<?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>2215-3470</journal-id>
<journal-title><![CDATA[Uniciencia]]></journal-title>
<abbrev-journal-title><![CDATA[Uniciencia]]></abbrev-journal-title>
<issn>2215-3470</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional, Costa Rica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-34702023000100382</article-id>
<article-id pub-id-type="doi">10.15359/ru.37-1.21</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Un estudio comparado del azonamiento proporcional de estudiantado costarricense y español en tareas de comparación de razones]]></article-title>
<article-title xml:lang="en"><![CDATA[A Comparative Study of Proportional reasoning of Costa Rican and Spanish students in ratio comparison problems]]></article-title>
<article-title xml:lang="pt"><![CDATA[Estudo comparativo do raciocínio proporcional de estudantes costarriquenhos e espanhóis em tarefas de comparação de razões]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[Carmen]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández-Solís]]></surname>
<given-names><![CDATA[Luis Armando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática ]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Estatal a Distancia Escuela de Ciencias Exactas y Naturales ]]></institution>
<addr-line><![CDATA[San José ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2023</year>
</pub-date>
<volume>37</volume>
<numero>1</numero>
<fpage>382</fpage>
<lpage>401</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702023000100382&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702023000100382&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702023000100382&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  (Objetivo)  El objetivo del trabajo fue evaluar el nivel de razonamiento proporcional y estrategias en problemas de comparación de razones de estudiantado costarricense y español entre 11 y 16 años.  (Metodología)  Mediante un enfoque de investigación interpretativo, se propone a 704 estudiantes uno de dos cuestionarios con tres ítems sobre comparación de razones (en total seis niveles diferentes de razonamiento proporcional, según Noelting). Se presenta el porcentaje de respuestas correctas y niveles de razonamiento proporcional y el resultado de un análisis de contenido de las estrategias correctas e incorrectas.  (Resultados)  La mayoría de estudiantes responden correctamente a los problemas de menor nivel de razonamiento proporcional de Noelting (IA a IIA), disminuyendo esta proporción en los cursos 6º a 8º de Educación General Básica al aumentar el nivel de razonamiento proporcional del problema. Resultados similares se obtienen respecto a las estrategias correctas. Las estrategias incorrectas más frecuentes fueron la comparación de los primeros términos de las razones y las comparaciones aditivas. Prácticamente la totalidad de estudiantes alcanza los dos primeros niveles de razonamiento proporcional de Noelting, y conforme avanza el curso, una proporción mayor consigue los siguientes niveles de razonamiento, pero una cantidad pequeña de estudiantes, ni siquiera en el décimo curso de Educación Diversificada llega al nivel IIIA correspondiente a las operaciones formales.  (Conclusiones) Se concluye la necesidad de reforzar en la enseñanza el razonamiento sobre comparación de razones, y tenerlo en cuenta en los temas matemáticos basados en este razonamiento.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  (Objective)  This study seeks to evaluate the level of proportional reasoning and strategies in ratio comparison problems of Costa Rican and Spanish students between 11 and 16 years old.  (Methodology)  Using an interpretative research approach, 704 students were given one of two questionnaires with three items on ratio comparison (a total of six different levels of proportional reasoning, according to Noelting). The percentage of correct answers and levels of proportional reasoning, and the result of a content analysis of correct and incorrect strategies are presented.  (Results)  The majority of students correctly answered the problems with the lowest Noelting proportional reasoning level (IA to IIA), with this proportion decreasing in grades 6 to 8 of General Basic Education as the proportional reasoning level of the problem increased. Similar results were obtained with respect to correct strategies. The most frequent incorrect strategies were the comparison of the first terms of ratios and additive comparisons. Virtually all students reached the first two proportional reasoning levels of Noelting, and as the course progressed, a higher proportion attained the following levels of reasoning, but few students achieved level IIIA, corresponding to formal operations, even in the highest grade (grade 10).  (Conclusions)  It was concluded that it is necessary to reinforce the teaching of reasoning about comparison of ratios, and to take it into account in the mathematical topics based on this reasoning.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo  (Objetivo)  O objetivo deste estudo foi avaliar o nível de raciocínio proporcional e estratégias em problemas de comparação de proporções de estudantes costarriquenhos e espanhóis entre 11 e 16 anos.  (Metodologia)  Através de uma abordagem de pesquisa interpretativa, é proposto a 704 alunos um de dois questionários com três itens sobre comparação de proporções (no total seis níveis diferentes de raciocínio proporcional, segundo Noelting). São apresentados o percentual de respostas corretas e os níveis de raciocínio proporcional e o resultado de uma análise de conteúdo das estratégias corretas e incorretas.  (Resultados)  A maioria dos alunos responde corretamente aos problemas de Noelting com um menor nível de raciocínio proporcional (IA a IIA), diminuindo essa proporção no 6º ao 8º ano da Base Nacional Comum, aumentando o nível de raciocínio proporcional do problema. Resultados semelhantes são obtidos com relação às estratégias corretas. As estratégias incorretas mais frequentes foram comparação dos primeiros termos das razões e comparações aditivas. Praticamente todos os alunos atingem os dois primeiros níveis de raciocínio proporcional de Noelting, e à medida que o curso avança, uma proporção maior atinge os seguintes níveis de raciocínio, mas um pequeno número de alunos, mesmo no décimo ano do Ensino Diversificado, não atinge o nível IIIA correspondente às operações formais.  (Conclusões)  Conclui-se a necessidade de reforçar no ensino o raciocínio sobre comparação de razões, e levá-lo em conta nos tópicos matemáticos baseados nesse raciocínio.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Evaluación]]></kwd>
<kwd lng="es"><![CDATA[Nivel de razonamiento]]></kwd>
<kwd lng="es"><![CDATA[Proporcionalidad]]></kwd>
<kwd lng="es"><![CDATA[Comparación de razones]]></kwd>
<kwd lng="es"><![CDATA[Estudio comparado]]></kwd>
<kwd lng="en"><![CDATA[Evaluation]]></kwd>
<kwd lng="en"><![CDATA[level of reasoning]]></kwd>
<kwd lng="en"><![CDATA[proportionality]]></kwd>
<kwd lng="en"><![CDATA[comparison of ratios]]></kwd>
<kwd lng="en"><![CDATA[comparative study.]]></kwd>
<kwd lng="pt"><![CDATA[avaliação]]></kwd>
<kwd lng="pt"><![CDATA[nível de raciocínio]]></kwd>
<kwd lng="pt"><![CDATA[proporcionalidade]]></kwd>
<kwd lng="pt"><![CDATA[comparação de proporções]]></kwd>
<kwd lng="pt"><![CDATA[estudo comparativo.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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