<?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>S2448-80892025000100161</article-id>
<article-id pub-id-type="doi">10.24844/em3701.06</article-id>
<title-group>
<article-title xml:lang="fr"><![CDATA[Place et rôle du contre-exemple dans la classe de mathématiques: pratiques déclarées des enseignants tunisiens]]></article-title>
<article-title xml:lang="en"><![CDATA[Place and role of the counterexample in the mathematics classroom: declared practices of Tunisian teachers]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kilani]]></surname>
<given-names><![CDATA[Imed]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Université Virtuelle de Tunis ISEFC-Institut Supérieur de l&#8217;Education et de la Formation Continue ]]></institution>
<addr-line><![CDATA[Tunis ]]></addr-line>
<country>Tunesia</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>1</numero>
<fpage>161</fpage>
<lpage>192</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892025000100161&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892025000100161&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892025000100161&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="fr"><p><![CDATA[Résumé: Dans cette recherche et à partir d&#8217;une enquête par questionnaire ouvert, nous avons étudié, auprès de vingt-neuf enseignants de mathématiques tunisiens en exercice deux questions liées à leurs pratiques enseignantes déclarées concernant la notion de contre-exemple: la place qu&#8217;ils accordent à cette notion dans leurs enseignements et les types de réfutation qu&#8217;ils mettent en place lorsqu&#8217;un élève affirme la vérité d&#8217;une proposition mathématique universelle fausse. Les résultats ont montré que beaucoup d&#8217;enseignants déclarent donner de l&#8217;importance à cette notion (ce résultat est toutefois à nuancer) et ont montré également que la quasi-totalité des enseignants restreint le rôle du contre-exemple dans l&#8217;activité mathématique à son rôle logique ; ce qui ne laisse pas de place aux «réfutations par contre-exemple général», lesquelles possèdent un pouvoir explicatif plus fort que celui des autres types de réfutation par contre-exemple.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In this research, based on an open questionnaire survey, we asked twenty-nine practising Tunisian mathematics teachers two questions related to their declared teaching practices concerning the notion of counterexample : the place they give to this notion in their teaching and the types of refutation they put in place when a student asserts the truth of a false universal mathematical statement. The results showed that many teachers declare that they attach importance to this notion (although this result needs to be nuanced) and also showed that almost all teachers restrict the role of the counterexample in mathematical activity to its logical role; this leaves no place for «general counterexample refutations», which have a stronger explicative power than other types of counterexample refutation.]]></p></abstract>
<kwd-group>
<kwd lng="fr"><![CDATA[Réfutation par contre-exemple spécifique]]></kwd>
<kwd lng="fr"><![CDATA[réfutation par contre-ex-emple semi-général]]></kwd>
<kwd lng="fr"><![CDATA[réfutation par contre-exemple général]]></kwd>
<kwd lng="fr"><![CDATA[enseignants]]></kwd>
<kwd lng="fr"><![CDATA[prop-osition fausse]]></kwd>
<kwd lng="en"><![CDATA[Refutation by specific counterexample]]></kwd>
<kwd lng="en"><![CDATA[Refutation by semi-general counterexample]]></kwd>
<kwd lng="en"><![CDATA[Refutation by general counterexample]]></kwd>
<kwd lng="en"><![CDATA[teatchers]]></kwd>
<kwd lng="en"><![CDATA[false proposition]]></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[Balacheff]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Processus de preuve et situations de validation]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1987</year>
<volume>18</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>147-76</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Balacheff]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<source><![CDATA[Une étude des processus de preuve en mathématiques chez des élèves de collège]]></source>
<year>1988</year>
<publisher-name><![CDATA[l&#8217;Institut National Polytechnique Grenoble]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barrier]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Les exemples dans l&#8217;élaboration des démonstrations mathématiques : une approche sémantique et dialogique]]></article-title>
<source><![CDATA[Recherches en éducation]]></source>
<year>2016</year>
<volume>27</volume>
<page-range>94-117</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Benbachir]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Zaki]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Production d&#8217;exemples et de contre-exemples en analyse : Étude de cas en première année d&#8217;université]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2001</year>
<volume>47</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>273-95</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[BenBachir]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Zaki]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reconnaissance de contre-exemples en analyse : Approche par questionnaire en première année universitaire]]></article-title>
<source><![CDATA[Annales de Didactique et de Sciences Cognitives]]></source>
<year>2001</year>
<volume>7</volume>
<page-range>117-45</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bloch]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Les interactions mathématiques entre professeurs et élèves. Comment travailler leur pertinence en formation]]></article-title>
<source><![CDATA[Petit x]]></source>
<year>2009</year>
<volume>81</volume>
<page-range>25-52</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Borasi]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Exploring mathematics through the analysis of errors]]></article-title>
<source><![CDATA[For the Learning of Mathematics]]></source>
<year>1987</year>
<volume>7</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>2-8</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bressoux]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Diversité des pratiques d&#8217;enseignement à l&#8217;école élémentaire]]></article-title>
<source><![CDATA[Revue française de pédagogie]]></source>
<year>1999</year>
<volume>126</volume>
<page-range>97-110</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cerclé]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Faire vivre les énoncés contingents dans la classe de mathématiques :Pourquoi et comment ?]]></article-title>
<source><![CDATA[Petit x]]></source>
<year>2019</year>
<volume>110-111</volume>
<page-range>27-55</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Coulange]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[L&#8217;ordinaire dans l&#8217;enseignement des mathématiques : Les pratiques enseignantes et leurs effets sur les apprentissages des élèves]]></source>
<year>2012</year>
<publisher-name><![CDATA[Université Paris-Diderot - Paris VII]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Creager]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Geometric refutations of prospective secondary mathematics teachers]]></article-title>
<source><![CDATA[International Journal of Education in Mathematics, Science, and Technology]]></source>
<year>2022</year>
<volume>10</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>74-99</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Durand-Guerrier]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<source><![CDATA[Recherches sur l&#8217;articulation entre la logique et le raisonnement mathématique dans une perspective didactique : Un cas exemplaire de l&#8217;interaction entre analyses épistémologique et didactique. Apports de la théorie élémentaire des modèles pour une analyse didactique du raisonnement mathématique]]></source>
<year>2005</year>
<publisher-name><![CDATA[Université Lyon]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Durand-Guerrier]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Retour sur le schéma de la validation explicite dans la théorie des situations didactiques, à la lumière de la théorie des modèles de Tarski]]></article-title>
<source><![CDATA[Actes du colloque Didactiques : quelles références épistémologiques ?]]></source>
<year>2007</year>
<publisher-loc><![CDATA[Bordeaux, France ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fisher]]></surname>
<given-names><![CDATA[R. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Social desirability bias and the validity of indirect questioning]]></article-title>
<source><![CDATA[Journal of Consumer Research]]></source>
<year>1993</year>
<volume>20</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>303-15</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grenier]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[De la nécessité de définir les notions de logique au lycée]]></article-title>
<source><![CDATA[Repères-IREM]]></source>
<year>2015</year>
<volume>100</volume>
<page-range>65-83</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hersant]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Analyse didactique des séances et des productions des élèves]]></article-title>
<source><![CDATA[Pratiques enseignantes en mathématiques]]></source>
<year>2013</year>
<page-range>31-51</page-range><publisher-name><![CDATA[Presse Universitaire de Bordeau]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hitt]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Utilisation de calculatrices symboliques dans le cadre d&#8217;une méthode d&#8217;apprentissage collaboratif, de débat scientifique et d&#8217;auto-réflexion]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Baron]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Guin]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Trouche]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Environnements informatisés et ressources numériques pour l&#8217;apprentissage. Conception et usages, regards croisés]]></source>
<year>2007</year>
<page-range>65-88</page-range><publisher-loc><![CDATA[Paris : Hermès ]]></publisher-loc>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hitt]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Systèmes sémiotiques de représentation liés au concept de fonction]]></article-title>
<source><![CDATA[Annales de Didactique et de Sciences Cognitives]]></source>
<year>1998</year>
<volume>6</volume>
<page-range>7-26</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hitt]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Researching a problem of convergence with MATHEMATICA. Hystory and visualization of a mathematical idea]]></article-title>
<source><![CDATA[International Journal of Mathematics Education in Science and Technology]]></source>
<year>1998</year>
<volume>28</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>697-706</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Horoks]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Des pratiques aux apprentissages mathématiques, en passant par la formation. : Circulation des savoirs issus des recherches en Didactique des Mathématiques]]></source>
<year>2022</year>
<publisher-name><![CDATA[CY Cergy Paris Université]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Huang]]></surname>
<given-names><![CDATA[C.-H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Engineering students&#8217; generating counterexamples of calculus concepts]]></article-title>
<source><![CDATA[Global Journal of Engineering Education]]></source>
<year>2014</year>
<volume>16</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>93-7</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Klymchuk]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Using counter-examples in teaching &amp; learning of calculus: Students&#8217; attitudes and performance]]></article-title>
<source><![CDATA[Mathematics Teaching-Research Journal Online]]></source>
<year>2012</year>
<volume>5</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1-30</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Knuth]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Proof as a tool for learning mathematics]]></article-title>
<source><![CDATA[Mathematics Teacher]]></source>
<year>2002</year>
<volume>95</volume>
<numero>7</numero>
<issue>7</issue>
<page-range>486-90</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lakatos]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Preuves et réfutations : essai sur la logique de la découverte mathématique]]></source>
<year>1984</year>
<publisher-name><![CDATA[Éditions Hermann]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lockwood]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Ellis]]></surname>
<given-names><![CDATA[A. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Lynch]]></surname>
<given-names><![CDATA[A. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Mathematicians&#8217; example-related activity when exploring and proving conjectures]]></article-title>
<source><![CDATA[International Journal of Research in Undergraduate Mathematics Education]]></source>
<year>2016</year>
<volume>2</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>165-96</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mercier]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Buty]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Évaluer et comprendre les effets de l&#8217;enseignement sur les apprentissages des élèves : problématiques et méthodes en didactique des mathé-matiques et des sciences]]></article-title>
<source><![CDATA[Revue française de pédagogie]]></source>
<year>2004</year>
<volume>148</volume>
<page-range>47-59</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Peled]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Zaslavsky]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Counter-Examples That (Only) Prove and Counter-Examples That (Also) Explain]]></article-title>
<source><![CDATA[Focus on Learning Problems in Mathematics]]></source>
<year>1997</year>
<volume>19</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>4961</page-range></nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Selden]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Selden]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[The role of examples in learning mathematics. Research Sampler columns, The Mathematical Association of America Online]]></source>
<year>1998</year>
</nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tanguay]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Mathieu-Sousy]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Logique et enseignement des mathématiques]]></article-title>
<source><![CDATA[Bulletin AMQ]]></source>
<year>2015</year>
<volume>55</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>15-38</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zeybek]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Pre-service elementary teachers&#8217; conceptions of counterexamples]]></article-title>
<source><![CDATA[International Journal of Education in Mathematics, Science and Technology (IJEMST)]]></source>
<year>2017</year>
<volume>5</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>295-316</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="">
<collab>Ministère de l&#8217;Éducation nationale de Tunisie</collab>
<source><![CDATA[Programmes officiels de l&#8217;enseignement des mathématiques du collège]]></source>
<year>2011</year>
</nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="">
<collab>Ministère de l&#8217;Éducation nationale de Tunisie</collab>
<source><![CDATA[Programmes officiels de l&#8217;enseignement des mathématiques du secondaire]]></source>
<year>2008</year>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
