<?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>S2215-34702023000100001</article-id>
<article-id pub-id-type="doi">10.15359/ru.37-1.1</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Significados parciales del teorema de Pitágoras usados por docentes en la creación de tareas en el marco de un programa de formación continua]]></article-title>
<article-title xml:lang="en"><![CDATA[Partial meanings of the Pythagorean theorem used by teachers in the creation of tasks within the framework of a continuing education program]]></article-title>
<article-title xml:lang="pt"><![CDATA[Significados parciais do teorema de Pitágoras utilizado pelos professores na criação de tarefas no âmbito de um programa de educação continuada]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Calle]]></surname>
<given-names><![CDATA[Eulalia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Breda]]></surname>
<given-names><![CDATA[Adriana]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Font]]></surname>
<given-names><![CDATA[Vicenç]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Cuenca Facultad de Filosofía, Letras y Ciencias de la Educación Departamento de Educación Eulalia Calle]]></institution>
<addr-line><![CDATA[Cuenca ]]></addr-line>
<country>Ecuador</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universitat de Barcelona Lingüística y Literaria, y Didáctica de las Ciencias Experimentales y de la Matemática ]]></institution>
<addr-line><![CDATA[Barcelona ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universitat de Barcelona Lingüística y Literaria, y Didáctica de las Ciencias Experimentales y de la Matemática ]]></institution>
<addr-line><![CDATA[Barcelona ]]></addr-line>
<country>Spain</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>1</fpage>
<lpage>23</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702023000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702023000100001&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702023000100001&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  (Objetivo)  El objetivo de este artículo es presentar resultados de una investigación sobre la enseñanza y el aprendizaje del criterio ''implementar una muestra representativa de la complejidad del objeto matemático que se quiere enseñar&#8221;, implementado con profesorado de secundaria de matemáticas de Ecuador enun máster de formación continua.  (Metodología)  Después de explicar el proceso de instrucción en elque se enseñó este criterio, se presenta el análisis cualitativo de las respuestas a una de las tareas quese propuso al alumnado de este máster: crear tareas en las que, para su resolución, se tenía que aplicarun determinado significado parcial del teorema de Pitágoras (el geométrico o el aritmético-algebraico),como ejemplo de evidencia del aprendizaje conseguido.  (Resultados)  Los resultados muestran que algunos alumnos del máster proponen tareas para trabajar el teorema de Pitágoras, pero no especifican ni justifican si las tareas diseñadas por ellos están relacionadas con el significado aritmético-algebraico, con el geométrico o con ambos; otros no propusieron ninguna tarea para trabajar el significado aritméticoalgebraico y un participante del máster no propuso ninguna tarea para trabajar el significado geométrico. También se observa que algunos crearon tareas que no se corresponden con el significado que señalan.  (Conclusiones)  Se concluye que los profesores tienen dificultades para crear una tarea y señalar el tipo del significado del teorema de Pitágoras que se debe usar para resolverla y que el significado geométrico es el que mejor relacionan con la tarea que proponen.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  (Objective) This article presents the results of research on the teaching and learning of the criterion ''implement a representative sample of the complexity of the mathematical object to be taught,''which was carried out with high school mathematics teachers from Ecuador in a master's degree program in continuing education.  (Methodology)  After a discussion of the instructional process which was used when teaching this criterion, a qualitative analysis of the responses to one of the tasks proposed for the students in this master's degree program is presented: creating tasks for whose resolution the students had to apply a certain partial meaning of the Pythagorean theorem (geometric or arithmetic-algebraic), as a demonstration of the learning that they had achieved.  (Results)  The results show that some students in the master's degree program proposed tasks to work on the Pythagorean theorem, but did not specify or justify whether the tasks they designed were related to arithmetic-algebraic meaning, to geometric meaning or to both; other students did not propose any task to work on arithmetic-algebraic meaning; and one participant in the master's program did not propose any task to work on geometric meaning. It was also observed that some students created tasks that did not correspond to either of these meanings.  (Conclusions)  It was concluded that teachers have difficulties in creating a task and indicating the type of meaning of the Pythagorean theorem that should be used to solve it, and that geometric meaning was most related to the tasks that they proposed.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo  (Objetivo)  O objetivo deste artigo é apresentar os resultados de uma pesquisa sobre o ensino e a aprendizagem do critério ''implementar uma amostra representativa da complexidade do objeto matemático a ser ensinado&#8221;, executado com professores de matemática do Ensino Médio do Equador em um mestrado de educação continuada.  (Metodologia)  Depois de explicar o processo instrucional no qual este critério foi ensinado, apresentou-se a análise qualitativa das respostas a uma das tarefas propostas aos alunos deste mestrado: criar tarefas nas quais, para sua resolução, eles tinham que aplicar um determinado significado parcial do teorema de Pitágoras (geométrico ou aritmético e algébrico), como um exemplo de evidência da aprendizagem alcançada.  (Resultados)  Os resultados mostram que alguns alunos de mestrado propuseram tarefas para trabalhar o teorema de Pitágoras, mas não especificaram ou justificaram se as tarefas projetadas por eles estão relacionadas ao significado aritmético e algébrico, ao significado geométrico ou a ambos; outros não propuseram nenhuma tarefa para trabalhar o significado aritmético e algébrico e um participante do mestrado não propôs nenhuma tarefa para trabalhar o significado geométrico. Observa-se, também, que alguns deles criaram tarefas que não correspondem ao significado que indicam.  (Conclusões)  Conclui-se que os professores têm dificuldade em criar uma tarefa e apontar o tipo de significado do teorema de Pitágoras que deve ser usado para resolvê-la e que o significado geométrico é aquele que eles relacionam melhor com a tarefa que propõem.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Formación continua de profesores]]></kwd>
<kwd lng="es"><![CDATA[significados parciales del teorema de Pitágoras]]></kwd>
<kwd lng="es"><![CDATA[idoneidad didáctica]]></kwd>
<kwd lng="es"><![CDATA[creación de tareas]]></kwd>
<kwd lng="en"><![CDATA[Continuing education of teachers]]></kwd>
<kwd lng="en"><![CDATA[partial meanings of the Pythagorean theorem]]></kwd>
<kwd lng="en"><![CDATA[didactic suitability]]></kwd>
<kwd lng="en"><![CDATA[task creation]]></kwd>
<kwd lng="pt"><![CDATA[educação continuada de professores]]></kwd>
<kwd lng="pt"><![CDATA[significados parciais do teorema de Pitágoras]]></kwd>
<kwd lng="pt"><![CDATA[idoneidade didática]]></kwd>
<kwd lng="pt"><![CDATA[criação de tarefas]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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