<?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>1665-2436</journal-id>
<journal-title><![CDATA[Revista latinoamericana de investigación en matemática educativa]]></journal-title>
<abbrev-journal-title><![CDATA[Relime]]></abbrev-journal-title>
<issn>1665-2436</issn>
<publisher>
<publisher-name><![CDATA[Comité Latinoamericano de Matemática Educativa A.C.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1665-24362018000200203</article-id>
<article-id pub-id-type="doi">10.12802/relime.18.2124</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Trayectoria de aprendizaje de la longitud y su medida como instrumento conceptual usado por futuros maestros de educación infantil]]></article-title>
<article-title xml:lang="en"><![CDATA[A learning trajectory of length and measure as a conceptual instrument used by prospective kindergarten teachers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Sánchez - Matamoros García]]></surname>
<given-names><![CDATA[Gloria]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Moreno Moreno]]></surname>
<given-names><![CDATA[Mar]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pérez Tyteca]]></surname>
<given-names><![CDATA[Patricia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Callejo de la Vega]]></surname>
<given-names><![CDATA[M. Luz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Sevilla  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Alicante  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Alicante  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Alicante  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2018</year>
</pub-date>
<volume>21</volume>
<numero>2</numero>
<fpage>203</fpage>
<lpage>228</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362018000200203&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362018000200203&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362018000200203&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo de este trabajo es caracterizar el uso de una trayectoria de aprendizaje de la longitud y su medida como instrumento conceptual para favorecer la adquisición de la competencia docente &#8220;mirar profesionalmente&#8221; el pensamiento matemático de los niños. Participaron 64 estudiantes de la carrera de maestro de educación infantil que siguieron un módulo de enseñanza. Este módulo estaba articulado en torno a una trayectoria de aprendizaje sobre la longitud y su medida, con objeto de que los futuros maestros la usaran como instrumento conceptual para describir e interpretar las respuestas de niños de educación infantil a situaciones de enseñanza-aprendizaje (primer esquema de acción instrumental) y proponer tareas en función de la comprensión inferida (segundo esquema de acción instrumental). Los resultados muestran que hay estudiantes que se preparan para ser maestros que no desarrollan ningún esquema de acción instrumental, y otros desarrollan el primer esquema y algunos, ambos; esto proporciona evidencias de la adquisición de la competencia arriba señalada.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This study characterizes the use of a learning trajectory for length, as a magnitude and its measurement, as a conceptual instrument for gaining the professional competence of noticing mathematical thinking of children by the prospective kindergarten teachers. A total amount of 64 prospective kindergarten teachers enrolled on a teaching module about teaching and learning the concept of length in their training programmer. This module is based on a learning trajectory of length to be used as a conceptual instrument which let prospective kindergarten teachers describe and interpret children&#8217;s answers to an specific learning situation (first instrumental action scheme) and take appropriate learning decisions related to the interpretation inferred (second instrumental action scheme). The results exhibit there are some prospective kindergarten teachers who do not develop any schemes, some of them develop only the first scheme, and few of them develop the second instrumental action scheme. These results give evidences of the acquisition of noticing.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O objetivo deste trabalho é caracterizar o uso da um &#8220;caminho de aprendizagem&#8221; da magnitude comprimento e medida como um instrumento conceitual para favorecer a aquisição da competência docente &#8220;para olhar profissionalmente&#8221; no pensamento matemático das crianças. Um total de 64 alunos participaram de um professor de educação pré-escolar que seguiu um módulo de ensino. Este módulo foi estruturado em torno da um caminho de aprendizado sobre o comprimento e sua medição, com o objetivo de que os futuros professores o utilizarão como um instrumento conceitual para descrever e interpretar as respostas das crianças na primeira infância às situações de ensino-aprendizagem (primeiro esquema de ação instrumental) e propor tarefas baseadas no entendimento inferido (segundo esquema de ação instrumental). Os resultados mostram que há estudantes para professores que não desenvolvem nenhum esquema de ação instrumental, outros desenvolvem o primeiro e alguns de ambos; esses resultados evidenciam a aquisição dessa competência.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé Le but de ce travail est de caractériser l&#8217;usage d&#8217;une trajectoire d&#8217;apprentissage de la longueur et sa mesure comme instrument conceptuel pour favoriser l&#8217;acquisition de la compétence des enseignants « regarder professionnellement » la pensée mathématique chez les enfants. Dans cette étude participèrent soixante-quatre étudiants à maîtres qui ont suivi un cycle de formation d&#8217;enseignement. Ce cycle portait sur une trajectoire d&#8217;apprentissage sur la longueur et sa mesure, afin d&#8217;être utilisée par les futurs enseignants comme instrument conceptuel pour décrire et interpréter les réponses chez les élèves de maternel à des situations d&#8217;enseignement-apprentissage (premier schéma d&#8217;action instrumentale) et proposer des tâches en fonction de la compréhension inférée (deuxième schéma d&#8217;action instrumentale). Les résultats montrent qu&#8217;il y a des étudiants à maîtres qui ne développent aucun schéma d&#8217;action instrumentale, d&#8217;autres développent le premier et certains tous les deux ; cela fournit des évidences de l&#8217;acquisition de cette compétence.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[mirar profesionalmente]]></kwd>
<kwd lng="es"><![CDATA[trayectoria de aprendizaje]]></kwd>
<kwd lng="es"><![CDATA[instrumento conceptual]]></kwd>
<kwd lng="es"><![CDATA[magnitud longitud y medida]]></kwd>
<kwd lng="es"><![CDATA[educación infantil]]></kwd>
<kwd lng="en"><![CDATA[professional noticing]]></kwd>
<kwd lng="en"><![CDATA[preservice teacher learning]]></kwd>
<kwd lng="en"><![CDATA[learning trajectories]]></kwd>
<kwd lng="en"><![CDATA[early childhood education]]></kwd>
<kwd lng="en"><![CDATA[length and measure]]></kwd>
<kwd lng="en"><![CDATA[learning experiment]]></kwd>
<kwd lng="pt"><![CDATA[olhar profissionalmente]]></kwd>
<kwd lng="pt"><![CDATA[caminho de aprendizagem]]></kwd>
<kwd lng="pt"><![CDATA[instrumento conceitual]]></kwd>
<kwd lng="pt"><![CDATA[magnitude comprimento e medida]]></kwd>
<kwd lng="pt"><![CDATA[educação infantil]]></kwd>
<kwd lng="fr"><![CDATA[regard professionnel]]></kwd>
<kwd lng="fr"><![CDATA[trajectoire d&#8217;apprentissage]]></kwd>
<kwd lng="fr"><![CDATA[instrument conceptuel]]></kwd>
<kwd lng="fr"><![CDATA[grandeur longueur et mesure]]></kwd>
<kwd lng="fr"><![CDATA[enseignement maternel]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barnhart]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Es]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Studying teacher noticing: examining the relationship among pre-service science teachers&#8217; ability to attend, analyze and respond to student thinking]]></article-title>
<source><![CDATA[Teaching and Teacher Education]]></source>
<year>2015</year>
<numero>45</numero>
<issue>45</issue>
<page-range>83-93</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Choy]]></surname>
<given-names><![CDATA[B.H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Snapshots of mathematics teacher noticing during task design]]></article-title>
<source><![CDATA[Mathematics Education Research Journal]]></source>
<year>2016</year>
<numero>28</numero>
<issue>28</issue>
<page-range>421-40</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clements]]></surname>
<given-names><![CDATA[D. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teaching length measurement: Research challenges]]></article-title>
<source><![CDATA[School Science and Mathematics]]></source>
<year>2010</year>
<volume>99</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>5-11</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clements]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Sarama]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning trajectories in mathematics education]]></article-title>
<source><![CDATA[Mathematical Thinking and Learning]]></source>
<year>2004</year>
<volume>6</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>81-9</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Confrey]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Maloney]]></surname>
<given-names><![CDATA[A. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Wilson]]></surname>
<given-names><![CDATA[P. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Nguyen]]></surname>
<given-names><![CDATA[K. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Understanding over time: The cognitive underpinnings of learning trajectories]]></article-title>
<source><![CDATA[annual meeting of the American Education Research Association]]></source>
<year>2010</year>
<publisher-loc><![CDATA[Denver, CO, USA ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Drijvers]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Kieran]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Mariotti]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Integrating technology into mathematics education: Theoretical perspectives]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Hoyles]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Lagrange]]></surname>
<given-names><![CDATA[J.B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics education and technology: Rethinking the terrain]]></source>
<year>2010</year>
<page-range>89-132</page-range><publisher-loc><![CDATA[New York, USA ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Drijvers]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Trouche]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[From artifacts to instruments: A theoretical framework behind the orchestra metaphor]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Blume]]></surname>
<given-names><![CDATA[G. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Heid]]></surname>
<given-names><![CDATA[M. K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Research on technology and the teaching and learning of mathematics: Vol. 2. Cases and perspectives]]></source>
<year>2008</year>
<page-range>363-92</page-range><publisher-loc><![CDATA[Charlotte, NC, USA ]]></publisher-loc>
<publisher-name><![CDATA[Information Age]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ellis]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Siegler]]></surname>
<given-names><![CDATA[R. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Voorhis]]></surname>
<given-names><![CDATA[F. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Developmental changes in children&#8217;s understanding of measurement procedures and principles]]></source>
<year>2003</year>
<publisher-loc><![CDATA[Tampa, FL, USA ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gupta]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Soto]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Dick]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Broderick]]></surname>
<given-names><![CDATA[S.D.]]></given-names>
</name>
<name>
<surname><![CDATA[Appelgate]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Noticing and deciding the next steps for teaching: A cross-university study with elementary pre-service teachers]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Stylianides]]></surname>
<given-names><![CDATA[G.J.]]></given-names>
</name>
<name>
<surname><![CDATA[Hino]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Research advances in the mathematical education of pre-service elementary teachers, ICME-13 Monographs]]></source>
<year>2018</year>
<page-range>261-75</page-range><publisher-loc><![CDATA[Cham, Germany ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jacobs]]></surname>
<given-names><![CDATA[V.R.]]></given-names>
</name>
<name>
<surname><![CDATA[Lamb]]></surname>
<given-names><![CDATA[L.C.]]></given-names>
</name>
<name>
<surname><![CDATA[Philipp]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Professional noticing of children&#8217;s mathematical thinking]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>2010</year>
<volume>41</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>169-202</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Krupa]]></surname>
<given-names><![CDATA[E. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Huey]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Lesseig]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Casey]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Monson]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Investigating secondary preservice teacher noticing of studets&#8217; mathematical thinking]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Schack]]></surname>
<given-names><![CDATA[E.O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks]]></source>
<year>2017</year>
<page-range>49-71</page-range><publisher-loc><![CDATA[Cham, Germany ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Llinares]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La generación y uso de instrumentos para la práctica de enseñar matemáticas en educación primaria]]></article-title>
<source><![CDATA[UNO. Revista de Didáctica de la Matemática]]></source>
<year>2004</year>
<numero>36</numero>
<issue>36</issue>
<page-range>93-115</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mason]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Researching your own practice: The discipline of noticing]]></source>
<year>2002</year>
<publisher-loc><![CDATA[London, U.K. ]]></publisher-loc>
<publisher-name><![CDATA[Routledge Falmer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<collab>NCTM</collab>
<source><![CDATA[Principles and Standards for School Mathematics]]></source>
<year>2000</year>
<publisher-loc><![CDATA[Reston, VA, USA ]]></publisher-loc>
<publisher-name><![CDATA[NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nunes]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Bryant]]></surname>
<given-names><![CDATA[P. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Children doing mathematics]]></source>
<year>1996</year>
<publisher-loc><![CDATA[Cambridge, MA, USA ]]></publisher-loc>
<publisher-name><![CDATA[Blackwell]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Parks]]></surname>
<given-names><![CDATA[A.M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wager]]></surname>
<given-names><![CDATA[A.A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[What knowledge is shaping teacher preparation in early childhood mathematics?]]></article-title>
<source><![CDATA[Journal of Early Childhood Teacher Education]]></source>
<year>2015</year>
<volume>36</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>124-41</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Judgment and reasoning in the child]]></source>
<year>1972</year>
<publisher-loc><![CDATA[MD, USA ]]></publisher-loc>
<publisher-name><![CDATA[Littlefield]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rabardel]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Les hommes et les technologies: approche cognitive des instruments contemporains]]></source>
<year>1995</year>
<publisher-loc><![CDATA[Paris, France ]]></publisher-loc>
<publisher-name><![CDATA[Armand Colin]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sánchez-Matamoros]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Llinares]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Developing pre-service teachers&#8217; noticing of students&#8217; understanding of the derivative concept]]></article-title>
<source><![CDATA[International Journal of Science and Mathematics Education]]></source>
<year>2015</year>
<volume>13</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>305-1329</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Santagata]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Yeh]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The role of perception, interpretation, and decision making in the development of beginning teachers&#8217; competence]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2016</year>
<volume>48</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>153-65</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sarama]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Clements]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Early Childhood Mathematics Education Research. Learning Trajectories for Young Children]]></source>
<year>2009</year>
<publisher-loc><![CDATA[London ]]></publisher-loc>
<publisher-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schack]]></surname>
<given-names><![CDATA[E.O.]]></given-names>
</name>
<name>
<surname><![CDATA[Fisher]]></surname>
<given-names><![CDATA[M.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Thomas]]></surname>
<given-names><![CDATA[J.N.]]></given-names>
</name>
<name>
<surname><![CDATA[Eisenhardt]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Tassell]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Yoder]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Prospective elementary school teachers&#8217; professional noticing of children&#8217;s early numeracy]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2013</year>
<volume>16</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>379-97</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sherin]]></surname>
<given-names><![CDATA[M. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Jacobs]]></surname>
<given-names><![CDATA[V. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Philipp]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics teacher noticing: Seeing through teachers&#8217; eyes]]></source>
<year>2011</year>
<publisher-loc><![CDATA[New York, USA ]]></publisher-loc>
<publisher-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skoumpourdi]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Kindergartners measuring length]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Krainer]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Vondrová]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the Ninth Conference of the European Society for Research in Mathematics Education (CERME 9)]]></source>
<year>2015</year>
<page-range>89-1995</page-range><publisher-loc><![CDATA[Prague, Czech Republic ]]></publisher-loc>
<publisher-name><![CDATA[Charles University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Son]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[How preservice teachers interpret and respond to student errors: ratio and proportion in similar rectangles]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2013</year>
<volume>84</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>49-70</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stahnke]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Schueler]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Roeskem-Winter]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; perception, interpretation, and decision-making: a systematic review of empirical mathematics education research]]></article-title>
<source><![CDATA[ZDM Mathematics Education]]></source>
<year>2016</year>
<numero>48</numero>
<issue>48</issue>
<page-range>1-17</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stephan]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Bowers]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Cobb]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Gravemeijer]]></surname>
<given-names><![CDATA[K. P. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Supporting students&#8217; development of measuring conceptions: Analyzing students&#8217; learning in social context]]></source>
<year>2003</year>
<volume>12</volume>
<publisher-loc><![CDATA[Reston, VA, USA ]]></publisher-loc>
<publisher-name><![CDATA[National Council of Teachers of Mathematics]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Strauss]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Corbin]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Grounded theory methodology]]></article-title>
<source><![CDATA[Handbook of Qualitative Research]]></source>
<year>1994</year>
<numero>17</numero>
<issue>17</issue>
<page-range>273-85</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Szilagyi]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Clements]]></surname>
<given-names><![CDATA[D.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Sarama]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Young children&#8217;s understanding of length measurement: Evaluating a learning trajectory]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>2013</year>
<volume>44</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>581-620</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sztajn]]></surname>
<given-names><![CDATA[P]]></given-names>
</name>
<name>
<surname><![CDATA[Confrey]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Wilson]]></surname>
<given-names><![CDATA[P. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Edgington]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning trajectory based instruction: Toward a theory of teaching]]></article-title>
<source><![CDATA[Educational Researcher]]></source>
<year>2012</year>
<volume>41</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>147-56</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Thomas]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Tabor]]></surname>
<given-names><![CDATA[P.D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Developing quantitative mental imagery]]></article-title>
<source><![CDATA[Teaching Children Mathematics]]></source>
<year>2012</year>
<volume>19</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>174-83</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Trouche]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Managing the complexity of human/machine interactions environments: Guiding student's command process through instrumental orchestrations]]></article-title>
<source><![CDATA[International Journal of Computers for Mathematical Learning]]></source>
<year>2004</year>
<volume>9</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>281-307</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van den Heuvel-Panhuizen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Elia]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Kindergartners&#8217; performance in length measurement and the effect of picture book reading]]></article-title>
<source><![CDATA[ZDM Mathematics Education]]></source>
<year>2011</year>
<numero>43</numero>
<issue>43</issue>
<page-range>621-35</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Verillon]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Rabardel]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cognition and artifacts: A contribution to the study of thought in relation to instrument activity]]></article-title>
<source><![CDATA[European Journal of psychology of education]]></source>
<year>1995</year>
<volume>10</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>77-101</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wilson]]></surname>
<given-names><![CDATA[P.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Mojica]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Confrey]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning trajectories in teacher education: Supporting teachers&#8217; understanding of students&#8217; mathematical thinking]]></article-title>
<source><![CDATA[Journal of Mathematical Behavior]]></source>
<year>2013</year>
<volume>32</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>103-21</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wilson]]></surname>
<given-names><![CDATA[P. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Sztajn]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Edgington]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Confrey]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; use of their mathematical knowledge for teaching in learning a mathematics learning trajectory]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2014</year>
<volume>17</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>149-75</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wilson]]></surname>
<given-names><![CDATA[P.H.]]></given-names>
</name>
<name>
<surname><![CDATA[Sztajn]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Edgington]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Myers]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; use of a learning trajectory in student-centered instructional practices]]></article-title>
<source><![CDATA[Journal of Teacher Education]]></source>
<year>2015</year>
<volume>66</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>227-44</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
