<?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>1870-3542</journal-id>
<journal-title><![CDATA[Revista mexicana de física E]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fís. E]]></abbrev-journal-title>
<issn>1870-3542</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1870-35422007000200007</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Dificultades de entendimiento en el uso de vectores en cursos introductorios de mecánica]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Flores-García]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gonzalez-Quezada]]></surname>
<given-names><![CDATA[M.D]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Herrera-Chew]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidad Autónoma de Ciudad Juárez  ]]></institution>
<addr-line><![CDATA[Ciudad Juárez Chih]]></addr-line>
</aff>
<aff id="A02">
<institution><![CDATA[,Instituto Tecnológico de Ciudad Juárez  ]]></institution>
<addr-line><![CDATA[Ciudad Juárez Chih]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2007</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2007</year>
</pub-date>
<volume>53</volume>
<numero>2</numero>
<fpage>178</fpage>
<lpage>185</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1870-35422007000200007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1870-35422007000200007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1870-35422007000200007&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Una comprensión de las propiedades básicas de los vectores es fundamental para el entendimiento de las operaciones entre vectores. Muchos estudiantes en los cursos introductorios de física no desarrollan un aprendizaje significativo de la naturaleza vectorial de las cantidades físicas como: fuerza, aceleración, tensión y velocidad. Para promover el entendimiento conceptual de estas cantidades es necesaria una exploración de los problemas de orden cognitivo que los estudiantes presentan a través de una enseñanza tradicional o por medio de una modificación en la instrucción. Esta investigación muestra las dificultades de los alumnos que fueron detectadas y caracterizadas durante el proceso de aprendizaje de las operaciones de suma y diferencia de vectores en su contexto. Las fuentes de información son algunas universidades de Estados Unidos y una universidad en México]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[An understanding of the basic properties of vectors is fundamental to understand vector operations. Many students in the introductory physics courses do not develop a meaningful understanding of the vector nature of some physical quantities such as: Force, acceleration, tension and velocity. To foster a conceptual understanding of these quantities, an exploration of the cognitive problems is necessary through a traditional or a modified instruction. This investigation shows the students' difficulties detected and characterized during the teaching process of the operations of addition and subtraction of vectors in their context. The information sources are some universities in the United States and one university in Mexico]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Física conceptual]]></kwd>
<kwd lng="es"><![CDATA[dificultades de aprendizaje]]></kwd>
<kwd lng="en"><![CDATA[Conceptual physics]]></kwd>
<kwd lng="en"><![CDATA[learning difficulties]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Ense&ntilde;anza</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><b>Dificultades de entendimiento en el uso de vectores en cursos introductorios de mec&aacute;nica</b></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="2"><b>S. Flores&#150;Garc&iacute;a&ordf;, M.D. Gonzalez&#150;Quezada<sup>b</sup> y A. Herrera&#150;Chew<sup>b</sup></b>&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><i>&ordf; Universidad Aut&oacute;noma de Ciudad Ju&aacute;rez, Avenida del charro 450 Nte., 32310, Ciudad Ju&aacute;rez Chih.,</i> e&#150;mail: <a href="mailto:sergiflo@hotmail.com">sergiflo@hotmail.com</a></font></p>     <p align="justify"><font face="verdana" size="2"><i><sup>b</sup> Instituto Tecnol&oacute;gico de Ciudad Ju&aacute;rez, Avenida Tecnol&oacute;gico 1340, Fracc. Crucero 32500, Ciudad Ju&aacute;rez Chih., </i>e&#150;mail: <a href="mailto:doloresgo73@hotmail.com">doloresgo73@hotmail.com</a>, <a href="mailto:aleiz_herrera@yahoo.com.mx">aleiz_herrera@yahoo.com.mx</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2">Recibido el 7 de diciembre de 2006    ]]></body>
<body><![CDATA[<br> Aceptado el 5 de junio de 2007</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     <p align="justify"><font face="verdana" size="2">Una comprensi&oacute;n de las propiedades b&aacute;sicas de los vectores es fundamental para el entendimiento de las operaciones entre vectores. Muchos estudiantes en los cursos introductorios de f&iacute;sica no desarrollan un aprendizaje significativo de la naturaleza vectorial de las cantidades f&iacute;sicas como: fuerza, aceleraci&oacute;n, tensi&oacute;n y velocidad. Para promover el entendimiento conceptual de estas cantidades es necesaria una exploraci&oacute;n de los problemas de orden cognitivo que los estudiantes presentan a trav&eacute;s de una ense&ntilde;anza tradicional o por medio de una modificaci&oacute;n en la instrucci&oacute;n. Esta investigaci&oacute;n muestra las dificultades de los alumnos que fueron detectadas y caracterizadas durante el proceso de aprendizaje de las operaciones de suma y diferencia de vectores en su contexto. Las fuentes de informaci&oacute;n son algunas universidades de Estados Unidos y una universidad en M&eacute;xico.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Descriptores: </b>F&iacute;sica conceptual; dificultades de aprendizaje.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     <p align="justify"><font face="verdana" size="2">An understanding of the basic properties of vectors is fundamental to understand vector operations. Many students in the introductory physics courses do not develop a meaningful understanding of the vector nature of some physical quantities such as: Force, acceleration, tension and velocity. To foster a conceptual understanding of these quantities, an exploration of the cognitive problems is necessary through a traditional or a modified instruction. This investigation shows the students' difficulties detected and characterized during the teaching process of the operations of addition and subtraction of vectors in their context. The information sources are some universities in the United States and one university in Mexico.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords: </b>Conceptual physics; learning difficulties.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2">PACS: 01.40.d; 01.40.Fk; 01.49.Ha</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/rmfe/v53n2/v53n2a7.pdf" target="_blank">DESCARGAR ART&Iacute;CULO EN FORMATO PDF</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Referencias</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. E.F. Redish, J.M. Saul y R.N. Steinberg, <i>Am. J. Phys. </i><b>66</b> (3) (1998) 212.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448177&pid=S1870-3542200700020000700001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">2. J. Aguirre y G. Erickson, <i>J. of Res. in Sci. Educ. </i><b>21</b> (5) (1984) 439.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448178&pid=S1870-3542200700020000700002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">3. R.D. Knight, <i>Phys. Teach. </i><b>33</b> (1995) 74.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448179&pid=S1870-3542200700020000700003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">4. N. Nguyen y D.E. Meltzer, <i>Am. J. of Phys. </i><b>71</b> (6) (2003) 630.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448180&pid=S1870-3542200700020000700004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">5. C.J. Hieggelke, D.P. Maloney, S.E. Kanim y T.L. O'Kuma, <i>E &amp; M TIPERs: Electricity and magnetism tasks, </i>1<sup>st</sup> Edition (Pearson Prentice Hall, New Jersey, 2006).</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448181&pid=S1870-3542200700020000700005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">6. L.C. McDermott, P. Shaffer y the Physics Education Group at the University of Washington, <i>Tutorials in Introductory Physics, 2<sup>nd</sup> Edition </i>(Prentice&#150;Hall, New Jersey, 2002).</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448182&pid=S1870-3542200700020000700006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">7. S. Flores, "Student use of vectors in mechanics", tesis para obtener el grado doctorado en f&iacute;sica, Universidad Estatal de Nuevo M&eacute;xico, (Julio 2006).</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=8448183&pid=S1870-3542200700020000700007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Redish]]></surname>
<given-names><![CDATA[E.F]]></given-names>
</name>
<name>
<surname><![CDATA[Saul]]></surname>
<given-names><![CDATA[J.M]]></given-names>
</name>
<name>
<surname><![CDATA[Steinberg]]></surname>
<given-names><![CDATA[R.N]]></given-names>
</name>
</person-group>
<source><![CDATA[Am. J. Phys]]></source>
<year>1998</year>
<volume>66</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>212</page-range></nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aguirre]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Erickson]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<source><![CDATA[J. of Res. in Sci. Educ]]></source>
<year>1984</year>
<volume>21</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>439</page-range></nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Knight]]></surname>
<given-names><![CDATA[R.D]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Teach]]></source>
<year>1995</year>
<numero>33</numero>
<issue>33</issue>
<page-range>74</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nguyen]]></surname>
<given-names><![CDATA[N]]></given-names>
</name>
<name>
<surname><![CDATA[Meltzer]]></surname>
<given-names><![CDATA[D.E]]></given-names>
</name>
</person-group>
<source><![CDATA[Am. J. of Phys]]></source>
<year>2003</year>
<volume>71</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>630</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hieggelke]]></surname>
<given-names><![CDATA[C.J]]></given-names>
</name>
<name>
<surname><![CDATA[Maloney]]></surname>
<given-names><![CDATA[D.P]]></given-names>
</name>
<name>
<surname><![CDATA[Kanim]]></surname>
<given-names><![CDATA[S.E]]></given-names>
</name>
<name>
<surname><![CDATA[O'Kuma]]></surname>
<given-names><![CDATA[T.L]]></given-names>
</name>
</person-group>
<source><![CDATA[E & M TIPERs: Electricity and magnetism tasks]]></source>
<year>2006</year>
<edition>1</edition>
<publisher-loc><![CDATA[New Jersey ]]></publisher-loc>
<publisher-name><![CDATA[Pearson Prentice Hall]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[McDermott]]></surname>
<given-names><![CDATA[L.C]]></given-names>
</name>
<name>
<surname><![CDATA[Shaffer]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
</person-group>
<collab>the Physics Education Group at the University of Washington</collab>
<source><![CDATA[Tutorials in Introductory Physics]]></source>
<year>2002</year>
<edition>2</edition>
<publisher-loc><![CDATA[New Jersey ]]></publisher-loc>
<publisher-name><![CDATA[Prentice-Hall]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Flores]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<source><![CDATA[Student use of vectors in mechanics]]></source>
<year></year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
