<?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>S2215-34702024000100117</article-id>
<article-id pub-id-type="doi">10.15359/ru.38-1.7</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Construcciones y mecanismos mentales para el aprendizaje de la función exponencial en contexto escolar]]></article-title>
<article-title xml:lang="en"><![CDATA[Construction and mental mechanisms for learning about the exponential function in a school setting]]></article-title>
<article-title xml:lang="pt"><![CDATA[Construções e mecanismos mentais para o aprendizado da função exponencial em contexto escolar]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Córdova-Cornejo]]></surname>
<given-names><![CDATA[Víctor]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Aravena-Díaz]]></surname>
<given-names><![CDATA[María]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Parraguez-González]]></surname>
<given-names><![CDATA[Marcela]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional a Distancia Facultad de Ciencias Básicas, Centro de Investigación en Educación Matemática y Estadística, Universidad Católica del Maule, Talca, Chile. Instituto Tecnológico de Costa Rica]]></institution>
<addr-line><![CDATA[San Carlos ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[Valparaíso ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional a Distancia Instituto Tecnológico de Costa Rica Universidad Nacional]]></institution>
<addr-line><![CDATA[San Carlos ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2024</year>
</pub-date>
<volume>38</volume>
<numero>1</numero>
<fpage>117</fpage>
<lpage>137</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702024000100117&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702024000100117&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702024000100117&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  (Objetivo)  El estudio tuvo como objetivo examinar bajo la mirada de la teoría APOE (acción, proceso, objeto y esquema), la producción de estudiantes de educación secundaria al aboradar 11 ítems relacionados con la función exponencial.  (Metodología)  El enfoque fue de corte cualitativo, a través del análisis de contenido. La muestra fue de 15 estudiantes (entre 15 a 18 años), nominados de manera no probabilística con interés de obtener la mayor cantidad de información. Para el diseño del instrumento intencionado desde la teoría, se construyó una descomposición genética hipotética del concepto de función exponencial como objeto cognitivo de acuerdo con las estructuras (acción, proceso, objeto y esquema) y mecanismos mentales (interiorización, coordinación, encapsulación, desencapsulación, reversión), para interpretar la construcción mental que realizan los estudiantes sobre la función en estudio, con base en su desarrollo histórico epistemológico, la presentación en textos escolares y la experiencia del investigador.  (Resultados)  En el nivel de resultados se evidenció que 13 estudiantes muestran una concepción acción de la función estudiada y 2 estudiantes que llegaron a construir el concepto como proceso.  (Conclusiones)  Se concluye que los estudiantes construyen el concepto de función exponencial como acción, es decir, todo lo relacionado con procesos repetitivos y mecánicos con potencias, cálculo de imágenes, representación gráfica, solución de ecuaciones exponenciales, incluso algunos estudiantes dan respuesta a los ítems sin realizar explícitamente todos los pasos requeridos en la resolución. Dichos resultados evidencian ausencia de un proceso mental de la función exponencial y por consecuencia la encapsulación de él en el objeto función exponencial.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  (Objective)  The objective of this study was to examine, in the light of the APOS theory (action, process, object, and schema), the results produced by secondary school students when addressing 11 items related to the exponential function.  (Methodology)  The approach was qualitative, using content analysis. The sample consisted of 15 students between 15 and 18 years old, chosen in a non-probabilistic way to obtain the greatest amount of information. Based upon the theory, an instrument was designed which consisted of a hypothetical genetic decomposition of the concept of exponential function as a cognitive object, according to structures (action, process, object and schema) and mental mechanisms (interiorization, coordination, encapsulation, decapsulation, and investment), to interpret the mental construct that students create about the function being studied, based on its historical epistemological development, its presentation in school textbooks and the experience of the researcher.  (Results)  At the level of results, it was found that 13 students showed an action conception of the function being studied and 2 students built the concept at the process level.  (Conclusion)  Students most often built the concept of an exponential function at the action level, that is, everything related to repetitive and mechanical processes with powers, image calculation, graphic representation, solution of exponential equations; some students even responded to the items without explicitly performing all the steps required for their resolution. These results demonstrated the absence of a mental process related to the exponential function and its consequent encapsulation into an exponential function object.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo  (Objetivo)  O objetivo do estudo foi examinar, soba perspectiva da teoria APOE (ação, processo, objeto e esquema), a produção de alunos do ensino médio ao lidarem com 11 itens relacionados à função exponencial.  (Metodologia)  A abordagem foi qualitativa, por meio de análise de conteúdo. A amostra consistiu em 15 alunos (com idades entre 15 e 18 anos), nomeados em uma base não probabilística com o objetivo de obter o máximo de informações possível. Para a elaboração do instrumento baseado na teoria, foi construída uma decomposição genética hipotética do conceito de função exponencial como objeto cognitivo, de acordo com as estruturas (ação, processo, objeto e esquema) e os mecanismos mentais (internalização, coordenação, encapsulamento, desencapsulamento, reversão), a fim de interpretar a construção mental feita pelos alunos sobre a função em estudo, com base no seu desenvolvimento epistemológico histórico, na apresentação em textos escolares e na experiência do pesquisador.  (Resultados)  Em nível de resultados, ficou evidente que 13 alunos apresentam uma concepção de ação da função estudada e 2 alunos que conseguiram construir o conceito como um processo.  (Conclusões)  Conclui-se que os alunos constroemo conceito de função exponencial como uma ação, ou seja, tudo o que está relacionado a processos repetitivos e mecânicos com potências, cálculo de imagens, representação gráfica, solução de equações exponenciais, inclusive alguns alunos dão respostas aos itens sem realizar explicitamente todos os passos exigidos na resolução. Esses resultados mostram a ausência de um processo mental da função exponencial e, consequentemente, o encapsulamento dele no objeto da função exponencial.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[teoría APOE]]></kwd>
<kwd lng="es"><![CDATA[función exponencial]]></kwd>
<kwd lng="es"><![CDATA[contexto escolar]]></kwd>
<kwd lng="en"><![CDATA[APOS theory]]></kwd>
<kwd lng="en"><![CDATA[exponential function]]></kwd>
<kwd lng="en"><![CDATA[school context.]]></kwd>
<kwd lng="pt"><![CDATA[teoria APOE]]></kwd>
<kwd lng="pt"><![CDATA[função exponencial]]></kwd>
<kwd lng="pt"><![CDATA[contexto escolar]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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