<?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>S2215-34702021000200129</article-id>
<article-id pub-id-type="doi">10.15359/ru.35-2.9</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Comparing probabilities in urns: A study with primary school students]]></article-title>
<article-title xml:lang="pt"><![CDATA[Comparação de probabilidades nas urnas: um estudo com estudantes do ensino fundamental]]></article-title>
<article-title xml:lang="es"><![CDATA[Comparación de probabilidades en urnas: Un estudio con estudiantes de Educación Primaria]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[Carmen]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández-Solís]]></surname>
<given-names><![CDATA[Luis Armando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gea]]></surname>
<given-names><![CDATA[María M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Álvarez-Arroyo]]></surname>
<given-names><![CDATA[Rocío]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Granada Department of Mathematics Education ]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Estatal a Distancia Faculty of Exact and Natural Sciences ]]></institution>
<addr-line><![CDATA[San José ]]></addr-line>
<country>Costa Rica</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Granada Department of Mathematics Education ]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Granada Department of Mathematics Education ]]></institution>
<addr-line><![CDATA[Granada ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>35</volume>
<numero>2</numero>
<fpage>129</fpage>
<lpage>143</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702021000200129&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702021000200129&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702021000200129&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract The study aimed to explore the strategies used by Costa Rican primary school students when comparing urn probabilities. The sample was intentional and consisted of 55 6th graders. Using an interpretive approach, we analyzed the children&#8217;s responses to a questionnaire of five probability comparison items taken from previous studies, including different levels of proportional reasoning. Results indicate that problems in the first levels of proportional reasoning were solved easily by students, while problems at higher levels increased in difficulty. One-variable strategies, which compare only the favorable or unfavorable cases in both urns, are predominant; although there are correspondence strategies, few students show complete proportional reasoning. Aside from slight variations, results are similar to previous studies, which suggests that this task is influenced more by the child&#8217;s level of maturity than by the instruction received.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo O estudo teve como objetivo explorar as estratégias aplicadas por estudantes do 6º ano do ensino fundamental costarriquenho ao comparar probabilidades no contexto das urnas. A amostragem participativa foi intencional e composta por 55 meninos e meninas do ensino fundamental. A pesquisa tem uma abordagem interpretativa, em que são analisadas as respostas desse público em um questionário conformado por cinco itens de comparação de probabilidades, coletados de pesquisas prévias que levam em consideração diferentes níveis de raciocínio proporcional. Os resultados indicam que os estudantes da amostra solucionam facilmente problemas que correspondem aos primeiros níveis de raciocínio proporcional, e aumentam a dificuldade em níveis superiores. São predominantes as estratégias de uma variável, nos quais são comparados somente os casos favoráveis ou desfavoráveis das duas urnas e, ainda que aparecem estratégias de correspondência, é pouca a quantidade de estudantes que demonstram um raciocínio proporcional completo. Os resultados são semelhantes, com ligeiras variações, aos estudos prévios, indicando que nesta tarefa a maturidade da infância influencia mais do que o ensino recebido.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen El objetivo del estudio fue explorar las estrategias que emplean niños y niñas de 6º curso de educación primaria costarricenses al comparar probabilidades en contextos de urnas. La muestra participante fue intencional y estuvo formada por 55 estudiantes de primaria. La investigación tiene un enfoque interpretativo, donde se analizan sus respuestas a un cuestionario formado por cinco ítems de comparación de probabilidades, tomados de investigaciones previas, que tienen en cuenta diferentes niveles de razonamiento proporcional. Los resultados indican que el estudiantado de la muestra resuelve con facilidad los problemas que corresponden a los primeros niveles de razonamiento proporcional, y aumentan su dificultad en los niveles superiores. Predominan las estrategias de una variable, en que se comparan solo los casos favorables o desfavorables de las dos urnas, y aunque aparecen estrategias de correspondencia, es poca la cantidad de estudiantes que muestran un razonamiento proporcional completo. Los resultados son similares, con ligeras variaciones, a los estudios previos, lo que indica que en esta tarea influye más la maduración del alumnado que la enseñanza recibida.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Probability comparison]]></kwd>
<kwd lng="en"><![CDATA[proportional reasoning]]></kwd>
<kwd lng="en"><![CDATA[primary education]]></kwd>
<kwd lng="en"><![CDATA[statistical education]]></kwd>
<kwd lng="en"><![CDATA[urns]]></kwd>
<kwd lng="en"><![CDATA[Costa Rica.]]></kwd>
<kwd lng="pt"><![CDATA[comparação de probabilidades]]></kwd>
<kwd lng="pt"><![CDATA[raciocínio proporcional]]></kwd>
<kwd lng="pt"><![CDATA[ensino fundamental, educação estatística, urnas, Costa Rica]]></kwd>
<kwd lng="es"><![CDATA[Comparación de probabilidades]]></kwd>
<kwd lng="es"><![CDATA[Razonamiento proporcional]]></kwd>
<kwd lng="es"><![CDATA[Educación primaria]]></kwd>
<kwd lng="es"><![CDATA[Educación Estadística]]></kwd>
<kwd lng="es"><![CDATA[Urnas]]></kwd>
<kwd lng="es"><![CDATA[Costa Rica]]></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[Alpízar]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Barrantes]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Bolaños]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Céspedes]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Freer]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Padilla]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Víquez]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Aspectos relevantes sobre la formación docente en I y II ciclos en los temas probabilidad y estadística.]]></article-title>
<source><![CDATA[EDUCARE]]></source>
<year>2012</year>
<volume>16</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>113-29</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Alpízar]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Chavarría]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Oviedo]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Percepción de un grupo de docentes de I y II ciclo de educación general básica de escuelas públicas de Heredia sobre los temas de estadística y probabilidad.]]></article-title>
<source><![CDATA[Actualidades Investigativas en Educación]]></source>
<year>2015</year>
<volume>15</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-23</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Razonamiento probabilístico en la vida cotidiana: Un desafío educativo.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Flores]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Lupiáñez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación en el aula de matemáticas. Estadística y Azar]]></source>
<year>2006</year>
<page-range>1-17</page-range><publisher-loc><![CDATA[Granada ]]></publisher-loc>
<publisher-name><![CDATA[Sociedad de Educación Matemática Thales.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Behr]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Harel]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Post]]></surname>
<given-names><![CDATA[T. R.]]></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[Grows]]></surname>
<given-names><![CDATA[D. D. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of research in mathematics teaching and learning]]></source>
<year>1992</year>
<page-range>296-333</page-range><publisher-name><![CDATA[Macmillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<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-name><![CDATA[Sense Publisher]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bisquerra]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Métodos de investigación educativa]]></source>
<year>1989</year>
<publisher-name><![CDATA[P.P.U]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Borovcnik]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Strengthening the role of probability within statistics curricula.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Burrill]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[C]]></surname>
<given-names><![CDATA[Reading]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching Statistics in School Mathematics-Challenges for Teaching and Teacher Education]]></source>
<year>2011</year>
<page-range>71-83</page-range><publisher-loc><![CDATA[Dordrecht ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cañizares]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Influencia del razonamiento proporcional y combinatorio y de creencias subjetivas en las intuiciones probabilísticas primarias]]></source>
<year>1997</year>
<publisher-loc><![CDATA[Universidad de Granada ]]></publisher-loc>
<publisher-name><![CDATA[España]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cañizares]]></surname>
<given-names><![CDATA[M. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Batanero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Influencia del razonamiento proporcional y de las creencias subjetivas en la comparación de probabilidades.]]></article-title>
<source><![CDATA[UNO]]></source>
<year>1997</year>
<volume>14</volume>
<page-range>99-114</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cerrón]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La investigación cualitativa en educación.]]></article-title>
<source><![CDATA[Horizonte de la Ciencia]]></source>
<year>2019</year>
<volume>9</volume>
<numero>17</numero>
<issue>17</issue>
<page-range>1-8</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Falk]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Falk]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Levin]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A potential for learning probability in young children.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1980</year>
<volume>11</volume>
<page-range>181-204</page-range></nlm-citation>
</ref>
<ref id="B12">
<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[Gazit]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Does the teaching of probability improve probabilistic intuitions?]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1984</year>
<volume>15</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-24</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gal]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Towards &#8220;probability literacy&#8221; for all citizens: Building blocks and instructional dilemmas.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Jones]]></surname>
<given-names><![CDATA[G.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Exploring probability in school]]></source>
<year>2005</year>
<page-range>39-63</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gil]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[León]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Morales]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Los paradigmas de investigación educativa, desde una perspectiva crítica.]]></article-title>
<source><![CDATA[Conrado]]></source>
<year>2017</year>
<volume>13</volume>
<numero>58</numero>
<issue>58</issue>
<page-range>72-4</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Green]]></surname>
<given-names><![CDATA[D. R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Probability concepts in school pupils aged 11-16 years (Doctoral dissertation)]]></source>
<year>1982</year>
<publisher-loc><![CDATA[United Kingdom ]]></publisher-loc>
<publisher-name><![CDATA[University of Loughborough]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jones]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Langrall]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Mooney]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Research in probability: Responding to classroom realities.]]></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>
<volume>2</volume>
<page-range>909-55</page-range><publisher-name><![CDATA[Information Age Publishing y NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<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>
<page-range>219-33</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Krippendorff]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Content analysis: An introduction to its methodology.]]></source>
<year>2013</year>
<publisher-name><![CDATA[SAGE]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Langrall]]></surname>
<given-names><![CDATA[C. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Mooney]]></surname>
<given-names><![CDATA[E. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Characteristics of elementary school students&#8217; probabilistic thinking.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Jones]]></surname>
<given-names><![CDATA[G. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Exploring probability in school. Challenges for teaching and learning]]></source>
<year>2005</year>
<page-range>95-119</page-range><publisher-loc><![CDATA[The Netherlands ]]></publisher-loc>
<publisher-name><![CDATA[Dordrech]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lecoutre]]></surname>
<given-names><![CDATA[M. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cognitive models and problem spaces in &#8220;purely random&#8221; situations.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1992</year>
<volume>23</volume>
<page-range>557-68</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<collab>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>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[Autor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<collab>Ministerio de Educación Pública (MEP)</collab>
<source><![CDATA[Programas de Estudio de Matemáticas. I, II y III Ciclos de la Educación General Básica y Ciclo Diversificado.]]></source>
<year>2012</year>
<publisher-name><![CDATA[Autor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="">
<source><![CDATA[Principles and standards for school mathematics. The Council]]></source>
<year>2000</year>
</nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Noelting]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The development of proportional reasoning and the ratio concept. Part I - Differentiation of stages.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1980</year>
<month>a</month>
<volume>11</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>217-53</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Noelting]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The development of proportional reasoning and the ratio concept. Part II - problem-structure at successive stages; problem-solving strategies and the mechanism of adaptive restructuring.]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1980</year>
<month>b</month>
<volume>11</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>331-63</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pérez Echeverría]]></surname>
<given-names><![CDATA[M. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Carretero]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Pozo]]></surname>
<given-names><![CDATA[J. I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Los adolescentes ante las matemáticas: Proporción y probabilidad.]]></article-title>
<source><![CDATA[Cuadernos de Pedagogía]]></source>
<year>1986</year>
<volume>133</volume>
<page-range>9-13</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Psicología de la inteligencia]]></source>
<year>1975</year>
<publisher-loc><![CDATA[Buenos Aires ]]></publisher-loc>
<publisher-name><![CDATA[Psique]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Piaget]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Inhelder]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[La genése de l'idée de hasard chez l'enfant.]]></source>
<year>1951</year>
<publisher-name><![CDATA[Presses Universitaires de France]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pratt]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Making sense of the total of two dice.]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>2000</year>
<volume>31</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>602-25</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Truran]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Examination of a relationship between children's estimation of probabilities and their understanding of proportion.]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Ponte]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Matos]]></surname>
<given-names><![CDATA[J. F.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the XVIII PME]]></source>
<year>1994</year>
<page-range>337-44</page-range><publisher-name><![CDATA[Universidad de Lisboa]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
