<?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>1607-4041</journal-id>
<journal-title><![CDATA[Revista electrónica de investigación educativa]]></journal-title>
<abbrev-journal-title><![CDATA[REDIE]]></abbrev-journal-title>
<issn>1607-4041</issn>
<publisher>
<publisher-name><![CDATA[Universidad Autónoma de Baja California, Instituto de Investigación y Desarrollo Educativo]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1607-40412018000100048</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Instrumentos consistentes para la enseñanza de fracciones en 4o. grado]]></article-title>
<article-title xml:lang="en"><![CDATA[Consistent Instruments for Teaching Fractions in 4 th Grade]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez Rojas]]></surname>
<given-names><![CDATA[Palmenia de la Cruz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Olfos]]></surname>
<given-names><![CDATA[Raimundo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de La Serena  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2018</year>
</pub-date>
<volume>20</volume>
<numero>1</numero>
<fpage>48</fpage>
<lpage>58</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1607-40412018000100048&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1607-40412018000100048&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1607-40412018000100048&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: En Chile y, en general, para todos los sistemas educativos del mundo es conveniente disponer de instrumentos consistentes que midan los conocimientos que requiere un profesor para lograr que sus alumnos aprendan; instrumentos útiles para la formación inicial y continua del profesorado. El propósito de este estudio consistió en elaborar dos instrumentos consistentes, uno sobre el conocimiento profundo del profesor acerca de las fracciones y otro sobre el saber del profesor acerca del conocimiento que el alumno pone en juego al conceptualizar las fracciones en 4o. grado. Los instrumentos fueron aplicados en dos oportunidades a grupos de 30 profesores de primaria y una vez a 20 estudiantes de la carrera de Pedagogía en Matemáticas. Tras los respectivos procedimientos psicométricos se obtuvieron dos instrumentos, de 12 y 10 preguntas, con una consistencia interna de 0.74 y 0.75 alfa de Cronbach.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In education systems both in Chile and worldwide, it is desirable to have consistent instruments to measure the knowledge required by teachers to help students learn. These would be useful instruments for teachers&#8217; initial and ongoing training. The purpose of this study was to develop two consistent instruments, one on teachers&#8217; in-depth knowledge of fractions, and one on teachers&#8217; understanding of the knowledge students bring into play when conceptualizing fractions in 4th grade. The instruments were administered on two occasions to groups of 30 elementary school teachers, and once to 20 students from the pedagogy in mathematics degree. After completing the corresponding psychometric procedures, two instruments with 12 and 10 questions were obtained, with an internal consistency of Cronbach&#8217;s alpha 0.74 and 0.75.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Fracciones]]></kwd>
<kwd lng="es"><![CDATA[validación de instrumentos]]></kwd>
<kwd lng="es"><![CDATA[enseñanza de las Matemáticas]]></kwd>
<kwd lng="en"><![CDATA[Fractions]]></kwd>
<kwd lng="en"><![CDATA[instrument validation]]></kwd>
<kwd lng="en"><![CDATA[Mathematics education]]></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>
<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. Un esquema para la investigación y la innovación en la enseñanza y el aprendizaje de las matemáticas]]></source>
<year>1995</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Grupo Editorial Iberoamérica]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ávalos]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Matus]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[La formación inicial docente en Chile desde una óptica internacional. Informe Nacional del Estudio Internacional IEA-TEDS-M]]></source>
<year>2010</year>
<publisher-loc><![CDATA[Santiago ]]></publisher-loc>
<publisher-name><![CDATA[Mineduc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Backhoff]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Larrazolo]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosas]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Nivel de dificultad y poder de discriminación del Examen de Habilidades y Conocimientos Básicos (EXHCOBA)]]></article-title>
<source><![CDATA[Revista Electrónica de Investigación Educativa]]></source>
<year>2000</year>
<volume>2</volume>
<numero>1</numero>
<issue>1</issue>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bridging Practices: Intertwining content and pedagogy in teaching and learning to teach]]></article-title>
<source><![CDATA[Journal of Teacher Education]]></source>
<year>2000</year>
<volume>51</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>241-7</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The mathematical understandings that prospective teachers bring to teacher education]]></article-title>
<source><![CDATA[The Elementary School Journal]]></source>
<year>1990</year>
<volume>90</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>449-66</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Bass]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Knowing mathematics for teaching. Who knows mathematics well enough to teach third grade, and how can we decide?]]></article-title>
<source><![CDATA[American Educator]]></source>
<year>2005</year>
<volume>29</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>14-7</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Thames]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Phelps]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Content knowledge for teaching: what makes it special?]]></article-title>
<source><![CDATA[Journal of Teacher Education]]></source>
<year>2008</year>
<volume>59</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>389-407</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barber]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Mourshed]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Cómo hicieron los sistemas educativos con mejor desempeño del mundo para alcanzar sus objetivos]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Buenos Aires ]]></publisher-loc>
<publisher-name><![CDATA[PREAL]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Harel]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Lesh]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rational numbers: toward a semantic analysis-emphasis on the operator construct]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Carpenter]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Fennema]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Romberg]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Rational numbers: an integration of research]]></source>
<year>1993</year>
<page-range>13-47</page-range><publisher-loc><![CDATA[Nueva Jersey, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Block]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Solares]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Las fracciones y la división en la escuela primaria: análisis didáctico de un vínculo]]></article-title>
<source><![CDATA[Educación Matemática]]></source>
<year>2001</year>
<volume>13</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>5-30</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bruns]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Luque]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Profesores excelentes: cómo mejorar el aprendizaje en América Latina y el Caribe. Serie del Foro sobre Desarrollo de América Latina]]></source>
<year>2014</year>
<publisher-loc><![CDATA[Washington ]]></publisher-loc>
<publisher-name><![CDATA[Banco Mundial]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Carpenter]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Fennema]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Romberg]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Rational numbers: an integration of research]]></source>
<year>1993</year>
<publisher-loc><![CDATA[Nueva Jersey, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Carrillo]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Climent]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Contreras]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Muñoz-Catalán]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determining specialized knowledge for mathematics teaching]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Ubuz]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Haser]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Mariotti]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings VIII Congress of the European Society for Research in Mathematics Education (CERME 8)]]></source>
<year>2013</year>
<page-range>2985-94</page-range><publisher-loc><![CDATA[Turquía ]]></publisher-loc>
<publisher-name><![CDATA[Middle East Technical University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cortina]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Cardoso]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Zúñiga]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[El significado cuantitativo que tienen las fracciones para estudiantes mexicanos de 6o. de primaria]]></article-title>
<source><![CDATA[Revista Electrónica de Investigación Educativa]]></source>
<year>2012</year>
<volume>14</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>70-85</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<collab>Eurydice</collab>
<source><![CDATA[Key data on teachers and school leaders. Eurydice Report]]></source>
<year>2013</year>
<publisher-loc><![CDATA[Luxemburgo ]]></publisher-loc>
<publisher-name><![CDATA[Publications Office European Union]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fandiño]]></surname>
<given-names><![CDATA[M. I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Las fracciones. Aspectos conceptuales y didácticos]]></source>
<year>2009</year>
<publisher-loc><![CDATA[Bogotá ]]></publisher-loc>
<publisher-name><![CDATA[Magisterio]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Freundenthal]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Didactical phenomenology of mathematical structures]]></source>
<year>1983</year>
<publisher-loc><![CDATA[Dordrecht, Países Bajos ]]></publisher-loc>
<publisher-name><![CDATA[Reidel Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gallardo]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[González]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Quispe]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Interpretando la comprensión matemática en escenarios básicos de valoración. Un estudio sobre las interferencias en el uso de los significados de la fracción]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2008</year>
<volume>11</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>355-82</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guilford]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Psycometric methods]]></source>
<year>1975</year>
<edition>2</edition>
<publisher-loc><![CDATA[Bombay ]]></publisher-loc>
<publisher-name><![CDATA[Tata McGraw-Hll]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning mathematics for teaching: results from California&#8217;s mathematics professional development institutes]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>2004</year>
<volume>35</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>330-51</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Schilling]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Unpacking pedagogical content knowledge: conceptualizing and measuring teachers&#8217; topic-specific knowledge of students]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>2008</year>
<volume>39</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>372-400</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kieren]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rational and fractional numbers: from quotient fields to recursive understanding]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Carpenter]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Fennema]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Romberg]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Rational numbers: An integration of research]]></source>
<year>1993</year>
<page-range>49-84</page-range><publisher-loc><![CDATA[Nueva Jersey, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Krauss]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Wie professionsspezifisch sind das fachdidaktische Wissen und das Fachwissen von Mathematiklehrkräften? Beiträge zum Mathematikunterricht bei der Gesellschaft für Didaktik der Mathematik]]></source>
<year>2007</year>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ma]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Knowing and teaching elementary mathematics: Teachers&#8217; understanding of fundamental mathematics in China and the United States]]></source>
<year>1999</year>
<publisher-loc><![CDATA[Mahwah, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ma]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Conocimiento y enseñanza de las matemáticas elementales. La comprensión de las matemáticas fundamentales que tienen los profesores en China y los EE.UU]]></source>
<year>2010</year>
<publisher-name><![CDATA[Academia Chilena de Ciencias]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="book">
<collab>Mineduc</collab>
<source><![CDATA[Programa de estudio 4o. Básico Matemática 2003]]></source>
<year>2003</year>
<publisher-loc><![CDATA[Chile ]]></publisher-loc>
<publisher-name><![CDATA[Autor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="book">
<collab>MT21</collab>
<source><![CDATA[Mathematic teaching in the 2st Century, The preparation gap: teacher education for middle school mathematics in six countries]]></source>
<year>2007</year>
<publisher-name><![CDATA[Michigan University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="book">
<collab>OCDE</collab>
<source><![CDATA[Política de educación y formación: los docentes son importantes. Atraer, formar y conservar a los docentes eficientes]]></source>
<year>2009</year>
<publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[Autor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Olfos]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Guzmán]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Galbiati]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Conocimiento pedagógico del Contenido y su incidencia en la Enseñanza de la Matemática Nivel de Educación Básica]]></source>
<year>2010</year>
<publisher-loc><![CDATA[Chile ]]></publisher-loc>
<publisher-name><![CDATA[Mineduc]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rojas]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Flores]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Carrillo]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Caracterización del conocimiento matemático de profesores de educación primaria y secundaria]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Marín]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Climent]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación en educación matemática. Comunicaciones de los grupos de investigación]]></source>
<year>2011</year>
<page-range>395-400</page-range><publisher-loc><![CDATA[Ciudad Real, España ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rowland]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Huckstep]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Thwaites]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Elementary teachers&#8217; mathematics subject knowledge: The knowledge quartet and the case of Naomi]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2005</year>
<volume>8</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>255-81</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Salazar]]></surname>
<given-names><![CDATA[M. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Martinic]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Maz]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Avances de una investigación sobre los modelos, representaciones y recursos utilizados por profesores de primaria para las fracciones]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lupiáñez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Cañadas]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Molina]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Palarea]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Maz]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigaciones en pensamiento numérico y algebraico e historia de la matemática y educación matemática]]></source>
<year>2011</year>
<page-range>39-47</page-range><publisher-loc><![CDATA[Universidad de Granada, España ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shulman]]></surname>
<given-names><![CDATA[L. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Those who understand: Knowledge growth in teaching]]></article-title>
<source><![CDATA[Educational Researcher]]></source>
<year>1986</year>
<volume>15</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>4-14</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sorto]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Marshall]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Luschei]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Carnoy]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teacher knowledge and teaching in Panama and Costa Rica: a comparative study in primary and secondary education]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2009</year>
<volume>12</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>251-90</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Streefland]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Fractions in realistic mathematics education: a paradigm of developmental research]]></source>
<year>1991</year>
<publisher-loc><![CDATA[Países Bajos ]]></publisher-loc>
<publisher-name><![CDATA[Kluwer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="book">
<collab>UNESCO</collab>
<source><![CDATA[Challenges in basic mathematics education]]></source>
<year>2012</year>
<publisher-loc><![CDATA[París ]]></publisher-loc>
<publisher-name><![CDATA[Autor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Valdemoros]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dificultades experimentadas por el maestro de primaria en la enseñanza de fracciones]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2010</year>
<volume>13</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>423-40</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
