<?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>2215-4132</journal-id>
<journal-title><![CDATA[Revista Innovaciones Educativas]]></journal-title>
<abbrev-journal-title><![CDATA[Innovaciones Educativas]]></abbrev-journal-title>
<issn>2215-4132</issn>
<publisher>
<publisher-name><![CDATA[Universidad Estatal a Distancia]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-41322023000100023</article-id>
<article-id pub-id-type="doi">10.22458/ie.v25i38.4549</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Las fracciones: conocimiento del profesorado y su contribución en la enseñanza para el estudiantado de cuarto grado en escuelas chilenas]]></article-title>
<article-title xml:lang="en"><![CDATA[Fractions: teachers&#8217; knowledge and their contribution to the teaching of fourth grade students in Chilean schools]]></article-title>
<article-title xml:lang="pt"><![CDATA[Frações: o conhecimento dos professores e sua contribuição para o ensino de frações para alunos da quarta série nas escolas chilenas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez Rojas]]></surname>
<given-names><![CDATA[Palmenia]]></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[La Serena ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2023</year>
</pub-date>
<volume>25</volume>
<numero>38</numero>
<fpage>23</fpage>
<lpage>35</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-41322023000100023&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-41322023000100023&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-41322023000100023&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Las fracciones son un tema matemático complejo, difícil de aprender y de enseñar. Estudios previos sugieren que el aprendizaje del estudiantado puede verse limitado por la comprensión que tiene el profesorado en fracciones. El objetivo de este estudio es examinar en qué medida el conocimiento del profesorado en asociación con el nivel socioeconómico, los conocimientos previos del alumnado y el nivel de conocimientos en matemáticas obtenido en las escuelas contribuye al logro de aprendizaje del alumnado en fracciones. Mediante una metodología cuantitativa, siendo los instrumentos del estudio pruebas estructuradas con preguntas cerra- das aplicadas a 714 personas estudiantes de cuarto grado y a 23 personas docentes de 23 escuelas chilenas. Los datos se analizan utilizando modelos multinivel. Los resultados muestran que de la variabilidad observada en la conceptualización de las fracciones, el 76% se podría atribuir a las variables de nivel del alumnado; mientras que el 24% restante, a las variables de nivel de la escuela. La varianza entre escuelas estaría explicada en un 26% por el conocimiento del profesorado y en un 8% por el nivel socioeconómico. Lo quiere decir que el conocimiento del profesorado, solo o en combinación con otros factores, explica alrededor del 6% de la variabilidad total del avance del alumnado, con una significación al 5%. El nivel de conocimientos matemáticos observado en las escuelas no se muestra significativo. En conclusión, en el presente estudio se reporta que el conocimiento del profesorado contribuye en el logro de aprendizaje del alumnado además del efecto del nivel socioeconómico.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Fractions are a complex mathematical subject, difficult to learn and to teach. Previous studies suggest that student learning may be limited by teachers' understanding of fractions. The objective of this study is to examine the extent to which teachers' knowledge in association with socioeconomic status, students' prior knowledge, and the level of mathematics knowledge obtained in schools contributes to students' learning achievement in fractions. Using a quantitative methodology, the study instruments were structured tests with closed questions applied to 714 fourth grade students and 23 teachers from 23 Chilean schools. The data are analyzed using multilevel models. The results show that of the variability observed in the conceptualization of fractions, 76% could be attributed to student level variables, while the remaining 24% could be attributed to school level variables. The variance between schools could be explained 26% by teacher knowledge and 8% by socioeconomic level. This means that teacher knowledge, alone or in combination with other factors, explains about 6% of the total variability in student progress, with a significance of 5%. The level of mathematical knowledge observed in the schools is not significant. In conclusion, the present study reports that teacher knowledge contributes to student learning achievement in addition to the effect of socioeconomic level.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo: As frações são uma matéria matemática complexa, difícil de aprender e de ensinar. Estudos anteriores sugerem que o aprendizado dos alunos pode ser limitado pela compreensão das frações por parte dos professores. O objetivo deste estudo é examinar até que ponto o conhecimento dos profesores em associação com o status socioeconômico, o conhecimento prévio dos alunos e o nível de alfabetização matemática alcançado nas escolas contribui para o sucesso do aprendizado dos alunos em frações. Usando uma metodologia quantitativa, os instrumentos de estudo são testes estruturados com perguntas fechadas aplicadas a 714 alunos da quarta série e 23 professores de 23 escolas chilenas. Os dados são analisados utilizando modelos multiníveis. Os resultados mostram que 76% da variabilidade observada na conceituação das frações poderia ser atribuída a variáveis de nível estudantil, enquanto os 24% restantes poderiam ser atribuídos a variáveis de nível escolar. A variação entre as escolas é explicada em 26% pelo conhecimento dos professores e 8% pelo status sócio-econômico. Isto significa que o conhecimento do professor, sozinho ou em combinação com outros fatores, explica cerca de 6% da variação total no progresso dos alunos, com significância de 5%. O nível de conhecimento matemático observado nas escolas não é significativo. Em conclusão, o presente estudo relata que o conhecimento dos professores contribui para a realização do aprendizado dos alunos, além do efeito do status sócio-econômico.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[profesorado de primaria]]></kwd>
<kwd lng="es"><![CDATA[enseñanza de las matemáticas]]></kwd>
<kwd lng="es"><![CDATA[aprendizaje]]></kwd>
<kwd lng="es"><![CDATA[educación]]></kwd>
<kwd lng="es"><![CDATA[matemáticas]]></kwd>
<kwd lng="en"><![CDATA[Primary school teachers]]></kwd>
<kwd lng="en"><![CDATA[math teaching]]></kwd>
<kwd lng="en"><![CDATA[learning]]></kwd>
<kwd lng="en"><![CDATA[education]]></kwd>
<kwd lng="en"><![CDATA[mathematics]]></kwd>
<kwd lng="pt"><![CDATA[professor de escola primária]]></kwd>
<kwd lng="pt"><![CDATA[ensino de matemática]]></kwd>
<kwd lng="pt"><![CDATA[aprendizagem]]></kwd>
<kwd lng="pt"><![CDATA[educação]]></kwd>
<kwd lng="pt"><![CDATA[matemática]]></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[Álvarez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[El Informe Coleman a Debate en su Cincuenta Aniversario]]></article-title>
<source><![CDATA[International Journal of Sociology of Education]]></source>
<year>2016</year>
<volume>5</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>87-106</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Avcu]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Turkish pre-service middle level mathematics teachers&#8217; knowledge for teaching fractions]]></article-title>
<source><![CDATA[Research in Middle Level Education Online]]></source>
<year>2019</year>
<volume>42</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>1-20</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Azid]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Hasan]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Nazarudin]]></surname>
<given-names><![CDATA[N. F. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Md-Ali]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Embracing Industrial Revolution 4.0: The Effect of Using Web 2.0 Tools on Primary Schools Students&#8217; Mathematics Achievement (Fraction)]]></article-title>
<source><![CDATA[International Journal of Instruction]]></source>
<year>2020</year>
<volume>13</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>711-28</page-range></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>
<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="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barbieri]]></surname>
<given-names><![CDATA[C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Young]]></surname>
<given-names><![CDATA[L. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Newton]]></surname>
<given-names><![CDATA[K. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Booth]]></surname>
<given-names><![CDATA[J. L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Predicting Middle School Profiles of Algebra Performance Using Fraction Knowledge]]></article-title>
<source><![CDATA[Child Development]]></source>
<year>2021</year>
<volume>92</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>1984-2005</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baumert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Kunter]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Blum]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Brunner]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Voss]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Jordan]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Klusmann]]></surname>
<given-names><![CDATA[U.]]></given-names>
</name>
<name>
<surname><![CDATA[Krauss]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Neubrand]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Tsai]]></surname>
<given-names><![CDATA[Y. M]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; mathematical knowledge, cognitive activation in the classroom, and student progress]]></article-title>
<source><![CDATA[American Educational Research Journal]]></source>
<year>2010</year>
<volume>47</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>133-80</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Lesh]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Silver]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rational numbers concepts]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lesh]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
<name>
<surname><![CDATA[Landau]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[Acquisition of mathematics concepts and processes]]></source>
<year>1983</year>
<page-range>91-125</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Braithwaite]]></surname>
<given-names><![CDATA[D. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Siegler]]></surname>
<given-names><![CDATA[R. S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Putting fractions together]]></article-title>
<source><![CDATA[Journal of Educational Psychology]]></source>
<year>2021</year>
<volume>113</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>556-71</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Charalambous]]></surname>
<given-names><![CDATA[C. Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Pitta-Pantazi]]></surname>
<given-names><![CDATA[D]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Drawing on a theoretical model to study students&#8217; understandings of fractions]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2007</year>
<volume>64</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>293-316</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coleman]]></surname>
<given-names><![CDATA[J. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Campbell]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Hobson]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[McPartland]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Mood]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Weinfeld]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[York]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Equality of educational opportunity]]></source>
<year>1966</year>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Copur-Gencturk]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; conceptual understanding of fraction operations: results from a national sample of elementary school teachers]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2021</year>
<volume>107</volume>
<page-range>525-45</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cueto]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[León]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Sorto]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Miranda]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teachers&#8217; pedagogical content knowledge and mathematics achievement of students in Peru]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2017</year>
<volume>94</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>329-45</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Deringöl]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Misconceptions of primary school students about the subject of fractions: views of primary teachers and primary pre-service teachers]]></article-title>
<source><![CDATA[International Journal of Evaluation and Research in Education]]></source>
<year>2019</year>
<volume>8</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>29-38</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heyneman]]></surname>
<given-names><![CDATA[S. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Loxley]]></surname>
<given-names><![CDATA[W. A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Influences on academic achievement across high and low income countries: a Re-Analysis of IEA data]]></article-title>
<source><![CDATA[Sociology of education]]></source>
<year>1982</year>
<volume>55</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>13-21</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Schilling]]></surname>
<given-names><![CDATA[S. G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Unpacking Pedagogical Content Knowledge: Conceptualizing and measuring teachers´ 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="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Rowan]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effects of teachers&#8217; mathematical knowledge for teaching on student achievement]]></article-title>
<source><![CDATA[American educational research journal]]></source>
<year>2005</year>
<volume>42</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>371-406</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jiang]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Mok]]></surname>
<given-names><![CDATA[I. A. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Chinese students&#8217; hierarchical understanding of part-whole and measure subconstructs]]></article-title>
<source><![CDATA[International Journal of Science and Mathematics Education]]></source>
<year>2020</year>
<volume>19</volume>
<numero>7</numero>
<issue>7</issue>
<page-range>1441-61</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kelcey]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Chin]]></surname>
<given-names><![CDATA[M. J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teacher mathematical knowledge, instructional quality, and student outcomes: a multilevel quantile mediation analysis]]></article-title>
<source><![CDATA[School Effectiveness and School Improvement]]></source>
<year>2019</year>
<volume>30</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>398-431</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kieren]]></surname>
<given-names><![CDATA[T. E]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the mathematical, cognitive, and instructional foundations of rational numbers]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lesh]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<source><![CDATA[Number and measurement: Papers from a research workshop]]></source>
<year>1976</year>
<page-range>101-44</page-range><publisher-name><![CDATA[ERIC/ SMEAC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lenz]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Dreher]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Holzäpfel]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Wittmann]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Are conceptual knowledge and procedural knowledge empirically separable? The case of fractions]]></article-title>
<source><![CDATA[British Journal of Educational Psychology]]></source>
<year>2019</year>
<volume>90</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>809-29</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ma]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conocimiento y enseñanza de las matemáticas elementales. La comprensión de las matemáticas fundamentales que tienen los profesores en China y los EE.UU]]></article-title>
<source><![CDATA[Academia Chilena de Ciencias]]></source>
<year>2010</year>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Maas]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Hox]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sufficient sample sizes for multilevel modeling. Methodology]]></article-title>
<source><![CDATA[European Journal of Research Methods for the Behavioral and Social Sciences]]></source>
<year>2005</year>
<volume>1</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>86-92</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="">
<collab>Ministerio de Educación</collab>
<source><![CDATA[Matemática: Programa de Estudio Cuarto Año Básico]]></source>
<year>2013</year>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pardo]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Ruiz]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[San Martín]]></surname>
<given-names><![CDATA[R]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cómo ajustar e interpretar modelos multinivel con SPSS]]></article-title>
<source><![CDATA[Psicothema]]></source>
<year>2007</year>
<volume>19</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>308-21</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ramadianti]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Priatna]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Kusnandi]]></surname>
<given-names><![CDATA[K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Misconception analysis of junior high school student in interpreting fraction]]></article-title>
<source><![CDATA[Journal for the Education of Gifted Young Scientists]]></source>
<year>2019</year>
<volume>7</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1159-73</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Reeder]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Utley]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[What is a fraction? Developing fraction understanding in prospective elementary teachers]]></article-title>
<source><![CDATA[School Science and Mathematics]]></source>
<year>2017</year>
<volume>117</volume>
<numero>7-8</numero>
<issue>7-8</issue>
<page-range>307-16</page-range></nlm-citation>
</ref>
<ref id="B27">
<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="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Siegler]]></surname>
<given-names><![CDATA[R. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Lortie-Forgues]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hard lessons: Why rational number arithmetic is so difficult for so many people]]></article-title>
<source><![CDATA[Current Directions in Psychological Science]]></source>
<year>2017</year>
<volume>26</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>346-51</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Soni]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Okamoto]]></surname>
<given-names><![CDATA[Y]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Improving children&#8217;s fraction understanding through the use of number lines]]></article-title>
<source><![CDATA[Mathematical Thinking and Learning]]></source>
<year>2020</year>
<volume>22</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>233-43</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stelzer]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Richard&#8217;s]]></surname>
<given-names><![CDATA[M. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Andrés]]></surname>
<given-names><![CDATA[M. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Vernucci]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Introzzi]]></surname>
<given-names><![CDATA[I]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cognitive and maths-specific predictors of fraction conceptual knowledge]]></article-title>
<source><![CDATA[Educational Psychology]]></source>
<year>2021</year>
<volume>41</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>172-90</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tchoshanov]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Cruz]]></surname>
<given-names><![CDATA[M. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Huereca]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Shakirova]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Shakirova]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Ibragimova]]></surname>
<given-names><![CDATA[E. N]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Examination of lower secondary mathematics teachers&#8217; content knowledge and its connection to students&#8217; performance]]></article-title>
<source><![CDATA[International Journal of Science and Mathematics Education]]></source>
<year>2017</year>
<volume>15</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>683-702</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Steenbrugge]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Lesage]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Valcke]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Desoete]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Preservice elementary school teachers&#8217; knowledge of fractions: a mirror of students&#8217; knowledge?]]></article-title>
<source><![CDATA[Journal of Curriculum Studies]]></source>
<year>2014</year>
<volume>46</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>138-61</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Varas]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Lacourly]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[López]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Giaconi]]></surname>
<given-names><![CDATA[V]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Evaluación del conocimiento pedagógico del contenido para enseñar matemáticas elementales]]></article-title>
<source><![CDATA[Enseñanza de las Ciencias]]></source>
<year>2013</year>
<volume>31</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>171-87</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wijaya]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Relationships between Indonesian Fourth Graders&#8217; Difficulties in Fractions and the Opportunity to Learn Fractions: A Snapshot of TIMSS Results]]></article-title>
<source><![CDATA[International Journal of Instruction]]></source>
<year>2017</year>
<volume>10</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>221-36</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Xu]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Burr]]></surname>
<given-names><![CDATA[S. D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Si]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[LeFevre]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Huang]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Divide and conquer: Relations among arithmetic operations and emerging knowledge of fraction notation for Chinese students in grade 4]]></article-title>
<source><![CDATA[Journal of Experimental Child Psychology]]></source>
<year>2022</year>
<volume>217</volume>
<numero>105371</numero>
<issue>105371</issue>
</nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yang]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Kaiser]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[König]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Blömeke]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Relationship between pre-service mathematics teachers&#8217; knowledge, beliefs and instructional practices in China]]></article-title>
<source><![CDATA[ZDM Mathematics Education]]></source>
<year>2020</year>
<volume>52</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>281-94</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Yu]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Xiao]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Liu]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Jiang]]></surname>
<given-names><![CDATA[T]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Effects of Concrete-Representational-Abstract Sequence Instruction on Fractions for Chinese Elementary Students with Mathematics Learning Disabilities]]></article-title>
<source><![CDATA[International Journal of Science and Mathematics Education]]></source>
<year>2021</year>
<page-range>1-18</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
