<?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>S2448-80892025000300236</article-id>
<article-id pub-id-type="doi">10.24844/em3703.09</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[El trapecio sin fórmula. Situación didáctica para profesores en formación]]></article-title>
<article-title xml:lang="en"><![CDATA[The trapezium with no formula. Didactical situation for pre-service teachers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cuevas-Morales]]></surname>
<given-names><![CDATA[Ismael]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Castañeda]]></surname>
<given-names><![CDATA[Apolo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Palmas]]></surname>
<given-names><![CDATA[Santiago]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Benemérita Escuela Normal Veracruzana "Enrique C. Rébsamen"  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Instituto Politécnico Nacional Centro de Investigación en Ciencia Aplicada y Tecnología Avanzada ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Autónoma Metropolitana Departamento de Estudios Culturales ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2025</year>
</pub-date>
<volume>37</volume>
<numero>3</numero>
<fpage>236</fpage>
<lpage>261</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892025000300236&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892025000300236&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892025000300236&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: Este artículo reporta parte de los resultados de una investigación desarrollada con estudiantes de la Licenciatura en Educación Primaria, centrada en los procesos de adaptación independiente dentro del marco de la Teoría de Situaciones Didácticas (TSD). El estudio se enfocó en el diseño y organización de una situación didáctica orientada a favorecer la autonomía del profesorado en formación, así como en el análisis de las interacciones entre este y el milieu diseñado. La metodología incluyó un análisis a priori de la situación, fundamentado en condiciones derivadas de la TSD, y un análisis a posteriori de las estrategias de resolución desplegadas por los participantes. Entre los hallazgos sobresale el tránsito de los dibujos a esquemas interpreta-dos como "pruebas", en el sentido de Eschenburg (2022), como punto crucial en la evolución de la situación. Asimismo, se concluye que las condiciones establecidas en el análisis a priori desde la TSD fueron cruciales para el diseño de la situación didáctica, pues orientaron las posibilidades de adaptación independiente y enmarcaron la emergencia de estrategias de resolución.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: This article reports part of the results of a study conducted with students of the Primary Education Degree, focused on the processes of independent adaptation within the framework of the Theory of Didactic Situations (TDS). The study focused on the design and organization of a didactic situation aimed at fostering the autonomy of preservice teachers, as well as on the analysis of the interactions between them and the designed milieu. The methodology included an a priori analysis of the situation, based on conditions derived from the TDS, and an a posteriori analysis of the resolution strategies deployed by the participants. Among the findings, the transition from drawings to schemes interpreted as "proofs" in the sense of Eschenburg (2022), stands out as a crucial point in the evolution of the situation. Likewise, it is concluded that the conditions established in the a priori analysis from the TDS were crucial for the design of the didactic situation, since they guided the possibilities of independent adaptation and framed the emergence of resolution strategies.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Teoría de Situaciones Didácticas]]></kwd>
<kwd lng="es"><![CDATA[formación docente]]></kwd>
<kwd lng="es"><![CDATA[geometría]]></kwd>
<kwd lng="es"><![CDATA[adaptación independiente]]></kwd>
<kwd lng="es"><![CDATA[representaciones matemáticas.]]></kwd>
<kwd lng="en"><![CDATA[Theory of Didactic Situations]]></kwd>
<kwd lng="en"><![CDATA[teacher education]]></kwd>
<kwd lng="en"><![CDATA[geometry]]></kwd>
<kwd lng="en"><![CDATA[indepen-dent adaptation]]></kwd>
<kwd lng="en"><![CDATA[mathematical representations]]></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[Angulo]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Arteaga]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Carmenates]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La formación de conceptos matemáticos en el proceso de enseñanza- aprendizaje de la Matemática]]></article-title>
<source><![CDATA[Revista Conrado]]></source>
<year>2020</year>
<volume>16</volume>
<numero>74</numero>
<issue>74</issue>
<page-range>298-305</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Artigue]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Haspekian]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Corblin-Lenfant]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Introduction to the Theory of Didactical Situations (TDS)]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Bikner-Ahsbahs]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Prediger]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Networking of theories as a research practice in mathematics education]]></source>
<year>2014</year>
<page-range>47-65</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baldor]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Geometría plana y del espacio]]></source>
<year>1983</year>
<publisher-name><![CDATA[Publicaciones Cultural]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<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[Iniciación al estudio de la teoría de las situaciones didácticas]]></source>
<year>2007</year>
<publisher-name><![CDATA[Zorzal]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Clements]]></surname>
<given-names><![CDATA[D. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Battista]]></surname>
<given-names><![CDATA[M. T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Geometry and spatial reasoning]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Grouws]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of research on mathematics teaching and learning]]></source>
<year>1992</year>
<page-range>420-64</page-range><publisher-name><![CDATA[Macmillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A cognitive analysis of problems of comprehension in a learning of mathematics]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2006</year>
<volume>61</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>103-31</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Eschenburg]]></surname>
<given-names><![CDATA[J.-H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Geometry - intuition and concepts]]></source>
<year>2022</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[López]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<source><![CDATA[La enseñanza de la geometría]]></source>
<year>2008</year>
<publisher-name><![CDATA[Instituto nacional para la evaluación de la educación]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gutiérrez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Visualization in 3-dimensional geometry: In search of a framework]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Puig]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Gutiérrez]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education (PME 20)]]></source>
<year>1996</year>
<volume>1</volume>
<page-range>3-19</page-range><publisher-name><![CDATA[Universidad de Valencia]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gutiérrez-Rubio]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Maz-Machado]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[León-Mantero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Jiménez-Fanjul]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Estudio de la percepción de la utilidad de la geometría en futuros profesores de educación primaria]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Rodríguez-Muñiz]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Muñiz-Rodríguez]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Aguilar-González]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Alonso]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Bruno]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Investigación en Educación Matemática XXII]]></source>
<year>2018</year>
<page-range>261-9</page-range><publisher-name><![CDATA[Universidad de Oviedo]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hershkowitz]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Psychological aspects of learning geometry]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Nesher]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Kilpatrick]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education]]></source>
<year>1990</year>
<page-range>70-95</page-range><publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pasani]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Analyzing elementary school student&#8217;s geometry comprehension based on Van Hiele&#8217;s theory]]></article-title>
<source><![CDATA[Journal of Southwest Jiaotong University]]></source>
<year>2019</year>
<volume>54</volume>
<numero>5</numero>
<issue>5</issue>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Skovsmose]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Valero]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Acceso democrático a ideas matemáticas poderosas]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Valero]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Skovsmose]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educación matemática crítica. Una visión sociopolítica del aprendizaje y la enseñanza de las matemáticas]]></source>
<year>2012</year>
<page-range>25-61</page-range><publisher-name><![CDATA[Universidad de los Andes]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
