<?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>S2448-80892023000200170</article-id>
<article-id pub-id-type="doi">10.24844/em3502.07</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Modos de pensar el conjunto 																					Z																						4																		 en docentes que enseñan álgebra en los primeros años escolares]]></article-title>
<article-title xml:lang="en"><![CDATA[Modes of thinking the set 																								Z																									4																					 in teachers who teach algebra in the first years of school]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Vidal-Szabó]]></surname>
<given-names><![CDATA[Pedro]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Parraguez]]></surname>
<given-names><![CDATA[Marcela]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bonilla]]></surname>
<given-names><![CDATA[Daniela]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Campos]]></surname>
<given-names><![CDATA[Samuel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad del Desarrollo Facultad de Educación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Católica de Valparaíso Facultad de Ciencias Instituto de Matemáticas]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Pontificia Universidad Católica de Valparaíso  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Pontificia Universidad Católica de Chile Facultad de Educación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</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>2</numero>
<fpage>170</fpage>
<lpage>195</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892023000200170&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892023000200170&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892023000200170&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Para vincular la aritmética con el pensar práctico y teórico del álgebra, esta investigación exploratoria enmarcada en la Teoría Modos de Pensamiento realizó un estudio de caso, con el objetivo de caracterizar modos de pensar el conjunto    Z  4 y sus interacciones en docentes chilenos de primaria. Para ello, se analizaron las respuestas que dieron 30 docentes en servicio a un cuestionario en línea, con base en un modelo cognitivo propuesto que define los modos de pensar el conjunto    Z  4 con sus articuladores. Los resultados muestran que estos docentes, en general, adhieren al modelo cognitivo y evidencian más articulación entre los modos sintético-geométrico y analítico-aritmético que entre los modos analítico-aritmético y analítico-estructural, lo que muestra un pensamiento teórico menos privilegiado. En conclusión, el álgebra de docentes de primaria puede activarse concibiendo al conjunto    Z  4 como un fragmento matemático que posee 4 elementos construidos. Cada uno es considerado un conjunto distinto de números congruentes módulo 4 que particionan el conjunto &#8484;, haciendo que el concepto clase de equivalencia tribute a la construcción cognitiva del conjunto    Z  4 como grafo cíclico de orden 4.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: To link arithmetic with the practical and theoretical thinking of algebra, this exploratory research framed in the Modes of Thinking Theory conducted a case study to characterize modes of thinking about the set    Z  4 and its interactions in Chilean primary school teachers. For this purpose, the answers given by 30 in-service teachers to an online questionnaire were analyzed, based on a proposed cognitive model that defines the modes of thinking about the set    Z  4 with its articulators. The results show that these teachers, generally adhere to the cognitive model and evidence more articulation between synthetic-geometric and analytic-arithmetic modes than between analytic-arithmetic and analytic-structural modes, which shows less privileged theoretical thinking. In conclusion, the algebra of primary teachers can be activated by conceiving the set    Z  4 as a mathematical fragment with 4 elements constructed. Each one is considered a distinct set of congruent numbers modulo 4 that partition the set &#8484;, making the concept of equivalence class contribute to the cognitive construction of the set    Z  4 as a cyclic graph of order 4.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Teoría Modos de Pensamiento]]></kwd>
<kwd lng="es"><![CDATA[Modelo Cognitivo del conjunto &#8484; 4]]></kwd>
<kwd lng="es"><![CDATA[Fragmento matemático]]></kwd>
<kwd lng="es"><![CDATA[Docentes de primaria]]></kwd>
<kwd lng="es"><![CDATA[Aritmética modular]]></kwd>
<kwd lng="en"><![CDATA[Modes of Thinking Theory]]></kwd>
<kwd lng="en"><![CDATA[Cognitive Model of the set &#8484; 4]]></kwd>
<kwd lng="en"><![CDATA[Mathematical fragment]]></kwd>
<kwd lng="en"><![CDATA[Primary teachers]]></kwd>
<kwd lng="en"><![CDATA[Modular arithmetic]]></kwd>
</kwd-group>
</article-meta>
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