<?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>2448-8089</journal-id>
<journal-title><![CDATA[Educación matemática]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. mat.]]></abbrev-journal-title>
<issn>2448-8089</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Investigación y Divulgación de la Educación Matemática A.C.; Universidad de Guadalajara]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2448-80892020000100038</article-id>
<article-id pub-id-type="doi">10.24844/em3201.03</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Definiciones e imágenes del concepto de ángulo y su medida en estudiantes que inician la educación superior]]></article-title>
<article-title xml:lang="en"><![CDATA[Definitions and images of the concept of angle and its measurement among students who are beginning their undergraduate studies]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pachuca Herrera]]></surname>
<given-names><![CDATA[Yanira]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Zubieta Badillo]]></surname>
<given-names><![CDATA[Gonzalo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Politécnico Nacional Cinvestav ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Instituto Politécnico Nacional Cinvestav ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</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>32</volume>
<numero>1</numero>
<fpage>38</fpage>
<lpage>66</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892020000100038&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892020000100038&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892020000100038&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: El título de este escrito provoca a priori desconcierto, pues el lector podría considerar que el concepto de ángulo y su medida, está superado por los estudiantes al iniciar una licenciatura, no obstante, aunque algunas dificultades reportadas en la literatura si lo están, otras todavía persisten. En matemáticas la definición de un concepto resulta relevante, sin embargo, en la práctica los estudiantes recurren usualmente a la imagen evocada del concepto, lo que con frecuencia les trae dificultades para realizar una tarea específica. Se diseñó un cuestionario basado en la noción de ángulo y su medida. Los ítems fueron contestados por 22 estudiantes mexicanos del primer semestre de la Licenciatura en Física y Matemáticas. Para conocer las imágenes y definiciones, se aplicó el modelo de Tall y Vinner. Encontramos una amplia variedad en las definiciones personales de ángulo de los estudiantes, que no son una memorización de las definiciones dadas en los cursos o en los libros de texto. Además, no poseen una única imagen del concepto de ángulo y su medida, pues evocan diferentes imágenes según el problema a resolver.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The title of this paper causes a priori bewilderment, because the reader might consider that the concept of angle and its measurement is understood by students starting a bachelor&#8217;s degree; however, although some difficulties reported in investigations has been overcome, others still persist. In mathematics, the concept definition is relevant, however, in practice, students usually resort to the evoked concept image, which often makes it difficult for them to perform a specific task. A questionnaire was designed based on the notion of angle and its measurement. These questions were answered by 22 Mexican under-graduate students. To identify students&#8217; images and definitions, the Tall and Vinner&#8217;s model was applied. We found a wide variety in the students&#8217; personal definitions of angle, which are not memorization of definitions given in their courses or textbooks. In addition, they do not have a single image concept of angle and its measurement, because they evoked different images according to the problem to be solved.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[ángulo]]></kwd>
<kwd lng="es"><![CDATA[medida de ángulo]]></kwd>
<kwd lng="es"><![CDATA[definición del concepto]]></kwd>
<kwd lng="es"><![CDATA[imagen del concepto]]></kwd>
<kwd lng="es"><![CDATA[nivel superior]]></kwd>
<kwd lng="en"><![CDATA[angle]]></kwd>
<kwd lng="en"><![CDATA[angle measurement]]></kwd>
<kwd lng="en"><![CDATA[concept definition]]></kwd>
<kwd lng="en"><![CDATA[concept image]]></kwd>
<kwd lng="en"><![CDATA[under-graduate level]]></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[Acuña]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[La visualización como forma de ver en matemáticas; un acercamiento a la investigación]]></source>
<year>2012</year>
<publisher-name><![CDATA[Gedisa]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Akkoc]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pre-service mathematics teachers&#8217; concept images of radian]]></article-title>
<source><![CDATA[International Journal of Mathematical Education in Science and Technology]]></source>
<year>2008</year>
<volume>39</volume>
<numero>7</numero>
<issue>7</issue>
<page-range>857-78</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ayres]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Moyer]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Trigonometría]]></source>
<year>1991</year>
<edition>2da</edition>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[McGraw-Hill Interamericana]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baldor]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Geometría Plana y del Espacio y Trigonometría]]></source>
<year>1983</year>
<publisher-name><![CDATA[Publicaciones Cultural]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Browning]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Garza-Kling]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Sundling]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[What&#8217;s your angle on angles?]]></article-title>
<source><![CDATA[Teaching Children Mathematics]]></source>
<year>2007</year>
<volume>14</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>283-7</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Driver]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Guesne]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Tiberghien]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Las ideas de los niños y el aprendizaje de las ciencias]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Driver]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Guesne]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Tiberghien]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Las Ideas científicas en la infancia y en la Adolescencia]]></source>
<year>1985</year>
<publisher-name><![CDATA[Morata/MEC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heath]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[The thirteen books of Euclid&#8217;s Elements. Translated from the text of Heiberg with introduction and commentary]]></source>
<year>1956</year>
<volume>I</volume>
<edition>2nd</edition>
<publisher-name><![CDATA[Dover]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hilbert]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Unger]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[The foundations of Geometry]]></source>
<year>1971</year>
<edition>2nd</edition>
<publisher-name><![CDATA[La Salle, Open Court]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Keiser]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Struggles with developing the concept of angle: Comparing sixth-grade students&#8217; discourse to the history of the angle concept.]]></article-title>
<source><![CDATA[Mathematical Thinking and Learning]]></source>
<year>2004</year>
<volume>6</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>285-306</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leithold]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[El Cálculo con Geometría Analítica]]></source>
<year>1992</year>
<edition>6ta</edition>
<publisher-name><![CDATA[Harla]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Matos]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The historical development of the concept of angle]]></article-title>
<source><![CDATA[The Mathematics Educator]]></source>
<year>1990</year>
<volume>1</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>4-11</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Matos]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The historical development of the concept of angle (2)]]></article-title>
<source><![CDATA[The Mathematics Educator]]></source>
<year>1991</year>
<volume>2</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>18-24</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Moise]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Downs]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Geometría Moderna]]></source>
<year>1986</year>
<publisher-loc><![CDATA[Wilmington ]]></publisher-loc>
<publisher-name><![CDATA[Addison-Wesley Iberoamericana]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pachuca]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Concepciones sobre el argumento de la función sen x en profesores del nivel medio superior y alumnos del nivel superior mexicano]]></source>
<year>2014</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Cinvestav, IPN]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rösken]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Rolka]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Integrating intuition: The role of concept image and concept definition for students&#8217; learning of integral calculus]]></article-title>
<source><![CDATA[The Montana Mathematics Enthusiast]]></source>
<year>2007</year>
<numero>3</numero>
<issue>3</issue>
<page-range>181-204</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sampieri]]></surname>
<given-names><![CDATA[R. H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Metodología de la investigación: las rutas cuantitativa, cualitativa y mixta]]></source>
<year>2018</year>
<publisher-name><![CDATA[McGraw Hill]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Spivak]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Calculus: Cálculo infinitesimal]]></source>
<year>1993</year>
<publisher-name><![CDATA[Reverté]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<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 particular reference to limits and continuity]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1981</year>
<volume>12</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>151-69</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vinner]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Hershkowitz]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Karplus]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Concept images and common cognitive paths in the development of some simple geometrical concepts]]></source>
<year>1980</year>
<conf-name><![CDATA[ FourthInternational Conference for the Psychology of Mathematics Education]]></conf-name>
<conf-loc> </conf-loc>
<page-range>177-84</page-range><publisher-name><![CDATA[University of California, Lawrence Hall of Science]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vinner]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Concept definition, concept image and the notion of function]]></article-title>
<source><![CDATA[International Journal of Mathematical Education in Science and Technology]]></source>
<year>1983</year>
<volume>14</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>293-305</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vinner]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The role of definitions in the teaching and learning of mathematics]]></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>65-81</page-range><publisher-name><![CDATA[Kluwer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vinner]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The role of examples in the learning of mathematics and in everyday thought processes]]></article-title>
<source><![CDATA[ZDM The International Journal on Mathematics Education]]></source>
<year>2011</year>
<volume>43</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>247-56</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[White]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mitchelmore]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Pateman]]></surname>
<given-names><![CDATA[N. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Dougherty]]></surname>
<given-names><![CDATA[B. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Zilliox]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching angles by abstraction from physical activities with concrete materials]]></source>
<year>2003</year>
<volume>4</volume>
<conf-name><![CDATA[ 27th Annual Conference of the International Group for the Psychology of Mathematics Education]]></conf-name>
<conf-loc> </conf-loc>
<page-range>403-10</page-range><publisher-name><![CDATA[PME]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
