<?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>S2448-80892015000200095</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Construcciones y mecanismos mentales para el aprendizaje del teorema matriz asociada a una transformación lineal]]></article-title>
<article-title xml:lang="en"><![CDATA[Construction and mental mechanisms for learning matrix theorem associated with a linear transformation]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Trigueros Gaisman]]></surname>
<given-names><![CDATA[María]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Maturana Peña]]></surname>
<given-names><![CDATA[Isabel]]></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 contrib-type="author">
<name>
<surname><![CDATA[Rodríguez Jara]]></surname>
<given-names><![CDATA[Miguel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Tecnológico Autónomo de México División de Actuaría Estadística y Matemáticas Depto. de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso Instituto de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Playa Ancha Depto. de Matemáticas ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2015</year>
</pub-date>
<volume>27</volume>
<numero>2</numero>
<fpage>95</fpage>
<lpage>124</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892015000200095&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892015000200095&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892015000200095&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Con base en la teoría APOE (Acciones, Procesos, Objetos y Esquemas) como marco teórico y metodológico, investigamos las construcciones y mecanismos mentales necesarios para construir la Matriz Asociada a una Transformación Lineal (MATL). Diseñamos una descomposición genética (DG) del teorema de la MATL para analizar la forma en que estudiantes universitarios lo aprenden. Reportamos tres casos de estudio que muestran cómo los estudiantes construyen el concepto de coordenadas de un vector como objeto, pero tienen dificultades para utilizarlo en la construcción de un proceso de la matriz de coordenadas de imágenes de vectores mediante la transformación. Esta dificultad parece vinculada a que no han coordinado los procesos involucrados en términos del cuantificador. Específicamente, se muestran las dificultades en la construcción de la MATL como objeto y el papel determinante que juega la consideración de la transformación lineal como una función en la comprensión profunda del TMATL.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Based on apos theory (Actions, Processes, Objects and Schemes) as a theoretical and methodological framework, we investigate the mental constructions and mechanisms required to construct the associated matrix of a Linear Transformation (MATL). We design a genetic decomposition (DG) of the theorem matl to discuss how college students learn it We report three cases of study. The results show how students construct the concept of coordinates of a vector as an object, but have difficulty using it in the construction of the coordinate matrix associated to the image of vectors. Results also show students' difficulties to construct matl as an object and the crucial role of considering TL as a function in order to attain a deep comprehension of TMATL.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Matriz asociada]]></kwd>
<kwd lng="es"><![CDATA[Transformación Lineal]]></kwd>
<kwd lng="es"><![CDATA[teoría APOE]]></kwd>
<kwd lng="es"><![CDATA[Álgebra Lineal]]></kwd>
<kwd lng="en"><![CDATA[Matrix associate]]></kwd>
<kwd lng="en"><![CDATA[Linear Transformation]]></kwd>
<kwd lng="en"><![CDATA[apos Theory]]></kwd>
<kwd lng="en"><![CDATA[Linear Algebra]]></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[Arnon]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Cottril]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Dubinsky]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Oktaç]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Roa]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Trigueros]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Weller]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[APOS Theory. A Framework for Research and Curriculum Development in Mathematics Education]]></source>
<year>2014</year>
<publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bagley]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Rasmussen]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Zandieh]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Brown]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Larsen]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Marrongelle]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Oehrtman]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Inverse, composition, and identity: The case of function and linear transformation]]></source>
<year>2012</year>
<conf-name><![CDATA[ 15Annual Conference on Research in Undergraduate Mathematics]]></conf-name>
<conf-loc> </conf-loc>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Font]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The onto-semiotic approach to research in mathematics education]]></article-title>
<source><![CDATA[ZDM. The International Journal on Mathematics Education]]></source>
<year>2007</year>
<volume>39</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>127-35</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Harel]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Applying the principle of multiple embodiments in teaching linear algebra: aspects of familiarity and mode of representation]]></article-title>
<source><![CDATA[School Science and Mathematics]]></source>
<year>1989</year>
<volume>89</volume>
<page-range>49-57</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Harel]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teaching in learning linear algebra; difficulties and an alternative approach to visualizing concepts and processes]]></article-title>
<source><![CDATA[Focus on Learning Problems in Mathematics]]></source>
<year>1989</year>
<volume>11</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>139-48</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Karrer]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Jahn]]></surname>
<given-names><![CDATA[A-P]]></given-names>
</name>
</person-group>
<source><![CDATA[Studying plane linear transformations on a dynamic geometry environment: analysis of tasks emphasizing the graphic register]]></source>
<year>2008</year>
<conf-name><![CDATA[ ICME, 11]]></conf-name>
<conf-loc> </conf-loc>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Molina]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Oktaç]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Concepciones de la transformación lineal en contexto geométrico]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2007</year>
<volume>10</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>241-73</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Roa]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Oktaç]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Construcción de una descomposición genética]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2010</year>
<volume>13</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>89-112</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<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[On some aspects of students' thinking in linear algebra]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Dorier]]></surname>
<given-names><![CDATA[J.-L]]></given-names>
</name>
</person-group>
<source><![CDATA[On the Teaching of Linear Algebra]]></source>
<year>2000</year>
<page-range>209-46</page-range><publisher-loc><![CDATA[Dortrecht ]]></publisher-loc>
<publisher-name><![CDATA[Kluwer Academic Publishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sierpinska]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Nnadozie]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Oktac]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[A study of relationships between theoretical thinking and high achievement in Linear Algebra]]></source>
<year>2002</year>
<publisher-name><![CDATA[Concordia University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sierpinska]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Dreyfus]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Hillel]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Evaluation of the teaching design in linear algebra: the case of linear transformations]]></article-title>
<source><![CDATA[Recherches en didactique des mathématiques]]></source>
<year>1999</year>
<volume>19</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>7-40</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stake]]></surname>
<given-names><![CDATA[R.E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación con estudio de casos]]></source>
<year>2010</year>
<publisher-loc><![CDATA[Barcelona ]]></publisher-loc>
<publisher-name><![CDATA[Labor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Uicab]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Oktaç]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Transformaciones lineales en un ambiente de geometría dinámica]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2006</year>
<volume>9</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>459-90</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wawro]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Larson]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Zandieh]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Rasmussen]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[A hypothetical collective progression for conceptualizing matrices as linear transformations]]></source>
<year>2012</year>
<conf-name><![CDATA[ FifteenthConference on Research in Undergraduate Mathematics Education]]></conf-name>
<conf-loc>Portland, OR </conf-loc>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Weller]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
<name>
<surname><![CDATA[Montgomery]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Clark]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Cottrill]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Arnon]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Trigueros]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Dubinsky]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Learning Linear Algebra with ISETL]]></source>
<year>2002</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
