<?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>S2215-34702021000200237</article-id>
<article-id pub-id-type="doi">10.15359/ru.35-2.16</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estructuras en las formas directa e inversa de una función por estudiantes de 7-8 años]]></article-title>
<article-title xml:lang="en"><![CDATA[Structures in direct and inverse forms of a function evidenced by 7-8-year-old students]]></article-title>
<article-title xml:lang="pt"><![CDATA[Estruturas nas formas direta e inversa de uma função por estudantes de 7-8 anos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Torres]]></surname>
<given-names><![CDATA[María D.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cañadas]]></surname>
<given-names><![CDATA[María C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[Pedro]]></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[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de los Andes &#8220;Una empresa docente&#8221; ]]></institution>
<addr-line><![CDATA[Bogotá ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>35</volume>
<numero>2</numero>
<fpage>237</fpage>
<lpage>252</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702021000200237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702021000200237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702021000200237&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo de este estudio ha sido identificar y comparar las estructuras que evidencian los estudiantes de educación primaria en las formas directa e inversa de una función, tanto para el trabajo con casos particulares como en la generalización desde un enfoque funcional del early algebra. El estudio que se lleva a cabo es de tipo cualitativo y de carácter exploratorio y descriptivo. Se diseña una tarea contextualizada que involucra la función lineal y=x+4, en sus formas directa e inversa. Los seis estudiantes participantes de este estudio de educación primaria (7-8 años) trabajaron la tarea durante entrevistas semiestructuradas que se desarrollaron en el curso académico 2017/2018. Los estudiantes proceden de un colegio de Granada (España). Se describen las estructuras evidenciadas en ambas formas de la función y tanto en el trabajo con casos particulares como cuando se les pregunta por el caso general. Los seis estudiantes identificaron estructuras adecuadas de la forma directa de la función en al menos una ocasión durante la entrevista. En la forma inversa se observaron estructuras también adecuadas, pero hubo estudiantes que no respondieron o a los que no se les hicieron preguntas de esta parte. La mayoría de las estructuras generalizadas se evidenciaron al preguntarles explícitamente por la generalización tanto en la forma directa como en la forma inversa de la función. Al trabajar con la relación entre dos variables se identificaron diferencias entre las estructuras identificadas por el estudiantado en ambas formas de una función: directa e inversa. La mayor parte de las estructuras identificadas fueron adecuadas al problema y esto anima al trabajo con ambas formas de las funciones lineales en educación primaria.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This study aimed to identify and compare the structures evidenced by primary school students in direct and inverse forms of a function, both working with particular cases and generalizing from an early algebra functional approach. The study was qualitative, exploratory, and descriptive. A contextualized task was designed involving the linear functiony=x+4 in direct and inverse variations. Six 2nd graders (7-8 years of age) from a school in Granada (Spain) participated in the study performing a designed task during semi-structured interviews conducted in the 2017-2018 school year. We described the structures evidenced in both variations with particular cases and the general case. All six students identified adequate structures in the direct variation of the function at least once during the interview. Adequate structures were also observed in the inverse variation. However, some students did not respond to this section or were not asked these questions. The majority of the structures that students generalized were produced when explicitly asked for generalization, in both direct and inverse variations of the function. When using the relationship between two variables, differences were found between structures identified by students in both direct and inverse variations. Most of the structures identified were adequate for the problem, which encourages work with both variations of linear functions in primary education.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Este estudo teve como objetivo identificar e comparar as estruturas evidenciadas por estudantes do ensino fundamental nas formas direta e inversa de uma função, tanto para o trabalho com casos particulares quanto na generalização a partir de uma abordagem funcional da Early Algebra. O estudo efetuado é do tipo qualitativo e de carácter exploratório e descritivo. Projeta-se uma tarefa contextualizada que envolve a função linear y=x+4, em suas formas direta e inversa. Os seis estudantes que participam deste estudo de educação fundamental (7-8 anos) trabalharam na tarefa durante entrevistas semiestruturadas desenvolvidas no período acadêmico 2017/2018. Os estudantes provêm de um colégio de Granada (Espanha). São descritas as estruturas evidenciadas em ambas as formas da função, tanto no trabalho com casos particulares quanto ao ser questionados sobre o caso geral. Os seis estudantes identificaram estruturas adequadas da forma direta da função em ao menos uma ocasião durante a entrevista. Na forma inversa, foram observadas estruturas também adequadas, porém houve estudantes que não responderam ou aos que não foram feitas perguntas dessa parte. A maioria das estruturas generalizadas ficaram evidentes quando lhes perguntaram explicitamente sobre a generalização tanto na forma direta quanto na inversa da função. Ao se trabalhar com a relação entre duas variáveis foram identificadas diferenças entre as estruturas discernidas pelos alunos em ambas as formas de uma função: direta e inversa. A maior parte das estruturas identificadas foram adequadas para o problema, animando o trabalho com ambas as formas das funções lineares na educação fundamental.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Estructura]]></kwd>
<kwd lng="es"><![CDATA[forma directa de una función]]></kwd>
<kwd lng="es"><![CDATA[forma inversa de una función]]></kwd>
<kwd lng="es"><![CDATA[generalización]]></kwd>
<kwd lng="es"><![CDATA[pensamiento funcional]]></kwd>
<kwd lng="en"><![CDATA[direct variation of a function]]></kwd>
<kwd lng="en"><![CDATA[functional thinking]]></kwd>
<kwd lng="en"><![CDATA[generalization]]></kwd>
<kwd lng="en"><![CDATA[inverse variation of a function]]></kwd>
<kwd lng="en"><![CDATA[structure.]]></kwd>
<kwd lng="pt"><![CDATA[Estrutura]]></kwd>
<kwd lng="pt"><![CDATA[forma direta de uma função]]></kwd>
<kwd lng="pt"><![CDATA[forma inversa de uma função]]></kwd>
<kwd lng="pt"><![CDATA[generalização]]></kwd>
<kwd lng="pt"><![CDATA[pensamento funcional.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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