<?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>S2215-34702021000200271</article-id>
<article-id pub-id-type="doi">10.15359/ru.35-2.18</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Análisis de las definiciones de límite que brindan estudiantes universitarios]]></article-title>
<article-title xml:lang="en"><![CDATA[Analysis of definitions of limit provided by University students]]></article-title>
<article-title xml:lang="pt"><![CDATA[Análise das definições de limite fornecidas por estudantes universitários]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[González-Flores]]></surname>
<given-names><![CDATA[Yosenith]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montoro-Medina]]></surname>
<given-names><![CDATA[Ana Belén]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ruiz-Hidalgo]]></surname>
<given-names><![CDATA[Juan Francisco]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Escuela de Matemática ]]></institution>
<addr-line><![CDATA[Heredia ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática ]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática ]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</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>271</fpage>
<lpage>290</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702021000200271&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702021000200271&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702021000200271&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Este trabajo tiene un doble objetivo; por un lado, analizar las definiciones que brindan estudiantes universitarios sobre el concepto de límite en un punto de una función y, por otro, tanto diseñar como validar un sistema de categorías para llevarlo a cabo. Se estudiaron las definiciones de límite proporcionadas por 38 estudiantes universitarios de Biología e Ingeniería en Química Industrial, matriculados en un curso de Cálculo Diferencial e Integral, durante el primer semestre del 2018, en la Universidad Nacional, Costa Rica. Para ello, se utilizaron categorías a priori y fue necesario complementarlas con otras de naturaleza inductiva, surgidas durante el análisis de contenido de las respuestas. Estas categorías fueron ratificadas mediante un análisis de fiabilidad. Los estudiantes evidenciaron la categoría límite como objeto en la mitad de sus respuestas, aproximadamente, y la categoría límite como proceso en más de tres cuartas partes. Además, constataron las categorías términos de posición relativa y descoordinación general de los procesos, en un estimado de la mitad de sus respuestas. El sistema de categorías creado permitió examinar unidades de información de una manera ordenada, simple y replicable. Finalmente, los estudiantes muestran una concepción dual del límite ya sea como un objeto, noción fija y estática, o como un proceso, noción procesual y dinámica. Asimismo, consideramos que el análisis de contenido descrito en la metodología puede permitir a futuros investigadores crear un sistema de categorías similar o usar este para indagaciones en otros contextos.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper serves two objectives: analyze the definitions provided by college students for the concept of limit at a point in a function as well as design and validate a category system to carry it out. The definitions of limit were provided by 38 university students in the Biology and Engineering in Industrial Chemistry program, enrolled in a Differential and Integral Calculus course during the first semester of 2018, at Universidad Nacional, Costa Rica. A priori categories were used and complemented with other categories of an inductive nature, which emerged during the analysis of the responses. These categories were validated through a reliability analysis. Approximately half of the students&#8217; answers showed the limit category as an object and over three-quarters showed the limit category as a process. In addition, approximately half of their answers showed the categories terms of relative position and general lack of coordination of the processes. The category system created allowed for the analysis of information units in an organized, simple, and replicable way. Finally, students showed a dual conception of limit either as an object, fixed and static notion, or as a process, processual and dynamic notion. Furthermore, the content analysis described in the methodology may allow future researchers to create a similar category system or use this one for research in other contexts.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Este trabalho tem um objetivo duplo: por um lado, analisar as definições que estudantes universitários oferecem sobre o conceito de limite em um ponto de uma função e, por outro lado, desenhar e validar um sistema de categorias para realizá-lo. Foram estudadas as definições de limite proporcionadas por 38 estudantes universitários de Biologia e Engenharia em Química Industrial, matriculados em uma cadeira de Cálculo Diferencial e Integral, durante o primeiro semestre de 2018, na Universidade Nacional, Costa Rica. Para isso, foram utilizadas categorias a priori e foi preciso complementá-las com outras de natureza indutiva, surgidas durante a análise de conteúdo das respostas. Estas categorias foram ratificadas por médio de uma análise de fiabilidade. Os estudantes demonstraram a categoria limite como objeto na metade de suas respostas, aproximadamente, e a categoria limite como processo em mais de três quartos. Também, constataram as categorias termos de posição relativa e descoordenação geral dos processos, em uma média da metade de suas respostas. O sistema de categorias criado permitiu examinar unidades de informação de uma maneira estruturada, simples e replicável. Finalmente, os estudantes mostram uma concepção dual do limite, seja como um objeto, noção fixa e estática, ou como um processo, noção processual e dinâmica. Igualmente, consideramos que a análise de conteúdo descrito na metodologia pode permitir que futuros pesquisadores criem um sistema de categorias semelhante ou usem este para indagações em outros contextos.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Concepto de límite]]></kwd>
<kwd lng="es"><![CDATA[cálculo]]></kwd>
<kwd lng="es"><![CDATA[contenido matemático, didáctica del análisis matemático]]></kwd>
<kwd lng="es"><![CDATA[estudiantes universitarios]]></kwd>
<kwd lng="es"><![CDATA[pensamiento matemático avanzado]]></kwd>
<kwd lng="en"><![CDATA[limit concept]]></kwd>
<kwd lng="en"><![CDATA[calculus]]></kwd>
<kwd lng="en"><![CDATA[mathematical content]]></kwd>
<kwd lng="en"><![CDATA[didactics of mathematical analysis]]></kwd>
<kwd lng="en"><![CDATA[university students]]></kwd>
<kwd lng="en"><![CDATA[advanced mathematical thinking]]></kwd>
<kwd lng="pt"><![CDATA[conceito de limite]]></kwd>
<kwd lng="pt"><![CDATA[cálculo]]></kwd>
<kwd lng="pt"><![CDATA[conteúdo matemático]]></kwd>
<kwd lng="pt"><![CDATA[didática da análise matemática]]></kwd>
<kwd lng="pt"><![CDATA[estudantes universitários]]></kwd>
<kwd lng="pt"><![CDATA[pensamento matemático avançado]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Artigue]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La enseñanza de los principios del cálculo: Problemas epistemológicos, cognitivos y didácticos.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Artigue]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Douady]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Gómez]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ingeniería didáctica en educación matemática]]></source>
<year>1995</year>
<page-range>97-140</page-range><publisher-name><![CDATA[Grupo Editorial Iberoamérica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Azcárate]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Camacho]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sobre la investigación en didáctica del análisis.]]></article-title>
<source><![CDATA[Boletín de la Asociación Matemática Venezolana]]></source>
<year>2003</year>
<volume>10</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>135-49</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bell]]></surname>
<given-names><![CDATA[A. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Costello]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Küchemann]]></surname>
<given-names><![CDATA[D. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[A review of research in mathematical education: research on learning and teaching]]></source>
<year>1983</year>
<publisher-name><![CDATA[The NFER-NELSON Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Blázquez]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sobre la noción del límite en las matemáticas aplicadas a las ciencias sociales.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Ortega]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación en educación matemática III]]></source>
<year>1999</year>
<page-range>167-84</page-range><publisher-name><![CDATA[SEIEM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Blázquez]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Noción de límite en matemáticas aplicadas a las ciencias sociales (Tesis doctoral no publicada).]]></source>
<year>2000</year>
<publisher-name><![CDATA[Universidad de Valladolid]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Blázquez]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Ortega]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rupturas en la comprensión del concepto de límite en alumnos de bachillerato.]]></article-title>
<source><![CDATA[Aula]]></source>
<year>1998</year>
<volume>10</volume>
<page-range>119-35</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Blázquez]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Ortega]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nueva definición de límite funcional]]></article-title>
<source><![CDATA[UNO]]></source>
<year>2002</year>
<volume>30</volume>
<page-range>67-82</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Byerley]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Thompson]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Secondary mathematics teachers&#8217; meanings for measure, slope, and rate of change.]]></article-title>
<source><![CDATA[Journal of Mathematical Behavior]]></source>
<year>2017</year>
<volume>48</volume>
<page-range>168-93</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Castro]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Castro]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Representaciones y modelización]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[La educación matemática en la enseñanza secundaria]]></source>
<year>1997</year>
<page-range>95-124</page-range><publisher-name><![CDATA[Horsori]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cohen]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Manion]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Morrison]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Research Methods in Education]]></source>
<year>2007</year>
<volume>sixth</volume>
<publisher-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cornu]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Limits]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Tall]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Advanced Mathematical Thinking]]></source>
<year>2002</year>
<page-range>153-66</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández-Plaza]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Análisis del contenido]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elementos de didáctica de la matemática para el profesor de secundaria]]></source>
<year>2016</year>
<page-range>103-18</page-range><publisher-name><![CDATA[Ediciones Pirámide]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández-Plaza]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruiz-Hidalgo]]></surname>
<given-names><![CDATA[J. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Castro]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Definiciones personales y aspectos estructurales del concepto de límite finito de una función en un punto.]]></source>
<year>2013</year>
<volume>7</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>117-30</page-range><publisher-name><![CDATA[PNA]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Baptista]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Metodología de la investigación]]></source>
<year>2014</year>
<volume>Sexta</volume>
<publisher-name><![CDATA[McGraw Hill]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hiebert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Lefevre]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Hiebert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Conceptual and Procedural Knowledge in Mathematics: The case of Mathematics]]></source>
<year>1986</year>
<page-range>1-28</page-range><publisher-name><![CDATA[Lawrence Erlbaum Associates]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Juter]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Students&#8217;Concept Development of Limits. Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (CERME)]]></source>
<year>2007</year>
<month>a</month>
<volume>14</volume>
<page-range>2320-9</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Juter]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Students&#8217;Conceptions of Limits: High Achievers versus Low Achievers.]]></article-title>
<source><![CDATA[The Montana Mathematics Enthusiast (TMME)]]></source>
<year>2007</year>
<month>b</month>
<volume>4</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>53-65</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kaput]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Representations Systems and Mathematics.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Janvier]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Problems of representation in the teaching and learning of mathematics]]></source>
<year>1987</year>
<page-range>19-26</page-range><publisher-name><![CDATA[Lawrence Erlbaum Associated]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kidron]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Calculus teaching and learning]]></article-title>
<source><![CDATA[Encyclopedia of mathematics education.]]></source>
<year>2014</year>
<page-range>69-75</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kidron]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Tall]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The roles of visualization and symbolism in the potential and actual infinity of the limit process.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2014</year>
<volume>88</volume>
<page-range>183-99</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kilpatrick]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Hoyles]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Skovsmose]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Meanings of meaning of mathematics.]]></article-title>
<source><![CDATA[Meaning in Mathematics Education]]></source>
<year>2005</year>
<page-range>9-16</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Krippendorff]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Content analysis: An introduction to its methodology]]></source>
<year>2004</year>
<edition>Second Edition</edition>
<publisher-name><![CDATA[Sage publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monaghan]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Problems with the Language of Limits.]]></article-title>
<source><![CDATA[For the Learning of Mathematics]]></source>
<year>1991</year>
<volume>11</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>20-4</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Neuendorf]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Content Analysis Guidebook]]></source>
<year>2017</year>
<edition>Second Edition</edition>
<publisher-name><![CDATA[Sage publications]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La educación matemática en la enseñanza secundaria.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Castro]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Coriat]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Marín]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Puig]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Sierra]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Socas]]></surname>
<given-names><![CDATA[M. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Consideraciones sobre el currículo de matemáticas para educación secundaria]]></source>
<year>1997</year>
<page-range>15-38</page-range><publisher-name><![CDATA[ice - Horsori]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Aproximación a la investigación en didáctica de la matemática.]]></article-title>
<source><![CDATA[Avances de Investigación en Educación Matemática]]></source>
<year>2012</year>
<volume>1</volume>
<page-range>39-63</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[El método del análisis didáctico]]></article-title>
<source><![CDATA[Revista Iberoamericana de Educación Matemática]]></source>
<year>2013</year>
<volume>33</volume>
<page-range>11-27</page-range></nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Matemática y análisis didáctico]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elementos de didáctica de la matemática para el profesor de secundaria]]></source>
<year>2016</year>
<month>a</month>
<page-range>85-100</page-range><publisher-name><![CDATA[Ediciones Pirámide]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Significados de los contenidos matemáticos.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elementos de didáctica de la matemática para el profesor de secundaria]]></source>
<year>2016</year>
<month>b</month>
<page-range>153-74</page-range><publisher-name><![CDATA[Ediciones Pirámide]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Fernández-Cano]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Análisis didáctico y metodología de investigación]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Lupiañez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Molina]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Análisis didáctico en educación matemática: Metodología de investigación, formación de profesores e innovación curricular]]></source>
<year>2013</year>
<page-range>1-22</page-range><publisher-name><![CDATA[Comares]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruiz-Hidalgo]]></surname>
<given-names><![CDATA[J. F]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ideas to Work for the Curriculum Change in School Mathematics]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Shimizu]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Vital]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[ICMI Study 24 Conference proceedings. School Mathematics Curriculum Reforms: Challenges, Changes and Opportunities]]></source>
<year>2018</year>
<page-range>301-8</page-range><publisher-name><![CDATA[ICMI]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Romero]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[La introducción del número real en educación secundaria: Una experiencia de investigación-acción.]]></source>
<year>1997</year>
<publisher-name><![CDATA[Comares]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz-Hidalgo]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sentido y modos de uso de un concepto.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rico]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elementos de didáctica de la matemática para el profesor de secundaria]]></source>
<year>2016</year>
<page-range>139-51</page-range><publisher-name><![CDATA[Ediciones Pirámide]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sierpinska]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Humanities students and epistemological obstacles related to limits.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1987</year>
<volume>18</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>371-97</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sfard]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin.]]></article-title>
<source><![CDATA[Educational Studies of Mathematics]]></source>
<year>1991</year>
<volume>22</volume>
<page-range>1-36</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sierra]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[González]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[López]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Concepciones de los alumnos de bachillerato y curso de orientación universitaria sobre límite funcional y continuidad.]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2000</year>
<volume>3</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>71-85</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sim]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Wright]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Kappa Statistic in Reliability Studies: Use, Interpretation, and Sample Size Requirements.]]></article-title>
<source><![CDATA[Physical Therapy]]></source>
<year>2005</year>
<volume>85</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>257-68</page-range></nlm-citation>
</ref>
<ref id="B38">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Steinbring]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Epistemological investigation of classroom interaction in elementary mathematics teaching.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1997</year>
<volume>32</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>49-92</page-range></nlm-citation>
</ref>
<ref id="B39">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Steinbring]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[What makes a sign a mathematical sign? - An epistemological perspective on mathematical interaction.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2006</year>
<volume>61</volume>
<page-range>133-62</page-range></nlm-citation>
</ref>
<ref id="B40">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Swinyard]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reinventing the formal definition of limit: The case of Amy and Mike]]></article-title>
<source><![CDATA[The Journal of Mathematical Behavior]]></source>
<year>2011</year>
<volume>7</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>765-90</page-range></nlm-citation>
</ref>
<ref id="B41">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tall]]></surname>
<given-names><![CDATA[D. O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Mathematical intuition, with special reference to limiting processes.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Karplus]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the Fourth International Conference for the Psychology of Mathematics Education]]></source>
<year>1980</year>
<page-range>170-6</page-range><publisher-name><![CDATA[PME]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B42">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tall]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
<name>
<surname><![CDATA[Vinner]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Concept image and concept definition in mathematics, with special reference to limits and continuity]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1981</year>
<volume>12</volume>
<page-range>151-69</page-range></nlm-citation>
</ref>
<ref id="B43">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tall]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Katz]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A cognitive analysis of Cauchy&#8217;s conceptions of function, continuity, limit, and infinitesimal, with implications for teaching the calculus.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2014</year>
<volume>86</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>97-124</page-range></nlm-citation>
</ref>
<ref id="B44">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thompson]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[In the absence of meaning&#8230;.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Leatham]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Vital directions for research in mathematics education]]></source>
<year>2013</year>
<page-range>57-93</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B45">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thompson]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Researching mathematical meanings for teaching.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[English]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Kirshner]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of International Research in Mathematics Education]]></source>
<year>2016</year>
<page-range>435-61</page-range><publisher-name><![CDATA[Taylor and Francis]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B46">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thompson]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Milner]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; Meanings for Function and Function Notation in South Korea and the United States.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Weigand]]></surname>
<given-names><![CDATA[H. G.]]></given-names>
</name>
<name>
<surname><![CDATA[McCallum]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Menghini]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Neubrand]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Schubring]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Legacy of Felix Klein]]></source>
<year>2019</year>
<page-range>55-66</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B47">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vergnaud]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Theory of Conceptual Fields]]></article-title>
<source><![CDATA[Human Development]]></source>
<year>2009</year>
<volume>52</volume>
<page-range>83-94</page-range></nlm-citation>
</ref>
<ref id="B48">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vergnaud]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conceptual development and learning]]></article-title>
<source><![CDATA[Revista Curriculum]]></source>
<year>2013</year>
<volume>26</volume>
<page-range>39-59</page-range></nlm-citation>
</ref>
<ref id="B49">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vrancken]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Gregorini]]></surname>
<given-names><![CDATA[M. I.]]></given-names>
</name>
<name>
<surname><![CDATA[Engler]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Muller]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Hecklein]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dificultades relacionadas con la enseñanza y el aprendizaje del concepto de límite.]]></article-title>
<source><![CDATA[Revista PREMISA]]></source>
<year>2006</year>
<volume>8</volume>
<numero>29</numero>
<issue>29</issue>
<page-range>9-19</page-range></nlm-citation>
</ref>
<ref id="B50">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<source><![CDATA[A Content Analysis of Reliability in Advertising Content Analysis Studies (Master's Thesis).]]></source>
<year>2011</year>
<publisher-name><![CDATA[East Tennessee State University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B51">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Williams]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Models of limit held by college calculus students.]]></article-title>
<source><![CDATA[Journal for research in Mathematics Education]]></source>
<year>1991</year>
<volume>22</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>219-36</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
