen en el nivel de las razones entre números naturales &#8220;tantos metros en tantos saltos&#8221;. Un programa de computadora realimentó las anticipaciones de los alumnos, permitiéndoles detectar sus errores. La secuencia buscó favorecer el aprendizaje de la noción de razón y, de manera más general, el desarrollo del pensamiento proporcional. Los resultados confirman que los problemas fueron adecuados para dicho propósito y también para favorecer el desarrollo de la capacidad de argumentación, al formular y debatir reglas generales.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: This paper is about a didactical study on comparison of ratios in fifth grade of primary school. A sequence of situations was designed and applied in the context of frogs that, with a certain number of jumps, advance a certain number of meters; it&#8217;s about figuring out which jumps are bigger. The measure of a jump is not a whole number, but it is not necessary to make this number explicit, the comparisons are made at the level of ratios between natural numbers. A computer program was used to allow students to detect errors in their anticipations. The sequence seeks to favor the learning of the notion of ratio and, more generally, the development of proportional thinking. The results confirm the adequacy of the problems to move in that direction and reveal an unforeseen achievement: the development of the capacity for argumentation, to formulate and debate general rules.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Enseñanza de las Matemáticas]]></kwd>
<kwd lng="es"><![CDATA[Educación Básica]]></kwd>
<kwd lng="es"><![CDATA[Proporcionalidad]]></kwd>
<kwd lng="es"><![CDATA[Razón]]></kwd>
<kwd lng="es"><![CDATA[Números racionales.]]></kwd>
<kwd lng="en"><![CDATA[Teaching of Mathematics]]></kwd>
<kwd lng="en"><![CDATA[Basic Education]]></kwd>
<kwd lng="en"><![CDATA[Proportionality]]></kwd>
<kwd lng="en"><![CDATA[Ratios]]></kwd>
<kwd lng="en"><![CDATA[Rational Numbers]]></kwd>
</kwd-group>
</article-meta>
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