<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1665-2436</journal-id>
<journal-title><![CDATA[Revista latinoamericana de investigación en matemática educativa]]></journal-title>
<abbrev-journal-title><![CDATA[Relime]]></abbrev-journal-title>
<issn>1665-2436</issn>
<publisher>
<publisher-name><![CDATA[Comité Latinoamericano de Matemática Educativa A.C.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1665-24362016000100041</article-id>
<article-id pub-id-type="doi">10.12802/relime.13.1912</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Nível de conhecimento em probabilidade condicionada e independência: um caso de estudo no ensino secundário português]]></article-title>
<article-title xml:lang="en"><![CDATA[Knowledge level in conditional probability and independence of events: a study case in the portuguese high school]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Carvalho]]></surname>
<given-names><![CDATA[Maria José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Freitas]]></surname>
<given-names><![CDATA[Adelaide]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Agrupamento de Escolas António Sérgio  ]]></institution>
<addr-line><![CDATA[Vila Nova de Gaia ]]></addr-line>
<country>Portugal</country>
</aff>
<aff id="A02">
<institution><![CDATA[,Universidade de Aveiro Departamento de Matemática & CIDMA ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Portugal</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2016</year>
</pub-date>
<volume>19</volume>
<numero>1</numero>
<fpage>41</fpage>
<lpage>69</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1665-24362016000100041&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1665-24362016000100041&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1665-24362016000100041&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo: Partindo de duas situações-problema envolvendo probabilidades condicionadas, independência e incompatibilidade, sugere- se quantificar, em paralelo, o grau de desempenho e o grau de rigor de uma resposta usando duas medidas ordinais, ambas em escala de Likert. Uma análise descritiva dessas medidas, num grupo de 43 alunos do 12.o ano, permitiu estabelecer o nível de conhecimento desses alunos naqueles conceitos e constatar que nem sempre uma resposta correta é acompanhada de rigor na sua elaboração. Uma análise interpretativa das mesmas respostas permitiu ainda constatar que, no ensino português, persistem conflitos na interpretação e cálculo da probabilidade condicionada e conflitos nas noções de independência e incompatibilidade. O estudo recomenda mais prática na formulação matemática de enunciados envolvendo probabilidade condicionada e mais ênfase no caracter probabilístico da noção de independência.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Partiendo de dos situaciones problemas que refieren a la probabilidad condicional, la independencia y eventos mutuamente excluyentes, se cuantifica, en paralelo, el grado de desempeño y el grado de rigor científico de una respuesta usando dos medidas ordinales en la escala de Likert. Un análisis descriptivo de las medidas, en 43 estudiantes del año terminal del liceo, determinó el grado de conocimiento de los alumnos en los referidos conceptos y apuntó que no siempre una respuesta correcta está descrita con rigor. Del análisis interpretativo de las respuestas se concluye que persisten, en la enseñanza en Portugal, conflictos en la interpretación y en el cálculo de la probabilidad condicionada y en los conceptos de independencia y de eventos mutuamente excluyentes. El estudio recomienda más prácticas involucrando la formulación matemática de problemas de probabilidad condicional y más énfasis en el carácter probabilístico que está asociado al concepto de independencia.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Taking two problem-situations involving conditional probability, independence and incompatibility, we suggest the measurements of the performance and the scientific rigor of a response using, in parallel, two ordinal Likert scale measures. Based on the responses given by 43 students in 12th grade (age 17), a descriptive analysis of these measurements was executed in order to evaluate the levels of knowledge of the students in those concepts. The results showed that not always a correct written response comes with rigor. Besides, an interpretative analysis of the same responses confirmed the existence of conflicts in the teaching of those concepts in Portugal. The conflicts are concerning with the interpretation and the calculation of conditional probabilities and the notions of independence and incompatibility. The present study recommends more practice on the mathematical formulation of statements involving conditional probability and more emphasis on the probabilistic feature of the notion of independence.]]></p></abstract>
<abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé: Partant de deux situations-problème impliquant des probabilités conditionnelles, indépendance et incompatibilité, on suggère de quantifier, en parallèle, le degré de performance et le degré de rigueur d'une réponse utilisant deux mesures ordinales, toutes deux sur l'échelle de Likert. Une analyse descriptive de ces mesures dans un groupe de 43 élèves de Terminal a permis d'établir le niveau de connaissance des élèves, en relation à ces concepts, et de constater qu'une réponse correcte n'est pas toujours accompagnée de rigueur dans son élaboration. Une analyse interprétative de ces réponses a encore permis de voir que, dans l'enseignement portugais, les conflits persistent dans l'interprétation et le calcul des probabilités conditionnelles ainsi que dans les notions d'indépendance et d'incompatibilité. L'étude recommande plus de pratique dans la formulation mathématique des énoncés de probabilités conditionnelles et de mettre davantage l'accent sur le caractère probabiliste associé à la notion d'indépendance.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Concepto de probabilidad condicional]]></kwd>
<kwd lng="es"><![CDATA[Concepto de eventos independientes]]></kwd>
<kwd lng="es"><![CDATA[Concepto de eventos mutuamente excluyentes]]></kwd>
<kwd lng="es"><![CDATA[Grado de desempeño]]></kwd>
<kwd lng="es"><![CDATA[Grado de rigor científico]]></kwd>
<kwd lng="en"><![CDATA[Concept of conditional probability]]></kwd>
<kwd lng="en"><![CDATA[Concept of independent events]]></kwd>
<kwd lng="en"><![CDATA[Concept of mutually exclusive events]]></kwd>
<kwd lng="en"><![CDATA[Degree of performance]]></kwd>
<kwd lng="en"><![CDATA[Degree of scientific rigor]]></kwd>
<kwd lng="pt"><![CDATA[Conceito de probabilidade condicionada]]></kwd>
<kwd lng="pt"><![CDATA[Conceito de acontecimentos independentes]]></kwd>
<kwd lng="pt"><![CDATA[Conceito de acontecimentos incompatíveis]]></kwd>
<kwd lng="pt"><![CDATA[Grau de desempenho]]></kwd>
<kwd lng="pt"><![CDATA[Grau de rigor]]></kwd>
<kwd lng="fr"><![CDATA[Concept de probabilité conditionnelle]]></kwd>
<kwd lng="fr"><![CDATA[Concept d'évènements indépendants]]></kwd>
<kwd lng="fr"><![CDATA[Concept d'évènements incompatibles]]></kwd>
<kwd lng="fr"><![CDATA[Degré de performance]]></kwd>
<kwd lng="fr"><![CDATA[Degré de rigueur]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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