<?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>S2215-34702025000100315</article-id>
<article-id pub-id-type="doi">10.15359/ru.39-1.18</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Modelización matemática en temas de Cálculo: dos aproximaciones tecnológicas a un problema de optimización]]></article-title>
<article-title xml:lang="en"><![CDATA[Mathematical modeling in calculus: two technological approaches to an optimization problem]]></article-title>
<article-title xml:lang="pt"><![CDATA[Modelagem matemática em cálculo: duas abordagens tecnológicas para um problema de otimização]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez-Miraval]]></surname>
<given-names><![CDATA[Mihály]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Cuéllar]]></surname>
<given-names><![CDATA[Daysi]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Tejera]]></surname>
<given-names><![CDATA[Mathías]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Curo Cubas]]></surname>
<given-names><![CDATA[Agustín]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Peruana de Ciencias Aplicadas Departamento de Ciencias Línea de Matemáticas]]></institution>
<addr-line><![CDATA[Lima ]]></addr-line>
<country>Peru</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Pontificia Universidad Católica del Perú Departamento Académico de Ciencias Sección Matemáticas]]></institution>
<addr-line><![CDATA[Lima ]]></addr-line>
<country>Peru</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Tecnológica Departamento de Innovación y Emprendimiento Especialización en Tecnología Educativa]]></institution>
<addr-line><![CDATA[Montevideo ]]></addr-line>
<country>Uruguay</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad Peruana de Ciencias Aplicadas Departamento de Ciencias Línea de Matemáticas]]></institution>
<addr-line><![CDATA[Lima ]]></addr-line>
<country>Peru</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2025</year>
</pub-date>
<volume>39</volume>
<numero>1</numero>
<fpage>315</fpage>
<lpage>339</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702025000100315&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702025000100315&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702025000100315&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  (Objetivo) El estudio tuvo por objetivo analizar el proceso de modelización que realizan estudiantes en etapa universitaria al resolver un problema que involucra la noción de optimización de funciones.  (Metodología) Se trata la modelización matemática desde la perspectiva denominada &#8220;modelos y modelización&#8221;, y se hace uso de los ciclos de modelización de Blum, Leiß y Borromeo-Ferri, así como del ciclo extendido para el uso de las tecnologías digitales, para describir los procesos que realiza el estudiantado en su resolución. El diseño de investigación es el estudio de casos múltiples de tipo instrumental. Se reporta el trabajo de dos estudiantes de segundo ciclo de la carrera de Administración de una universidad de Lima- Perú, matriculados en el curso Cálculo del primer semestre del 2022. La recolección de datos se llevó a cabo mediante fichas de trabajo, archivos de GeoGebra y entrevistas semiestructuradas.  (Resultados) Los resultados muestran que el alumnado desarrolló habilidades en tres ámbitos: en el mundo real, al entender que el costo del cableado varía según la longitud y el tipo de cable; en el mundo matemático, al crear y usar un modelo matemático para optimizar una función aplicando conocimientos previos de cálculo; y en el mundo computacional, al emplear GeoGebra para aplicar estos conceptos.  (Conclusiones) Se concluye que GeoGebra es una herramienta sólida para el desarrollo de problemas de modelización, dado que, en su interfaz se pueden conectar los campos numérico, algebraico, geométrico y variacional, así como brindar una mejor interpretación del fenómeno de cambio que subyace a un problema de optimización.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  (Objective)  The study aimed to analyze the modeling process conducted by university students when solving a problem involving the notion of function optimization.  (Methodology)  Mathematical modeling is approached from the perspective known as models and modeling, utilizing the modeling cycles from Blum, Leiß, and Borromeo-Ferri, as well as the extended cycle for the use of digital technologies, to describe the processes students conduct during their resolution. The research design is an instrumental multiple case study. The paper reports the work of two second-semester students from the Business Administration program at a university in Lima, Peru, enrolled in the Calculus course during the first semester of 2022. Data was collected using worksheets, GeoGebra files, and semi-structured interviews.  (Results)  Results show that students developed skills in three areas: in the real world, by understanding that the cost of wiring varies according to the length and type of cable; in the mathematical world, by creating and using a mathematical model to optimize a function by applying prior knowledge on calculus; and in the computational world, by using GeoGebra to apply these concepts.  (Conclusions)  It is concluded that GeoGebra is a solid tool for developing modeling problems since its interface allows connecting the numerical, algebraic, geometric, and variational fields, providing a better interpretation of the phenomenon of change underlying an optimization problem.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo  (Objetivo)  O estudo teve como objetivo analisar o processo de modelagem realizado por estudantes universitários na resolução de um problema que envolve a noção de otimização de funções.  (Metodologia)  A modelagem matemática é abordada sob a perspectiva denominada &#8220;modelos e modelagem&#8221;, utilizando os ciclos de modelagem de Blum, Leiß e Borromeo-Ferri, bem como o ciclo estendido para o uso de tecnologias digitais, para descrever os processos realizados pelos estudantes em sua resolução. O delineamento da pesquisa é o estudo de múltiplos casos de tipo instrumental. Relata-se o trabalho de dois alunos do segundo ciclo do programa de Administração de uma universidade em Lima, Peru, matriculados no curso de Cálculo para o primeiro semestre de 2022. A coleta de dados foi realizada por meio de planilhas, arquivos do GeoGebra e entrevistas semiestruturadas.  (Resultados)  Os resultados mostram que os alunos desenvolveram habilidades em três áreas: no mundo real, ao entender que o custo da fiação varia dependendo do comprimento e do tipo de cabo; no mundo matemático, ao criar e usar um modelo matemático para otimizar uma função aplicando conhecimentos prévios de cálculo; e no mundo computacional, ao usar o GeoGebra para aplicar esses conceitos.  (Conclusões)  Conclui-se que o GeoGebra é uma ferramenta sólida para o desenvolvimento de problemas de modelagem, uma vez que sua interface pode conectar os campos numérico, algébrico, geométrico e variacional, além de fornecer uma melhor interpretação do fenômeno de mudança subjacente a um problema de otimização.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[modelización matemática]]></kwd>
<kwd lng="es"><![CDATA[ciclos de modelización]]></kwd>
<kwd lng="es"><![CDATA[optimización]]></kwd>
<kwd lng="es"><![CDATA[GeoGebra]]></kwd>
<kwd lng="es"><![CDATA[funciones económicas]]></kwd>
<kwd lng="es"><![CDATA[criterios de derivación]]></kwd>
<kwd lng="es"><![CDATA[matemática educativa]]></kwd>
<kwd lng="en"><![CDATA[mathematical modeling]]></kwd>
<kwd lng="en"><![CDATA[modeling cycles]]></kwd>
<kwd lng="en"><![CDATA[optimization]]></kwd>
<kwd lng="en"><![CDATA[GeoGebra]]></kwd>
<kwd lng="en"><![CDATA[economic functions]]></kwd>
<kwd lng="en"><![CDATA[derivation criteria]]></kwd>
<kwd lng="en"><![CDATA[mathematics education]]></kwd>
<kwd lng="pt"><![CDATA[modelagem matemática]]></kwd>
<kwd lng="pt"><![CDATA[ciclos de modelagem]]></kwd>
<kwd lng="pt"><![CDATA[otimização]]></kwd>
<kwd lng="pt"><![CDATA[GeoGebra]]></kwd>
<kwd lng="pt"><![CDATA[funções econômicas]]></kwd>
<kwd lng="pt"><![CDATA[critérios de derivação]]></kwd>
<kwd lng="pt"><![CDATA[matemática educacional]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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