<?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>2215-3470</journal-id>
<journal-title><![CDATA[Uniciencia]]></journal-title>
<abbrev-journal-title><![CDATA[Uniciencia]]></abbrev-journal-title>
<issn>2215-3470</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional, Costa Rica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-34702022000100234</article-id>
<article-id pub-id-type="doi">10.15359/ru.36-1.14</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Guía de análisis de lecciones de libros de texto de Matemáticas en el tema de proporcionalidad]]></article-title>
<article-title xml:lang="en"><![CDATA[Guidelines for the analysis of mathematics textbooks lessons on the subject of proportionality]]></article-title>
<article-title xml:lang="pt"><![CDATA[Guia para a análise de lições de livros didáticos de Matemática sobre o tema da proporcionalidade]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castillo Céspedes]]></surname>
<given-names><![CDATA[María José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Burgos Navarro]]></surname>
<given-names><![CDATA[María]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Díaz Godino]]></surname>
<given-names><![CDATA[Juan]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica Departamento de Educación Matemática Facultad de Matemática]]></institution>
<addr-line><![CDATA[San José ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática Facultad de Ciencias de la Educación]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Granada Departamento de Didáctica de la Matemática Facultad de Ciencias de la Educación]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2022</year>
</pub-date>
<volume>36</volume>
<numero>1</numero>
<fpage>234</fpage>
<lpage>252</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702022000100234&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702022000100234&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702022000100234&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo de este trabajo es construir una pauta de indicadores de idoneidad didáctica específicos para el tema de la proporcionalidad, que pueda servir de apoyo para el análisis y valoración de lecciones de libros de texto, y como recurso para la reflexión de los profesores sobre procesos de instrucción efectivamente implementados sobre proporcionalidad. Dado que el estudio del razonamiento proporcional se ha constituido en un campo de investigación relevante en educación matemática, es posible identificar criterios de idoneidad específicos para orientar los procesos de enseñanza y aprendizaje, aplicando la metodología de análisis de contenido a una revisión bibliográfica de investigaciones claves en esta área. Las facetas, componentes e indicadores de la noción de idoneidad didáctica orientan la selección y categorización de conocimientos didáctico-matemáticos sobre la proporcionalidad en educación primaria y secundaria derivados de las investigaciones sobre este contenido. Finalmente, se obtiene una Guía de análisis de lecciones de libros de texto de Matemáticas adaptada al tema de proporcionalidad. Dado que el libro de texto es un material curricular que determina en gran medida lo que sucede en el aula y actúa como mediador en el aprendizaje del estudiante, y que el estudio de las razones, proporciones y la proporcionalidad en los currículos de educación primaria y secundaria es un hecho, la guía obtenida puede ser un recurso valioso para el docente. Es necesario el diseño e implementación de acciones formativas con profesores para su conocimiento y uso competente, entendiendo que no supone una propuesta cerrada.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The objective of this study is the construction of a guideline of indicators of didactic suitability related to the topic of proportionality, which can be used as a basis for the analysis and evaluation of textbook lessons, and as a resource for teachers&#8217; reflection on effectively implemented instructional processes about proportionality. Since the study of proportional reasoning has become a relevant field of research in mathematics education, it is possible to identify specific suitability criteria for guiding the teaching and learning processes, applying the methodology of content analysis to a bibliographic review of key research in this area. Various aspects, components, and indicators of the notion of didactic suitability guide the selection and categorization of didactic-mathematical knowledge about proportionality in elementary and secondary education derived from research about such content. Finally, a Mathematics Textbook Lesson Analysis Guide adapted to the topic of proportionality was created. Since the textbook contains curricular material that largely determines what happens in the classroom and acts as a mediator in student learning, and ratios, proportions, and proportionality are studied in the curricula of elementary and secondary education, the Guide obtained can be a valuable resource for teachers. It is necessary to design and implement training actions with teachers that they are familiar with and can use competently, bearing in mind that there is always room for further improvement.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O objetivo deste trabalho é construir um padrão de indicadores de idoneidade didática específicos ao tema da proporcionalidade, que possa servir de apoio para a análise e avaliação das aulas de livros didáticos, e como recurso para a reflexão dos professores sobre processos instrucionais efetivamente implementados sobre proporcionalidade. Uma vez que o estudo do raciocínio proporcional se tornou um campo relevante de pesquisa em educação matemática, é possível identificar critérios específicos de aptidão para orientar processos de ensino e aprendizagem, aplicando a metodologia de análise de conteúdo a uma revisão bibliográfica das principais pesquisas nessa área. As facetas, componentes e indicadores da noção de idoneidade didática orientam a seleção e categorização do conhecimento didático-matemático sobre proporcionalidade no ensino fundamental e médio derivado de pesquisas sobre este conteúdo. Por fim, é obtido um Guia para a análise de lições de livros didáticos de Matemática adaptado ao tema da proporcionalidade. Como o livro é um material curricular que determina em grande parte o que acontece em sala de aula e atua como mediador na aprendizagem dos alunos, e que o estudo da razão, das proporções e da proporcionalidade nos currículos do ensino fundamental e médio é um fato, a orientação obtida pode ser um recurso valioso para o professor. É necessário projetar e implementar ações formativas com os professores para seus conhecimentos e uso competente, entendendo que não se trata de uma proposta fechada.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[idoneidad didáctica]]></kwd>
<kwd lng="es"><![CDATA[libro de texto]]></kwd>
<kwd lng="es"><![CDATA[proporcionalidad]]></kwd>
<kwd lng="es"><![CDATA[formación de profesores]]></kwd>
<kwd lng="en"><![CDATA[didactic suitability]]></kwd>
<kwd lng="en"><![CDATA[textbook]]></kwd>
<kwd lng="en"><![CDATA[proportionality]]></kwd>
<kwd lng="en"><![CDATA[teacher education]]></kwd>
<kwd lng="pt"><![CDATA[idoneidade didática]]></kwd>
<kwd lng="pt"><![CDATA[livro didático]]></kwd>
<kwd lng="pt"><![CDATA[proporcionalidade]]></kwd>
<kwd lng="pt"><![CDATA[formação de professores]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="">
<source><![CDATA[Middle grades mathematics textbooks: A benchmarks-based evaluation.]]></source>
<year>2000</year>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aroza]]></surname>
<given-names><![CDATA[C. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Beltrán-Pellicer]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Iniciación a la innovación e investigación educativa mediante el análisis de la idoneidad didáctica de una experiencia de enseñanza sobre proporcionalidad.]]></article-title>
<source><![CDATA[Aires]]></source>
<year>2016</year>
<volume>6</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-29</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ávila]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La alfabetización matemática y su relación con el intercambio comercial, la escolaridad elemental y el trabajo]]></article-title>
<source><![CDATA[Bolema]]></source>
<year>2013</year>
<volume>27</volume>
<numero>45</numero>
<issue>45</issue>
<page-range>31-53</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Harel]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Lesh]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rational number, ratio and proportion.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Grouws]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of research on mathematics teaching and learning]]></source>
<year>1992</year>
<page-range>296333</page-range><publisher-loc><![CDATA[Nueva York, NY ]]></publisher-loc>
<publisher-name><![CDATA[MacMillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beltrán-Pellicer]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An onto-semiotic approach to the analysis of the affective domain in mathematics education.]]></article-title>
<source><![CDATA[Cambridge Journal of Education]]></source>
<year>2019</year>
<volume>50</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-20</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ben-Chaim]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Fey]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Fitzgerald]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Benedetto]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Miller]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proportional reasoning among 7th grade students with different curricular experiences.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1998</year>
<volume>36</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>247-73</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ben-Chaim]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Keret]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Ilany]]></surname>
<given-names><![CDATA[B. S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ratio and proportion: Research and teaching in mathematics teachers&#8217; education]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Róterdam, Países Bajos ]]></publisher-loc>
<publisher-name><![CDATA[Sense Publisher]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bolea]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Bosch]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Gascón]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La transposición didáctica de organizaciones matemáticas en procesos de algebrización: el caso de la proporcionalidad.]]></article-title>
<source><![CDATA[Recherches en Didactique des Mathématiques]]></source>
<year>2001</year>
<volume>21</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>247-304</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bosch]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[La dimensión ostensiva en la actividad matemática. El caso de la proporcionalidad (Tesis doctoral).]]></source>
<year>1994</year>
<publisher-loc><![CDATA[España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad Autónoma de Barcelona]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Breda]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Font]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Pino-Fan]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Criterios valorativos y normativos en la Didáctica de las Matemáticas: el caso del constructo idoneidad didáctica.]]></article-title>
<source><![CDATA[Bolema]]></source>
<year>2018</year>
<volume>32</volume>
<numero>60</numero>
<issue>60</issue>
<page-range>255-78</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Brousseau]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[The theory of didactical situations in mathematics.]]></source>
<year>1997</year>
<publisher-loc><![CDATA[Dordrecht, Países Bajos ]]></publisher-loc>
<publisher-name><![CDATA[Kluwer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Burgos]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Trabajando juntos situaciones introductorias de razonamiento proporcional en primaria. Análisis de una experiencia de enseñanza centrada en el profesor, en el estudiante y en el contenido.]]></article-title>
<source><![CDATA[Bolema]]></source>
<year>2018</year>
<volume>33</volume>
<numero>63</numero>
<issue>63</issue>
<page-range>389-410</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Butto]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Rojano]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pensamiento algebraico temprano: El papel del entorno Logo.]]></article-title>
<source><![CDATA[Educación Matemática]]></source>
<year>2010</year>
<volume>22</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>55-86</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Carraher]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Carraher]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Schliemann]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[En la vida diez, en la escuela cero.]]></source>
<year>1991</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Siglo XXI Editores]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Castillo]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Burgos]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Elaboración de una guía de análisis de libros de texto de matemáticas basada en la idoneidad didáctica. Educação e Pesquisa (en prensa)]]></source>
<year>2021</year>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cohen]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Manion]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Morrison]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Research methods in education]]></source>
<year>2011</year>
<publisher-loc><![CDATA[Londres ]]></publisher-loc>
<publisher-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cramer]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Connecting research to teaching proportional reasoning]]></article-title>
<source><![CDATA[Mathematics Teacher]]></source>
<year>1993</year>
<month>a</month>
<volume>86</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>404-7</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cramer]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Making connections: A case for proportionality.]]></article-title>
<source><![CDATA[Arithmetic Teacher]]></source>
<year>1993</year>
<month>b</month>
<volume>60</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>342-6</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cramer]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Currier]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning and teaching ratio and proportion: Research implications.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Owens]]></surname>
<given-names><![CDATA[D. T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Research ideas for the classroom: Middle grade mathematics]]></source>
<year>1992</year>
<page-range>159-78</page-range><publisher-loc><![CDATA[Nueva York, NY ]]></publisher-loc>
<publisher-name><![CDATA[MacMillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fan]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Zhu]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Miao]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Textbook research in mathematics education: development status and directions.]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2013</year>
<volume>45</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>633-46</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Precursores del racionamiento proporcional: un estudio con alumnos de primaria (Tesis doctoral).]]></source>
<year>2001</year>
<publisher-loc><![CDATA[Valencia, España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Valencia]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Puig]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Análisis fenomenológico de los conceptos de razón, proporción y proporcionalidad.]]></article-title>
<source><![CDATA[La Gaceta de la RSME]]></source>
<year>2002</year>
<volume>5</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>397-416</page-range></nlm-citation>
</ref>
<ref id="B23">
<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>
</person-group>
<article-title xml:lang=""><![CDATA[De la estructura aditiva a la multiplicativa: efecto de dos variables en el desarrollo del razonamiento proporcional.]]></article-title>
<source><![CDATA[Infancia y Aprendizaje]]></source>
<year>2011</year>
<volume>34</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>67-80</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fiol]]></surname>
<given-names><![CDATA[M. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Fortuny]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proporcionalidad directa.]]></article-title>
<source><![CDATA[La forma y el número]]></source>
<year>1990</year>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Síntesis]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Freudenthal]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Didactical phenomenology of mathematical structures.]]></source>
<year>1983</year>
<publisher-loc><![CDATA[Dordrecht, Países Bajos ]]></publisher-loc>
<publisher-name><![CDATA[Reidel Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gairín]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Oller]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Análisis histórico sobre la enseñanza de la razón y la proporción.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Estepa]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Contreras]]></surname>
<given-names><![CDATA[Á.]]></given-names>
</name>
<name>
<surname><![CDATA[Deulofeu]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Penalva]]></surname>
<given-names><![CDATA[M. C.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[F. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ordóñez]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación en Educación Matemática XVI]]></source>
<year>2012</year>
<page-range>249-59</page-range><publisher-loc><![CDATA[Jaén, España: ]]></publisher-loc>
<publisher-name><![CDATA[SEIEM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Indicadores de la idoneidad didáctica de procesos de enseñanza y aprendizaje de las matemáticas.]]></article-title>
<source><![CDATA[Cuadernos de Investigación y Formación en Educación Matemática]]></source>
<year>2013</year>
<volume>11</volume>
<page-range>111-32</page-range></nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Font]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The onto-semiotic approach to research in mathematics education.]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2007</year>
<volume>39</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>127-35</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Burgos]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Beltrán-Pellicer]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Gea]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Giacomone]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Structuring the system of didactical suitability criteria of mathematics instruction processes.]]></article-title>
<source><![CDATA[CIEAEM]]></source>
<year>2019</year>
<volume>71</volume>
<publisher-loc><![CDATA[Braga, Portugal ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Font]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Wilhelmi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Análisis ontosemiótico de la lección sobre la suma y la resta.]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática]]></source>
<year>2006</year>
<volume>9</volume>
<numero>especial</numero>
<issue>especial</issue>
<page-range>131-55</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Rivas]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Arteaga]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Inferencia de indicadores de idoneidad didáctica a partir de orientaciones curriculares.]]></article-title>
<source><![CDATA[Praxis Educativa]]></source>
<year>2012</year>
<volume>7</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>331-54</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="book">
<collab>Grupo Beta</collab>
<source><![CDATA[Proporcionalidad geométrica y semejanza]]></source>
<year>1990</year>
<publisher-loc><![CDATA[Madrid, Granada ]]></publisher-loc>
<publisher-name><![CDATA[Síntesis]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guacaneme]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Estudio didáctico de la proporción y la proporcionalidad: Una aproximación a los aspectos matemáticos formales y a los textos escolares de matemáticas (Tesis de maestría no publicada).]]></source>
<year>2001</year>
<publisher-loc><![CDATA[Cali, Colombia ]]></publisher-loc>
<publisher-name><![CDATA[Universidad del Valle]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hart]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ratio and proportion.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Hiebert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Concepts and operations in the Middle Grades]]></source>
<year>1988</year>
<volume>2</volume>
<page-range>198-219</page-range><publisher-loc><![CDATA[Reston, VA ]]></publisher-loc>
<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[Karplus]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Pulos]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Stage]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Early adolescents proportional reasoning on &#8220;rate&#8221; problems.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1983</year>
<volume>14</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>219-33</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lamon]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ratio and proportion: connecting content and children&#8217;s thinking.]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1993</year>
<volume>24</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>41-61</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lamon]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching fractions and ratios for understanding]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Mahwah, Nueva Jersey ]]></publisher-loc>
<publisher-name><![CDATA[Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B38">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lamon]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rational numbers and proportional reasoning: Toward a theoretical framework.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Lester]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Second Handbook of research on mathematics teaching and learning]]></source>
<year>2007</year>
<page-range>629-68</page-range><publisher-loc><![CDATA[Charlotte, Carolina del Norte ]]></publisher-loc>
<publisher-name><![CDATA[Information Age Publishing]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B39">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lesh]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proportional reasoning.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Hiebert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Number Concepts and operations in the Middle Grades]]></source>
<year>1988</year>
<page-range>93-118</page-range><publisher-loc><![CDATA[Reston, Virginia ]]></publisher-loc>
<publisher-name><![CDATA[The National Council of Teachers of Mathematics]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B40">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lim]]></surname>
<given-names><![CDATA[K. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Burning the candle at just one end: Using non-proportional examples helps students determine when proportional strategies apply.]]></article-title>
<source><![CDATA[Mathematics Teaching in the Middle School]]></source>
<year>2009</year>
<volume>14</volume>
<numero>8</numero>
<issue>8</issue>
<page-range>492500</page-range></nlm-citation>
</ref>
<ref id="B41">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Examining students&#8217; proportional reasoning strategy levels as evidence of the impact of an integrated LEGO robotics and mathematics learning experience.]]></article-title>
<source><![CDATA[Journal of Technology Education]]></source>
<year>2015</year>
<volume>26</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>46-73</page-range></nlm-citation>
</ref>
<ref id="B42">
<nlm-citation citation-type="book">
<collab>Ministerio de Educación, Cultura y Deporte de España (MECD)</collab>
<source><![CDATA[Real Decreto 126/2014, de 28 de febrero, por el que se establece el currículo básico de la Educación Primaria.]]></source>
<year>2014</year>
<month>a</month>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[MECD]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B43">
<nlm-citation citation-type="book">
<collab>Ministerio de Educación, Cultura y Deporte (MECD) de España</collab>
<source><![CDATA[Real Decreto1105/2014, de 26 de diciembre, por el que se establece el currículo básico de la Educación Secundaria Obligatoria y del Bachillerato.]]></source>
<year>2014</year>
<month>b</month>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[MECD]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B44">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mochón]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Enseñanza del razonamiento proporcional y alternativas para el manejo de la regla de tres.]]></article-title>
<source><![CDATA[Educación Matemática]]></source>
<year>2012</year>
<volume>24</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>133-57</page-range></nlm-citation>
</ref>
<ref id="B45">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Modestou]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Elia]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Gagatsis]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Spanoudis]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Behind the scenes of pseudo-proportionality.]]></article-title>
<source><![CDATA[International Journal of Mathematical Education in Science and Technology]]></source>
<year>2008</year>
<volume>39</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>313-24</page-range></nlm-citation>
</ref>
<ref id="B46">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Monterrubio]]></surname>
<given-names><![CDATA[M. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Ortega]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Diseño y aplicación de instrumentos de análisis y valoración de textos escolares de Matemáticas.]]></source>
<year>2011</year>
<volume>5</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>105-27</page-range><publisher-name><![CDATA[PNA]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B47">
<nlm-citation citation-type="book">
<collab>National Council of Teachers of Mathematics (NCTM)</collab>
<source><![CDATA[Principles and Standards for School Mathematics.]]></source>
<year>2000</year>
<publisher-loc><![CDATA[Reston, Virginia: ]]></publisher-loc>
<publisher-name><![CDATA[NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B48">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Obando]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Vasco]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Arboleda]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Enseñanza y aprendizaje de la razón, la proporción y la proporcionalidad: un estado del arte.]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2014</year>
<volume>17</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>59-81</page-range></nlm-citation>
</ref>
<ref id="B49">
<nlm-citation citation-type="book">
<collab>Piaget</collab>
<source><![CDATA[Psicología del niño.]]></source>
<year>1978</year>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Morata]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B50">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rivas]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Análisis epistémico y cognitivo de tareas de proporcionalidad en la formación de profesores de educación primaria (Tesis doctoral).]]></source>
<year>2013</year>
<publisher-loc><![CDATA[España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Granada]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B51">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Valdemoros]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Vínculo entre el pensamiento proporcional cualitativo y cuantitativo: el caso de Paulina.]]></article-title>
<source><![CDATA[Revista Latinoamericana de Investigación en Matemática Educativa]]></source>
<year>2006</year>
<volume>9</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>299-324</page-range></nlm-citation>
</ref>
<ref id="B52">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shield]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Dole]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Assessing the potential of mathematics textbooks to promote deep learning.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2013</year>
<volume>82</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>183-99</page-range></nlm-citation>
</ref>
<ref id="B53">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Silvestre]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Da-Ponte]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Una experiencia de enseñanza dirigida al desarrollo del razonamiento proporcional.]]></article-title>
<source><![CDATA[Revista Educación y Pedagogía]]></source>
<year>2011</year>
<volume>23</volume>
<numero>59</numero>
<issue>59</issue>
<page-range>137-58</page-range></nlm-citation>
</ref>
<ref id="B54">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Soto]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Rouche]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Problemas de proporcionalidad resueltos por campesinos chilenos.]]></article-title>
<source><![CDATA[Educación Matemática]]></source>
<year>1995</year>
<volume>7</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>77-95</page-range></nlm-citation>
</ref>
<ref id="B55">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tourniaire]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Pulos]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proportional reasoning: A review of the literature.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1985</year>
<volume>16</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>181-204</page-range></nlm-citation>
</ref>
<ref id="B56">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Dooren]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[De Bock]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Gillard]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Verschaffel]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Add? or multiply? A study on the development of primary school students&#8217; proportional reasoning skills.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Tzekaki]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Kaldrimidou]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sakonidis]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education]]></source>
<year>2009</year>
<volume>5</volume>
<page-range>281-8</page-range><publisher-loc><![CDATA[Thessalonika, Grecia ]]></publisher-loc>
<publisher-name><![CDATA[PME]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B57">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Van Dooren]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[De Bock]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Depaepe]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Janssens]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Verschaffel]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The illusion of linearity: expanding the evidence towards probabilistic reasoning.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2003</year>
<volume>53</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>113-38</page-range></nlm-citation>
</ref>
<ref id="B58">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vandercruysse]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Ter Vrugte]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[De Jong]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Wouters]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Van Oostendorp]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Verschaffel]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Moeyaert]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Elenet]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The effectiveness of a math game: the impact of integrating conceptual clarification as support.]]></article-title>
<source><![CDATA[Computers in Human Behavior]]></source>
<year>2016</year>
<volume>64</volume>
<page-range>21-33</page-range></nlm-citation>
</ref>
<ref id="B59">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vergnaud]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multiplicative structures.]]></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 mathematical concepts and processes]]></source>
<year>1983</year>
<page-range>127-74</page-range><publisher-loc><![CDATA[Orlando, Florida ]]></publisher-loc>
<publisher-name><![CDATA[Academic]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B60">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wilhelmi]]></surname>
<given-names><![CDATA[M. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proporcionalidad en educación primaria y secundaria.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Contreras]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Arteaga]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Cañadas]]></surname>
<given-names><![CDATA[G. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Gea]]></surname>
<given-names><![CDATA[M. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Giacomone]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[López-Martín]]></surname>
<given-names><![CDATA[M. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Actas del Segundo Congreso International Virtual sobre el Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemáticos]]></source>
<year>2017</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
