{"id":617,"date":"2018-09-01T16:50:00","date_gmt":"2018-09-01T12:50:00","guid":{"rendered":"https:\/\/iremi.univ-reunion.fr\/?p=617"},"modified":"2026-02-12T10:19:09","modified_gmt":"2026-02-12T06:19:09","slug":"abaque-de-gerbert","status":"publish","type":"post","link":"https:\/\/iremi.univ-reunion.fr\/?p=617","title":{"rendered":"Abaque de Gerbert"},"content":{"rendered":"\n<p>L&rsquo;abaque de Gerbert est un simple tableau, mais Gerbert d&rsquo;Aurillac y a adjoint <a href=\"http:\/\/revue.sesamath.net\/spip.php?article819\">des jetons num\u00e9rot\u00e9s<\/a> permettant le calcul d\u00e9cimal. On peut aujourd&rsquo;hui simuler l&rsquo;abaque de Gerbert \u00e0 l&rsquo;aide de la technologie num\u00e9rique.<\/p>\n\n\n\n<p>Des exemples d&rsquo;utilisation de l&rsquo;abaque de Gerbert peuvent \u00eatre vus sur <a href=\"https:\/\/www.youtube.com\/@gerbert9745\">sa cha\u00eene Youtube<\/a>. Mais la manipulation d&rsquo;objets virtuels sur un \u00e9cran tactile a ses limites, et rien ne vaut celle de vrais jetons en bois ou similaire. On peut pyrograver les chiffres sur des tranches de cylindre en bois (type tringle de rideau) ou de bouchons de li\u00e8ge, ou les graver et d\u00e9couper au laser, voire acheter des chiffres pr\u00e9d\u00e9coup\u00e9s. Noter que le chiffre 0 est inutile pour l&rsquo;abaque de Gerbert. Voici le recto<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertVerso.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 GerbertVerso.\"><\/object><a id=\"wp-block-file--media-5ae434e1-8755-4b8d-a443-69f7b0d10cd8\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertVerso.pdf\">GerbertVerso<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertVerso.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-5ae434e1-8755-4b8d-a443-69f7b0d10cd8\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>et le verso<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertRecto.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 GerbertRecto.\"><\/object><a id=\"wp-block-file--media-42969248-6a98-4f69-9a18-7ac73bbc3c5e\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertRecto.pdf\">GerbertRecto<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertRecto.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-42969248-6a98-4f69-9a18-7ac73bbc3c5e\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>de l&rsquo;abaque, utilis\u00e9s par la caravane de l&rsquo;IREM lors de la f\u00eate de la science et la semaine des maths.<\/p>\n\n\n\n<p>Un abaque sp\u00e9cial pour le CP a \u00e9t\u00e9 produit entre-temps :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/abaqueCP.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 abaqueCP.\"><\/object><a id=\"wp-block-file--media-35f2e223-2b68-4918-8a8e-ab739ef9965a\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/abaqueCP.pdf\">abaqueCP<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/abaqueCP.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-35f2e223-2b68-4918-8a8e-ab739ef9965a\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Gerbert \u00e0 l&rsquo;\u00e9cole<\/h2>\n\n\n\n<p>Parce qu&rsquo;il peut servir de glisse-nombres, l&rsquo;abaque de Gerbert est un facilitateur pour l&rsquo;apprentissage des nombres d\u00e9cimaux. Mais une s\u00e9ance avec l&rsquo;abaque de Gerbert est inutile avec des \u00e9l\u00e8ves qui n&rsquo;ont aucune connaissance pr\u00e9alable de cet outil. Il conviendrait donc de tester une progression pluri-annuelle avec l&rsquo;abaque de Gerbert. Voici des compte-rendus d&rsquo;exp\u00e9riences men\u00e9es dans diverses classes (d\u00e9cimaux en CM1 et CM2, multiplication en CE2, dict\u00e9es de nombres en CP), dans l&rsquo;ordre chronologique :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertCE2.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 GerbertCE2.\"><\/object><a id=\"wp-block-file--media-785cfb1f-0504-439a-a9d4-59812f5048ac\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertCE2.pdf\">GerbertCE2<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/GerbertCE2.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-785cfb1f-0504-439a-a9d4-59812f5048ac\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/Gerbert_nomogrammes-1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 Gerbert_nomogrammes-1.\"><\/object><a id=\"wp-block-file--media-6b86efa2-208d-4a74-a806-e1041f2215fc\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/Gerbert_nomogrammes-1.pdf\">Gerbert_nomogrammes-1<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/Gerbert_nomogrammes-1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-6b86efa2-208d-4a74-a806-e1041f2215fc\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/gerbert_CP1.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 gerbert_CP1.\"><\/object><a id=\"wp-block-file--media-6bfb3218-e571-4e91-bcb3-7651085880b3\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/gerbert_CP1.pdf\">gerbert_CP1<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/gerbert_CP1.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-6bfb3218-e571-4e91-bcb3-7651085880b3\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/Gerbert_et_les_decimaux.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Contenu embarqu\u00e9 Gerbert_et_les_d\u00e9cimaux.\"><\/object><a id=\"wp-block-file--media-c4c78419-9189-4671-a8cc-8fbd031b5d18\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/Gerbert_et_les_decimaux.pdf\">Gerbert_et_les_d\u00e9cimaux<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2018\/09\/Gerbert_et_les_decimaux.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-c4c78419-9189-4671-a8cc-8fbd031b5d18\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Une cohorte d&rsquo;\u00e9l\u00e8ves ayant une connaissance pluriannuelle de l&rsquo;abaque de Gerbert en entrant en 6e \u00e0 la rentr\u00e9e 2029 devrait \u00eatre envisageable parmi des \u00e9l\u00e8ves ayant manipul\u00e9 durant 5 ans avec l&rsquo;abaque de Gerbert en CM2, lesquels devraient donc avoir<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>manipul\u00e9 l&rsquo;abaque durant 4 ans en CM1 (2027-2028)<\/li>\n\n\n\n<li>manipul\u00e9 l&rsquo;abaque durant 3 ans en CE2 (2026-2027)<\/li>\n\n\n\n<li>manipul\u00e9 l&rsquo;abaque durant 2 ans en CE1 (2025-2026)<\/li>\n\n\n\n<li>manipul\u00e9 l&rsquo;abaque en CP durant l&rsquo;ann\u00e9e 2024-2025.<\/li>\n<\/ul>\n\n\n\n<p>Seules 5 classes de CP ont pu participer \u00e0 l&rsquo;exp\u00e9rimentation durant l&rsquo;ann\u00e9e 2024-2025. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>L&rsquo;abaque de Gerbert est un simple tableau, mais Gerbert d&rsquo;Aurillac y a adjoint des jetons num\u00e9rot\u00e9s permettant le calcul d\u00e9cimal. On peut aujourd&rsquo;hui simuler l&rsquo;abaque de Gerbert \u00e0 l&rsquo;aide de la technologie num\u00e9rique. Des exemples d&rsquo;utilisation de l&rsquo;abaque de Gerbert peuvent \u00eatre vus sur sa cha\u00eene Youtube. Mais la manipulation d&rsquo;objets virtuels sur un \u00e9cran [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":1072,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,5,6,10,14],"tags":[29,30,43,48,47,52],"coauthors":[54],"class_list":["post-617","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arithmetique-et-algebre","category-contextualiser-les-apprentissages","category-continuum-des-apprentissages","category-machines-information-codage","category-outils-numeriques","tag-cycle-2","tag-cycle-3","tag-histoire-des-mathematiques","tag-manipulation","tag-mathnipulez","tag-resolution-de-problemes"],"_links":{"self":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/617","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=617"}],"version-history":[{"count":15,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/617\/revisions"}],"predecessor-version":[{"id":1737,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/617\/revisions\/1737"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/media\/1072"}],"wp:attachment":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=617"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=617"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=617"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcoauthors&post=617"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}