<?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>1665-2436</journal-id>
<journal-title><![CDATA[Revista latinoamericana de investigación en matemática educativa]]></journal-title>
<abbrev-journal-title><![CDATA[Relime]]></abbrev-journal-title>
<issn>1665-2436</issn>
<publisher>
<publisher-name><![CDATA[Comité Latinoamericano de Matemática Educativa A.C.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1665-24362020000200203</article-id>
<article-id pub-id-type="doi">10.12802/relime.20.2323</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A study on the pre-service elementary mathematics teachers&#8217; knowledge on the convergence and divergence of series in the context of theory and application]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ergene]]></surname>
<given-names><![CDATA[Özkan]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Özdemir]]></surname>
<given-names><![CDATA[Ahmet &#350;ükrü]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Sakarya University Faculty of Education ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Turkey</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Marmara University Atatürk Faculty of Education ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Turkey</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2020</year>
</pub-date>
<volume>23</volume>
<numero>2</numero>
<fpage>203</fpage>
<lpage>232</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362020000200203&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362020000200203&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362020000200203&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The focus of this research is the examination of the theoretical and practical knowledge regarding the convergence and divergence of the series. In line with the research focus, it is aimed to reveal the approaches of pre-service elementary mathematics teachers on the convergence and divergence of the series with the help of the real-life problem in the context of theory and application by using the concept of harmonic series. The research carried out the qualitative research method is designed according to the case study. The data of the research have consisted of two written questions and one problem and four interview questions which were formed by the researchers and their validity and reliability were ensured. The study concluded that pre-service teachers have theoretical knowledge on the convergence of series and harmonic series. Also, their perception of series, harmonic series, convergence and divergence concepts changed in the application process and they performed different approaches in problem-solving.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El foco de esta investigación es el examen del conocimiento teórico y práctico sobre la convergencia y la divergencia de la serie. En línea con el enfoque de investigación, los maestros pre-servicio de matemática sobre la convergencia y divergencia de la serie con la ayuda del problema de la vida real en el contexto de la teoría y la aplicación utilizando el concepto de series armónicas. La investigación se guió de un método cualitativo, estudio de caso. Los datos de la investigación han consistido en dos preguntas escritas y un problema y cuatro preguntas de entrevista que fueron formadas por los investigadores y se aseguró su validez y confiabilidad. El estudio llegó a la conclusión de que maestros de pre-servicio matemática tienen conocimientos teoríco sobre la convergencia de series y series armónicas, su percepción de las series, las series armónicas, los conceptos de convergencia y divergencia cambiaron en el proceso de solicitud y adoptaron diferentes enfoques en la resolución de problemas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O foco desta investigação é a análise do conhecimento teórico/prático sobre a convergência e divergência de uma série. Em consonância com o foco da pesquisa, pretende-se analisar as abordagens dos professores estagiários de matemática sobre a convergência e divergência da série com a ajuda de problemas da vida real no contexto da teoria e da aplicação utilizando-se o conceito de série harmónica. A pesquisa foi realizada usando o método de pesquisa qualitativa e foi projetada de acordo com o estudo de caso. Os dados da pesquisa consistiram em duas questões escritas e um problema, e uma entrevista com quatro perguntas formadas pelos investigadores, sendo que a sua validade e fiabilidade foram garantidas. A investigação concluiu que os professores estagiários têm conhecimento suficiente sobre a convergência de séries e séries harmónicas. Além disso, a sua percepção de séries e séries harmônicas, conceitos de convergência e divergência mudaram durante o processo de aplicação, realizando diferentes abordagens na resolução dos problemas.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé L&#8217;objectif de cette recherche consiste à étudier les connaissances théoriques et pratiques relatives à la convergence et à la divergence des séries. Conformément à cet objectif, l&#8217;étude vise à révéler les approches des futurs enseignants de mathématiques au secondaire liées à la convergence et à la divergence de la série harmonique en théorie et en pratique à l&#8217;aide d&#8217;un problème de la vie réelle. La méthode de recherche adoptée relève d&#8217;une démarche qualitative dans le cadre d&#8217;une étude de cas. Les données de la recherche comprennent d&#8217;une part, deux questions et un problème écrit et d&#8217;autre part, quatre questions d&#8217;entretien dont la validité et la fiabilité sont assurées par le chercheur lui-même. Les résultats de l&#8217;étude montrent que les futurs enseignants atteignent un niveau de connaissances théoriques sur les séries et sur la convergence des séries harmoniques. Par ailleurs, l&#8217;étude révèle aussi que les futurs enseignants se diffèrent quant à l&#8217;attribution de sens aux concepts de série, de série harmonique, de divergence et d&#8217;infini, ainsi qu&#8217;à l&#8217;approche de la résolution de problèmes.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Calculus Teaching]]></kwd>
<kwd lng="en"><![CDATA[Harmonic Series]]></kwd>
<kwd lng="en"><![CDATA[Convergence and Divergence]]></kwd>
<kwd lng="en"><![CDATA[Theoretical and Application]]></kwd>
<kwd lng="es"><![CDATA[Enseñanza del cálculo]]></kwd>
<kwd lng="es"><![CDATA[Series armónicas]]></kwd>
<kwd lng="es"><![CDATA[Convergencia y divergencia]]></kwd>
<kwd lng="es"><![CDATA[Teoría y aplicación]]></kwd>
<kwd lng="pt"><![CDATA[Ensino de Cálculo]]></kwd>
<kwd lng="pt"><![CDATA[Série Harmônica]]></kwd>
<kwd lng="pt"><![CDATA[Convergência e Divergência]]></kwd>
<kwd lng="pt"><![CDATA[Teórica e Aplicação]]></kwd>
<kwd lng="fr"><![CDATA[Enseignement de l&#8217;Analyse]]></kwd>
<kwd lng="fr"><![CDATA[Série Harmonique]]></kwd>
<kwd lng="fr"><![CDATA[Convergence et Divergence]]></kwd>
<kwd lng="fr"><![CDATA[Théorique et Pratique]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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