{"id":375,"date":"2024-10-05T08:08:39","date_gmt":"2024-10-05T08:08:39","guid":{"rendered":"https:\/\/urff.app\/?page_id=375"},"modified":"2026-09-05T17:01:06","modified_gmt":"2026-09-05T17:01:06","slug":"zahlenstrahl","status":"publish","type":"page","link":"https:\/\/urff.app\/es\/zahlenstrahl\/","title":{"rendered":"l\u00ednea num\u00e9rica"},"content":{"rendered":"<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"404\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-1024x404.jpeg\" alt=\"\" class=\"wp-image-432\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-1024x404.jpeg 1024w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-300x118.jpeg 300w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-768x303.jpeg 768w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-1536x607.jpeg 1536w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-2048x809.jpeg 2048w, https:\/\/urff.app\/wp-content\/uploads\/2024\/11\/IMG_0210-18x7.jpeg 18w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<div class=\"urff-appbox\" style=\"display:flex;flex-wrap:wrap;align-items:center;gap:1rem;padding:1rem 1.25rem;margin:1.5rem 0;border:1px solid rgba(0,0,0,.12);border-radius:18px;background:rgba(0,0,0,.035)\">\n<a href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" target=\"_blank\" rel=\"noopener\" style=\"flex:0 0 auto;line-height:0\"><img decoding=\"async\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/09\/appicon-zahlenstrahl-6473689075.jpg\" alt=\"App-Icon Zahlenstrahl\" width=\"96\" height=\"96\" loading=\"lazy\" style=\"width:96px;height:96px;border-radius:22%;box-shadow:0 1px 4px rgba(0,0,0,.15)\"><\/a>\n<div style=\"flex:1 1 12rem;min-width:0\">\n<div style=\"font-weight:700;font-size:1.15em;line-height:1.3\"><a href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" target=\"_blank\" rel=\"noopener\" style=\"text-decoration:none\">l\u00ednea num\u00e9rica<\/a><\/div>\n<div style=\"font-size:.9em;opacity:.75;margin-top:.15em\">Christian Urff \u00b7 iPad, iPhone<\/div>\n<\/div>\n<a href=\"https:\/\/apps.apple.com\/de\/app\/zahlenstrahl\/id6473689075\" target=\"_blank\" rel=\"noopener\" style=\"flex:0 0 auto;display:inline-block;padding:.55em 1.1em;border-radius:999px;background:#0071e3;color:#fff;font-weight:600;font-size:.95em;text-decoration:none;white-space:nowrap\">Descargar en el App Store<\/a>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">la aplicaci\u00f3n <strong>l\u00ednea num\u00e9rica<\/strong> (antes <em>recta num\u00e9rica AR<\/em>La aplicaci\u00f3n se ha expandido significativamente: ha evolucionado de una simple aplicaci\u00f3n de realidad aumentada a una herramienta integral de aprendizaje para la recta num\u00e9rica, con un tutor de IA, un sistema de aprendizaje adaptativo y nueve tipos de ejercicios diferentes, adem\u00e1s de entornos experimentales con y sin RA. La aplicaci\u00f3n se basa en hallazgos cient\u00edficos de ensayos y es objeto de investigaci\u00f3n continua.<\/p>\n\n\n\n<figure class=\"wp-block-gallery has-nested-images columns-default is-cropped wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"763\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-1024x768.png\" alt=\"\" class=\"wp-image-763\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot5-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"758\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-1024x768.png\" alt=\"\" class=\"wp-image-758\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot4-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"762\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-1024x768.png\" alt=\"\" class=\"wp-image-762\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot1-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"759\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-1024x768.png\" alt=\"\" class=\"wp-image-759\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot3-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"760\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-1024x768.png\" alt=\"\" class=\"wp-image-760\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot2-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" data-id=\"761\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-1024x768.png\" alt=\"\" class=\"wp-image-761\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-1024x768.png 1024w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-300x225.png 300w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-768x576.png 768w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-1536x1151.png 1536w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-2048x1535.png 2048w, https:\/\/urff.app\/wp-content\/uploads\/2026\/02\/iPad-12.9-Inch-Display-Apple-iPad-Air-10.9-inch-4th-Generation-Screenshot6-16x12.png 16w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tres entornos experimentales<\/strong> \u2013 Neben dem Augmented-Reality-Modus gibt es einen mit Touch-Bedienung und Zeichenwerkzeugen sowie einen kombinierten Modus, der AR- und 2D-Ansicht synchron nebeneinander zeigt. In den Experimentierumgebungen kann mit den unterschiedlichen Zahlenstrahldarstellungen frei gearbeitet werden \u2013 hier sind keine Aufgabenstellungen enthalten.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Informes de progreso de aprendizaje<\/strong> \u2013 Los informes generados por IA muestran a los padres y maestros de un vistazo d\u00f3nde se encuentra el ni\u00f1o: fortalezas, debilidades y desarrollo a lo largo del tiempo.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Diferentes tipos de ejercicios<\/strong> \u2013 hacen un uso espec\u00edfico de las posibilidades de los medios digitales y giran en torno a las tareas de estimaci\u00f3n de l\u00edneas num\u00e9ricas (NLET):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>N\u00famero de marca<\/strong> \u2013 Estimar y ubicar n\u00fameros en la recta num\u00e9rica<\/li>\n\n\n\n<li><strong>Nombra el n\u00famero<\/strong> \u2013 Identificar qu\u00e9 n\u00famero corresponde a una posici\u00f3n marcada<\/li>\n\n\n\n<li><strong>Encontrar errores<\/strong> \u2013 Descubrir n\u00fameros extraviados<\/li>\n\n\n\n<li><strong>N\u00fameros coincidentes<\/strong> \u2013 Asignar n\u00fameros a las posiciones correctas<\/li>\n\n\n\n<li><strong>Los n\u00fameros se encuentran<\/strong> \u2013 Alcanza el n\u00famero objetivo movi\u00e9ndote<\/li>\n\n\n\n<li><strong>Encontrar extracto<\/strong> \u2013 Encuentra la secci\u00f3n correspondiente de la recta num\u00e9rica<\/li>\n\n\n\n<li><strong>Cifras en la zona<\/strong> \u2013 Reconocer n\u00fameros en \u00e1reas marcadas<\/li>\n\n\n\n<li><strong>n\u00fameros vecinos<\/strong> \u2013 Encontrar predecesores y sucesores<\/li>\n\n\n\n<li><strong>Rompecabezas de n\u00fameros<\/strong> \u2013 Resuelve emocionantes rompecabezas<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/urff.app\/es\/mehr-als-antworten-forschungsbasierte-anforderungen-an-ki-gestuetzte-lernbegleitung-im-mathematikunterricht\/\" data-type=\"post\" data-id=\"576\"><strong>Tutor de IA<\/strong> \u2013 Un compa\u00f1ero de aprendizaje inteligente<\/a> gibt kindgerechte, fachdidaktisch fundierte Hinweise bei Schwierigkeiten, erkennt Fehlermuster und erkl\u00e4rt geduldig. Er spricht Aufgaben und R\u00fcckmeldungen vor. Er ben\u00f6tigt f\u00fcr die KI-gest\u00fctzten Funktionen eine Internetverbindung (ohne zus\u00e4tzliche Kosten), aber funktioniert auch offline mit weniger fundierten R\u00fcckmeldungen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Sistema de aprendizaje adaptativo<\/strong> La dificultad se ajusta autom\u00e1ticamente a la capacidad del ni\u00f1o. El sistema busca una tasa de \u00e9xito de aproximadamente el 85%, lo que garantiza que los ni\u00f1os no se frustren ni se aburran. El progreso se guarda y se puede continuar la pr\u00f3xima vez.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Perfiles de usuario<\/strong> \u2013 Varios ni\u00f1os pueden usar la aplicaci\u00f3n con sus propios perfiles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La aplicaci\u00f3n es adecuada para su uso en <strong>Escuela primaria<\/strong>, en el <strong>Escuela de necesidades especiales<\/strong> (por ejemplo, en casos de discalculia), en el <strong>Tutor\u00eda<\/strong> y <strong>en casa<\/strong>. Los rangos num\u00e9ricos se pueden seleccionar con flexibilidad: 0-20, 0-100, 0-1000, 0-10000 o un rango personalizado. Un modo de experimentaci\u00f3n libre fomenta el descubrimiento. Tambi\u00e9n se pueden representar n\u00fameros negativos y decimales y practicar con estos rangos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La aplicaci\u00f3n es compatible <strong>Alem\u00e1n, ingl\u00e9s, franc\u00e9s, italiano y espa\u00f1ol<\/strong>. Sie enth\u00e4lt keine Werbung, keine In-App-K\u00e4ufe und funktioniert offline. Die Nutzung ist anonym m\u00f6glich. Optional k\u00f6nnen anonymisierte Daten f\u00fcr die Bildungsforschung freigegeben werden.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aqu\u00ed hay un v\u00eddeo de la l\u00ednea num\u00e9rica AR en acci\u00f3n:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Aplicaci\u00f3n de l\u00ednea num\u00e9rica de realidad aumentada de Christian Urff\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/kIytrIxvo60?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Einen Zahlenstrahl ohne AR gibt es hier als Webapp zum Ausprobieren, der Funktionsumfang des virtuellen Arbeitsmittels ist aber deutlich reduziert gegen\u00fcber der iPad-App:<br><br><a href=\"https:\/\/lernsoftware-mathematik.de\/zahlenstrahl\/\">https:\/\/lernsoftware-mathematik.de\/zahlenstrahl\/<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>Zahlenstrahl Christian Urff \u00b7 iPad, iPhone Im App Store laden Die App Zahlenstrahl (ehemals AR Zahlenstrahl) wurde grundlegend erweitert: Aus der reinen Augmented-Reality-App ist ein umfassendes Lernwerkzeug f\u00fcr den Zahlenstrahl geworden \u2013 mit KI-Tutor, adaptivem Lernsystem und neun verschiedenen \u00dcbungstypen und Experimentierumgebungen mit und ohne AR. Die App basiert auf wissenschaftlichen Erkenntnissen aus den Erprobungen [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-375","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/pages\/375","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/comments?post=375"}],"version-history":[{"count":20,"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/pages\/375\/revisions"}],"predecessor-version":[{"id":1352,"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/pages\/375\/revisions\/1352"}],"wp:attachment":[{"href":"https:\/\/urff.app\/es\/wp-json\/wp\/v2\/media?parent=375"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}