<?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>S1665-24362022000300289</article-id>
<article-id pub-id-type="doi">10.12802/relime.22.2532</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Anticipación de estrategias de resolución de problemas de división-medida con fracciones mediante una progresión de aprendizaje]]></article-title>
<article-title xml:lang="en"><![CDATA[The use of the progression in strategies of resolution of measurement-division fraction problems by preservice primary mathematics teachers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montero]]></surname>
<given-names><![CDATA[Eloísa]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Callejo]]></surname>
<given-names><![CDATA[María Luz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Valls]]></surname>
<given-names><![CDATA[Julia]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Escuni Centro Universitario de Educación ]]></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>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<volume>25</volume>
<numero>3</numero>
<fpage>289</fpage>
<lpage>310</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362022000300289&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362022000300289&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362022000300289&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo de esta investigación es caracterizar cómo los estudiantes para maestro, un año después de un experimento de enseñanza, reconocen diferentes etapas de progresión al anticipar estrategias de estudiantes de educación primaria al resolver problemas de división - medida con fracciones. Los 41 participantes cursaban el séptimo semestre del Grado en Maestro en Educación Primaria durante el curso 2018-2019. En el análisis se tuvo en cuenta el tipo de estrategias utilizadas y si estas evidenciaban la idea de progresión. Los resultados muestran tres categorías en el uso de la idea de progresión al anticipar respuestas a problemas de división-medida: (a) No usan la idea de progresión; (b) usan parcialmente la idea de progresión; (c) usan la idea de progresión. Pese a su dificultad, es posible comenzar a desarrollar la idea de progresión al anticipar estrategias en la formación de futuros maestros.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The objective of this research is to characterize how primary prospective teachers, one year after a teaching experiment, recognize different stages of progression anticipating solving strategies for measurement division problems with fractions used by elementary school children. The 41 participants were in the seventh semester of the Education Teaching Degree (eight semesters) during the 2018-2019 academic year. The analysis considered the type of strategies used and whether they evidenced the idea of progression. The results show three categories in the use of the idea of progression when anticipating answers to measurement division problems: They (a) do not use the idea of progression; (b) partially use the idea of progression; (c) use the idea of progression. Despite its difficulty, it is possible to begin to develop the idea of progression by anticipating strategies in the training of future teachers.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O objetivo desta pesquisa é caracterizar como estudantes para professores, um ano após a sua formação, são capazes de reconhecer a existência de diferentes níveis de progressão, antecipando estratégias de resolução de problemas com frações envolvendo divisão-medida, utilizadas por alunos dos anos iniciais. Os 41 participantes estavam em seu sétimo semestre do Graduação em Pedagogia nos anos iniciais (oito semestres) durante o ano acadêmico de 2018-2019, um ano após receberem formação em uma experiência de ensino. A análise teve em conta o tipo de estratégias utilizadas e se evidenciavam a ideia de progressão. Os resultados mostram três categorias no uso da ideia de progressão ao antecipar respostas a problemas de divisão-medida: (a) eles não usam a ideia de progressão; (b) usar parcialmente a ideia de progressão; (c) usar a ideia de progressão. Apesar de sua dificuldade, é possível começar a desenvolver a ideia de progressão antecipando estratégias na formação dos futuros professores.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé Le but de cette recherche est de caractériser comment les futurs professeurs des écoles, une année après une expérience d&#8217;enseignement, reconnaissent différentes étapes de progression différents quand ils anticipent des stratégies de résolution de problèmes de division-mesure avec des fractions employées par les élèves du Primaire. Les 41 participants étaient au septième semestre des études pour devenir professeurs d&#8217;Éducation Primaire (huit semestres) au cours de l&#8217;année académique 2018-2019, une année après une expérience d&#8217;enseignement. L&#8217;analyse a pris en compte le type de stratégies utilisées et si elles mettaient en évidence l&#8217;idée de progression. Les résultats montrent trois catégories face à l&#8217;usage de l&#8217;idée de progression: a) L&#8217;idée de progression n&#8217;est pas utilisée; (b) on utilise partiellement l&#8217;idée de progression; (c) on utilise l&#8217;idée de progression. Malgré sa difficulté, il est possible de commencer à développer l&#8217;idée de progression quand on anticipe des stratégies lors de la formation de futurs professeurs.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Anticipación de estrategias]]></kwd>
<kwd lng="es"><![CDATA[Progresión en el aprendizaje]]></kwd>
<kwd lng="es"><![CDATA[Estudiantes para maestro de primaria]]></kwd>
<kwd lng="es"><![CDATA[División-medida con fracciones]]></kwd>
<kwd lng="es"><![CDATA[Mirar profesionalmente]]></kwd>
<kwd lng="en"><![CDATA[Anticipation]]></kwd>
<kwd lng="en"><![CDATA[Progression in learning]]></kwd>
<kwd lng="en"><![CDATA[Prospective primary teachers]]></kwd>
<kwd lng="en"><![CDATA[Measurement division problems with fractions]]></kwd>
<kwd lng="en"><![CDATA[Professional noticing]]></kwd>
<kwd lng="pt"><![CDATA[Antecipação]]></kwd>
<kwd lng="pt"><![CDATA[Progressão da Aprendizagem]]></kwd>
<kwd lng="pt"><![CDATA[Estudantes para professor de anos iniciais]]></kwd>
<kwd lng="pt"><![CDATA[Problemas de divisão-medida com frações]]></kwd>
<kwd lng="pt"><![CDATA[Olhar profissionalmente]]></kwd>
<kwd lng="fr"><![CDATA[Anticipation]]></kwd>
<kwd lng="fr"><![CDATA[Progression dans l&#8217;apprentissage]]></kwd>
<kwd lng="fr"><![CDATA[Étudiants pour devenir professeurs des écoles]]></kwd>
<kwd lng="fr"><![CDATA[Problèmes de division-mesure avec des fractions]]></kwd>
<kwd lng="fr"><![CDATA[Regard professionnel]]></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[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Prospective elementary and secondary teachers&#8217; understanding of division]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1990</year>
<volume>21</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>132-44</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Thames]]></surname>
<given-names><![CDATA[M. H.]]></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="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bandura]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Self-efficacy: Toward a Unifying Theory of Behavioral Change]]></article-title>
<source><![CDATA[Psycological Review]]></source>
<year>1977</year>
<volume>84</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>191</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. H.]]></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[Depaepe]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Torbeyns]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Vermeersch]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Janssens]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Janssen]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Kelchtermans]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Verschaffel]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Dooren]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary teachers]]></article-title>
<source><![CDATA[Teaching and Teacher Education]]></source>
<year>2015</year>
<volume>47</volume>
<page-range>82-92</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duncan]]></surname>
<given-names><![CDATA[R. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Hmelo-Silver]]></surname>
<given-names><![CDATA[C. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning progressions: Aligning curriculum, instruction, and assessment]]></article-title>
<source><![CDATA[Journal of Research in Science Teaching]]></source>
<year>2009</year>
<volume>46</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>606-9</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duschl]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Maeng]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Sezen]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning progressions and teaching sequences: A review and analysis]]></article-title>
<source><![CDATA[Studies in Science Education]]></source>
<year>2011</year>
<volume>47</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>123182</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Edgington]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; uses of a learning trajectory as a tool for mathematics lesson planning]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[J. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Leatham]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Zoest]]></surname>
<given-names><![CDATA[L. Van]]></given-names>
</name>
</person-group>
<source><![CDATA[Research trends in mathematics teacher education]]></source>
<year>2014</year>
<page-range>261-84</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Edgington]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<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[Webb]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Translating learning trajectories into useable tools for teachers]]></article-title>
<source><![CDATA[Mathematics Teacher Educator]]></source>
<year>2016</year>
<volume>5</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>65-80</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Empson]]></surname>
<given-names><![CDATA[S. B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the idea of learning trajectories: Promises and pitfalls]]></article-title>
<source><![CDATA[The Mathematics Enthusiast]]></source>
<year>2011</year>
<volume>8</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>571-98</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Empson]]></surname>
<given-names><![CDATA[S. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Levi]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Extending Children&#8217;s Mathematics: Fractions and Decimals]]></source>
<year>2011</year>
<publisher-name><![CDATA[Heinemann]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Entwistle]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Promoting deep learning through teaching and assessment]]></article-title>
<source><![CDATA[1st Annual Conference ESRC Teaching and Learning Research Programme]]></source>
<year>2000</year>
<page-range>9-20</page-range><publisher-name><![CDATA[University of Leicester]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Llinares]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Valls]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning to notice students&#8217; mathematical thinking through on-line discussions]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2012</year>
<volume>44</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>747-59</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Sánchez-Matamoros]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Moreno]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Callejo]]></surname>
<given-names><![CDATA[M. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La coordinación de las aproximaciones en la comprensión del concepto de límite cuando los estudiantes para profesor anticipan respuestas de estudiantes]]></article-title>
<source><![CDATA[Enseñanza de las ciencias]]></source>
<year>2018</year>
<volume>36</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>143-62</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fischbein]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Deri]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Nello]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Marino]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The role of implicit models in solving verbal problems in multiplication and division]]></article-title>
<source><![CDATA[Journal for research in mathematics education]]></source>
<year>1985</year>
<volume>16</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>3-17</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gordon]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Debus]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Developing deep learning approaches and personal teaching efficacy within a preservice teacher education context]]></article-title>
<source><![CDATA[British Journal of Educational Psychology]]></source>
<year>2002</year>
<volume>72</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>483-511</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gotwals]]></surname>
<given-names><![CDATA[A. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Where are we now? Learning progressions and formative assessment]]></article-title>
<source><![CDATA[Applied Measurement in Education]]></source>
<year>2018</year>
<volume>31</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>157-64</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Graeber]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Tirosh]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Glover]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Preservice teachers&#8217; beliefs and performance on measurement and partitive division problems]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lappan]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Even]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education]]></source>
<year>1986</year>
<page-range>262-7</page-range><publisher-loc><![CDATA[East Lansing ]]></publisher-loc>
<publisher-name><![CDATA[Michigan State University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Herbst]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Chazan]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[C. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Chieu]]></surname>
<given-names><![CDATA[V. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Weiss]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Using comics-based representations of teaching, and technology, to bring practice to teacher education courses]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2011</year>
<volume>43</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>91-103</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Higgs]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Practice- Based Education Pedagogy. Situated capability-development, relationship practice(s)]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Higgs]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Barnett]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Billett]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Hutchings]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Trede]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Practice-Based Education. Perspective and Strategies]]></source>
<year>2012</year>
<page-range>71-80</page-range><publisher-name><![CDATA[Sense Publishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ivars]]></surname>
<given-names><![CDATA[P.]]></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[A learning Trajectory as a scaffold for pre-service Teachers&#8217; Noticing of Students&#8217; Mathematical Understanding]]></article-title>
<source><![CDATA[International Journal of Science and mathematics Education]]></source>
<year>2020</year>
<volume>18</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>529-48</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jacobs]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Lamb]]></surname>
<given-names><![CDATA[L.]]></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="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jansen]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Hohensee]]></surname>
<given-names><![CDATA[Ch.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Examining and elaborating upon the nature of elementary prospective teachers&#8217; conceptions of partitive division with fractions]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2016</year>
<volume>19</volume>
<page-range>503-22</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Kulm]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Knowledge and confidence of pre-service mathematics teachers: The case of fraction division]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2008</year>
<volume>40</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>833-43</page-range></nlm-citation>
</ref>
<ref id="B25">
<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[El desarrollo de la competencia docente &#8220;mirar profesionalmente&#8221; la enseñanza-aprendizaje de las matemáticas]]></article-title>
<source><![CDATA[Educar em Revista]]></source>
<year>2013</year>
<volume>50</volume>
<page-range>117-33</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Llinares]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Sánchez-Matamoros]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Changes in how prospective teachers anticipate secondary students&#8217; answers]]></article-title>
<source><![CDATA[Eurasia Journal of Mathematics, Science &amp; Technology Education]]></source>
<year>2016</year>
<volume>12</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>2155-70</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Luo]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Prospective elementary teachers&#8217; knowledge of fraction division]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2012</year>
<volume>15</volume>
<page-range>481-500</page-range></nlm-citation>
</ref>
<ref id="B28">
<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-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Montero]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Callejo]]></surname>
<given-names><![CDATA[M. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cambios en cómo estudiantes para maestro anticipan respuestas de niños de primaria]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Marbán]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Arce]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Maroto]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Muñoz-Escolano]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Alsina]]></surname>
<given-names><![CDATA[Á.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación en Educación Matemática XXIII]]></source>
<year>2019</year>
<page-range>433-42</page-range><publisher-loc><![CDATA[Valladolid ]]></publisher-loc>
<publisher-name><![CDATA[SEIEM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nillas]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Division of fractions: Preservice teachers&#8217; understanding and use of problem solving strategies]]></article-title>
<source><![CDATA[The mathematics educator]]></source>
<year>2003</year>
<volume>7</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>96-113</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Olanoff]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Tobias]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Mathematical Content Knowledge for Teaching Elementary Mathematics: A Focus on Fractions]]></article-title>
<source><![CDATA[The Mathematics Enthusiast]]></source>
<year>2014</year>
<volume>11</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>267-310</page-range></nlm-citation>
</ref>
<ref id="B32">
<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[Moreno]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Perez -Tyteca]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Callejo]]></surname>
<given-names><![CDATA[M.L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Trayectoria de aprendizaje de la longitud y su medida como instrumento conceptual usado por futuros maestros de educación infantil]]></article-title>
<source><![CDATA[RELIME. Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2018</year>
<volume>21</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>203-28</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Simon]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reconstructing mathematics pedagogy from a constructivist perspective]]></article-title>
<source><![CDATA[Journal for research in mathematics education]]></source>
<year>1995</year>
<volume>26</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>114-45</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Stein]]></surname>
<given-names><![CDATA[M.K.]]></given-names>
</name>
</person-group>
<source><![CDATA[5 practices for orchestrating productive mathematics discussions]]></source>
<year>2011</year>
<publisher-name><![CDATA[National Council of Teachers of Mathematics]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B35">
<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[Roesken-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>
<volume>48</volume>
<page-range>1-27</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Steffe]]></surname>
<given-names><![CDATA[L. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Olive]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Children&#8217;s fractional knowledge]]></source>
<year>2010</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stein]]></surname>
<given-names><![CDATA[M. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Engle]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Hughes]]></surname>
<given-names><![CDATA[E. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell]]></article-title>
<source><![CDATA[Mathematical Thinking and Learning]]></source>
<year>2008</year>
<volume>10</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>313-40</page-range></nlm-citation>
</ref>
<ref id="B38">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stevens]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Wilkins]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Lovin]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Siegfried]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Norton]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Busi]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Promoting sophisticated fraction constructs through instructional changes in a mathematics course for PreK-8 prospective teachers]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2020</year>
<volume>23</volume>
<page-range>153-81</page-range></nlm-citation>
</ref>
<ref id="B39">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stockero]]></surname>
<given-names><![CDATA[S. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Transitions in prospective mathematics teacher noticing]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[J. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Leatham]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Zoest]]></surname>
<given-names><![CDATA[L. Van]]></given-names>
</name>
</person-group>
<source><![CDATA[Research Trends in Mathematics Teacher Education]]></source>
<year>2014</year>
<page-range>239-59</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B40">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Teuscher]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Leatham]]></surname>
<given-names><![CDATA[K. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Peterson]]></surname>
<given-names><![CDATA[B. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[From a framework to a lens: Learning to notice student mathematical thinking]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Schack]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Fisher]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Wilhelm]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teacher noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks]]></source>
<year>2017</year>
<page-range>31-48</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B41">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tirosh]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Graeber]]></surname>
<given-names><![CDATA[A. O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Preservice elementary teachers&#8217; explicit beliefs about multiplication and division]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1989</year>
<volume>20</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>79-96</page-range></nlm-citation>
</ref>
<ref id="B42">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tyminski]]></surname>
<given-names><![CDATA[A. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Simpson]]></surname>
<given-names><![CDATA[A. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Land]]></surname>
<given-names><![CDATA[T. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Drake]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Dede]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Prospective elementary mathematics teachers &#8216;noticing of childrens&#8217; mathematics: a focus on extending moves]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2021</year>
<volume>24</volume>
<page-range>533-61</page-range></nlm-citation>
</ref>
<ref id="B43">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vula]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Kingji-Kastrati]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pre-service teacher procedural and conceptual knowledge of fractions]]></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]]></source>
<year>2018</year>
<page-range>111-23</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B44">
<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. F.]]></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="B45">
<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>
<page-range>149-75</page-range></nlm-citation>
</ref>
<ref id="B46">
<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; uses 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 id="B47">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zimmerman]]></surname>
<given-names><![CDATA[B. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A social cognitive view of self-regulated academic learning]]></article-title>
<source><![CDATA[Journal of Educational Psychology]]></source>
<year>1989</year>
<volume>81</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>329</page-range></nlm-citation>
</ref>
<ref id="B48">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zimmerman]]></surname>
<given-names><![CDATA[B. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Developing self-fulfilling cycles of academic regulation: An analysis of exemplary instructional models]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Schunk]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Zimmerman]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[Self regulated learning: From teaching to self-reflective practice]]></source>
<year>1998</year>
<page-range>1-19</page-range><publisher-name><![CDATA[Guilford Publications]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
