<?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>2448-8089</journal-id>
<journal-title><![CDATA[Educación matemática]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. mat.]]></abbrev-journal-title>
<issn>2448-8089</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Investigación y Divulgación de la Educación Matemática A.C.; Universidad de Guadalajara]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2448-80892023000300112</article-id>
<article-id pub-id-type="doi">10.24844/em3503.04</article-id>
<title-group>
<article-title xml:lang="fr"><![CDATA[Une approche socioculturelle pour la construction d&#8217;habiletés de généralisation arithmético-algébriques dans les écoles québécoises et mexicaines]]></article-title>
<article-title xml:lang="en"><![CDATA[Construction of arithmetic-algebraic generalization processes in a sociocultural approach skills-based approach in Quebec and Mexican schools]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hitt]]></surname>
<given-names><![CDATA[Fernando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Quiroz]]></surname>
<given-names><![CDATA[Samantha]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Saboya]]></surname>
<given-names><![CDATA[Mireille]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lupiáñez]]></surname>
<given-names><![CDATA[José Luis]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Université du Québec à Montréal  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Canada</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Coahuila  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Université du Québec à Montréal  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Canada</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Granada  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Spain</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2023</year>
</pub-date>
<volume>35</volume>
<numero>3</numero>
<fpage>112</fpage>
<lpage>150</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892023000300112&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892023000300112&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892023000300112&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé: Le monde de l&#8217;éducation a été marqué au début de ce siècle par l&#8217;implantation, notamment dans les écoles québécoises et mexicaines, de compétences et plus particulièrement en mathématiques. Dans cette nouvelle vision de l&#8217;enseignement et de l&#8217;apprentissage, la modélisation mathématique est omniprésente et liée à la pensée divergente. Notre projet porte sur le développement de cette pensée chez les élèves lors de la généralisation algébrique pour négocier le passage de l&#8217;arithmétique à l&#8217;algèbre dans la transition primaire-secondaire. À travers de la proposition de conditions d&#8217;enseignement et d&#8217;apprentissage misant sur un travail collaboratif et l&#8217;utilisation de ressources technologiques, nous rapportons le développement chez les élèves québécois et mexicains de ce que nous avons nommé la pensée arithmético-algébrique sollicitée lors de la généralisation de suites figurées. Dans cette expérimentation, les élèves des deux pays, ont mobilisé une structure cognitive arithmético-algébrique qui s&#8217;est opérationnalisée à travers des procédures de prédiction, des conjectures, du processus de généralisation d&#8217;un point de vue algébrique non institutionnel et d&#8217;une validation numérique à l&#8217;aide d&#8217;applets mis à la disposition des élèves. En outre, les résultats du côté mexicain ouvrent la voie sur la considération des représentations fonctionnelles-spontanées dès l&#8217;école primaire dans une perspective de transition primaire-secondaire liée à la pensée arithmético-algébrique.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The world of education was marked at the beginning of this century by the notion of competence, particularly in Quebec and Mexican schools, and more particularly in mathematics. In this new vision of teaching and learning, mathematical modeling is ubiquitous and linked to divergent thinking. Our project focuses on the development of this thinking in pupils during algebraic generalization to negotiate the transition from arithmetic to algebra in the primary-secondary transition. Through the proposal of teaching and learning conditions based on collaborative work and the use of technological resources, we report the development in Quebec and Mexican pupils of what we have called the arithmetic-algebraic thinking solicited during the generalization of figurative sequences. In this experiment, the pupils of the two countries mobilized an arithmetic-algebraic cognitive structure which was operationalized through prediction procedures, conjectures, the process of generalization from a non-institutional algebraic point of view and from a numerical validation using applets made available to pupils. In addition, the results from the Mexican side open the way to the consideration of functional-spontaneous representations from primary school in a perspective of primary-secondary transition linked to arithmetic-algebraic thinking.]]></p></abstract>
<kwd-group>
<kwd lng="fr"><![CDATA[pensée arithmético-algébrique]]></kwd>
<kwd lng="fr"><![CDATA[généralisation]]></kwd>
<kwd lng="fr"><![CDATA[représentations spontanées-fonctionnelles]]></kwd>
<kwd lng="fr"><![CDATA[ACODESA]]></kwd>
<kwd lng="en"><![CDATA[arithmetic-algebraic thinking]]></kwd>
<kwd lng="en"><![CDATA[generalization]]></kwd>
<kwd lng="en"><![CDATA[spontaneous-function-al representations]]></kwd>
<kwd lng="en"><![CDATA[ACODESA]]></kwd>
</kwd-group>
</article-meta>
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