{"id":998,"date":"2026-05-06T18:52:35","date_gmt":"2026-05-06T18:52:35","guid":{"rendered":"https:\/\/urff.app\/?page_id=998"},"modified":"2026-05-07T08:34:38","modified_gmt":"2026-05-07T08:34:38","slug":"schriftlich-rechnen","status":"publish","type":"page","link":"https:\/\/urff.app\/ja\/schriftlich-rechnen\/","title":{"rendered":"\u7b46\u7b97"},"content":{"rendered":"<p class=\"wp-block-paragraph\"><strong>\u7b46\u7b97\u306b\u3088\u308b\u8db3\u3057\u7b97\u3068\u5f15\u304d\u7b97\u3092\u3001\u7406\u89e3\u3092\u6df1\u3081\u306a\u304c\u3089\u63a2\u6c42\u3059\u308b\u305f\u3081\u306e\u30a2\u30d7\u30ea\u3002.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><!-- WP-Appbox (Version: 4.5.13 \/\/ Store: appstore \/\/ ID: 6765940539) -->\n<div class=\"wpappbox wpappbox-7890478185b442ef39218ed825cd8c32 appstore deprecated simple\">\n\t<div class=\"qrcode\"><img decoding=\"async\" src=\"https:\/\/api.qrserver.com\/v1\/create-qr-code\/?data=https%3A%2F%2Fapps.apple.com%2Fde%2Fapp%2Fschriftlich-rechnen%2Fid6765940539&size=200x200&ecc=M&margin=0\" alt=\"Schriftlich Rechnen\" \/><\/div>\n\t<div class=\"appicon\">\n\t\t<a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/app\/schriftlich-rechnen\/id6765940539\" aria-label=\"\u7b46\u7b97\"><img decoding=\"async\" src=\"\/\/is1-ssl.mzstatic.com\/image\/thumb\/PurpleSource221\/v4\/11\/46\/a3\/1146a3e4-bb09-f1b8-90d5-b2e111e24350\/Placeholder.mill\/200x200bb-75.png\" alt=\"Schriftlich Rechnen\" \/><\/a>\n\t<\/div>\n\t<div class=\"applinks\">\n\t\t<div class=\"appbuttons\">\n\t\t\t<a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/app\/schriftlich-rechnen\/id6765940539\" aria-label=\"\u7b46\u7b97\">\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9<\/a>\n\t\t\t<span onmouseover=\"jQuery('.wpappbox-7890478185b442ef39218ed825cd8c32 .qrcode').show();\" onmouseout=\"jQuery('.wpappbox-7890478185b442ef39218ed825cd8c32 .qrcode').hide();\">QR\u30b3\u30fc\u30c9<\/span>\n\t\t<\/div>\n\t<\/div>\n\t<div class=\"appdetails\">\n\t\t<div class=\"apptitle\"><a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/app\/schriftlich-rechnen\/id6765940539\" title=\"\u7b46\u7b97\" aria-label=\"\u7b46\u7b97\" class=\"apptitle\">\u7b46\u7b97<\/a><\/div>\n\t\t<div class=\"developer\">\n\t\t\t<span class=\"label\">\u958b\u767a\u8005: <\/span>\n\t\t\t<span class=\"value\"><a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/developer\/christian-urff\/id415894463\">\u30af\u30ea\u30b9\u30c1\u30e3\u30f3\u30fb\u30a6\u30eb\u30d5<\/a><\/span>\n\t\t<\/div>\n\t\t<div class=\"price\">\n\t\t\t<span class=\"label\">\u91d1\u984d: <\/span>\n\t\t\t<span class=\"value\">0,99\u00a0\u20ac<\/span> \n\t\t\t<span class=\"rating\"><div title=\"5\u3064\u661f\u306e\u3046\u30610\u3064\" class=\"rating-stars stars-monochrome stars00\"><\/div><\/span>\n\t\t<\/div>\n\t<\/div>\n<\/div><!-- \/WP-Appbox --><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30a2\u30d7\u30ea\u306f\u3001\u5404\u8acb\u6c42\u66f8\u3092\u8907\u6570\u306e\u8868\u793a\u5f62\u5f0f\u3067\u540c\u6642\u306b\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8868\u8a18\u6cd5<\/strong>\uff1a\u30ce\u30fc\u30c8\u306b\u66f8\u304b\u308c\u3066\u3044\u308b\u901a\u308a\u306e\u3001\u6570\u5b57\u3001\u7e70\u308a\u4e0a\u304c\u308a\u3001\u7e70\u308a\u4e0b\u304c\u308a\u3092\u542b\u3080\u53e4\u5178\u7684\u306a\u4f4d\u53d6\u308a\u8868\u3002.<\/li>\n\n\n\n<li><strong>\u30d7\u30ec\u30fc\u30c8<\/strong>\uff1a\u5404\u4f4d\u306e\u5024\u304c\u305d\u308c\u305e\u308c\u72ec\u7acb\u3057\u305f\u5217\u3068\u3057\u3066\u8868\u3055\u308c\u3001\u30bf\u30a4\u30eb\u304c\u675f\u306d\u3089\u308c\u305f\u308a\u675f\u306d\u3089\u308c\u3066\u3044\u306a\u3044\u72b6\u614b\u306b\u306a\u308b\u3068\u8996\u899a\u7684\u306b\u79fb\u52d5\u3059\u308b\u30012\u6b21\u5143\u306e\u4f4d\u53d6\u308a\u8868\u3002.<\/li>\n\n\n\n<li><strong>\u30c7\u30a3\u30fc\u30f3\u30ba3D<\/strong>\u7acb\u65b9\u4f53\u3001\u68d2\u3001\u677f\u3001\u305d\u3057\u3066\u5343\u500b\u306e\u7acb\u65b9\u4f53\u3067\u69cb\u6210\u3055\u308c\u305f\u7b49\u89d2\u6295\u5f71\u56f3\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u4f4d\u53d6\u308a\u306e\u7a7a\u9593\u7684\u306a\u95a2\u4fc2\u304c\u4e00\u76ee\u3067\u308f\u304b\u308b\u300210\u306f1\u306e10\u500d\u3001100\u306f10\u306e10\u500d\u3067\u3042\u308b\u3002.<\/li>\n\n\n\n<li><strong>\u8a00\u8a9e\u30b5\u30dd\u30fc\u30c8<\/strong>\u3059\u3079\u3066\u306e\u624b\u9806\u306b\u306f\u3001\u66f8\u9762\u3068\u97f3\u58f0\u51fa\u529b\u306e\u4e21\u65b9\u306b\u3088\u308b\u97f3\u58f0\u30ac\u30a4\u30c0\u30f3\u30b9\u304c\u4ed8\u968f\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u8868\u8a18\u306e\u6570\u5b57\u3092\u5909\u66f4\u3059\u308b\u3068\u3001\u4ed6\u306e\u8868\u73fe\u306b\u3082\u5373\u5ea7\u306b\u5bfe\u5fdc\u3059\u308b\u5909\u5316\u304c\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u675f\u306d\u305f\u308a\u307b\u3069\u3044\u305f\u308a\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u8aac\u660e\u3055\u308c\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3067\u3082\u793a\u3055\u308c\u307e\u3059\u300210\u500b\u306e1\u306f1\u3064\u306e10\u306b\u675f\u306d\u3089\u308c\u3001100\u306e\u5e73\u3089\u306a\u90e8\u5206\u306f10\u672c\u306e10\u306e\u68d2\u306b\u307b\u3069\u304b\u308c\u307e\u3059\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beide-subtraktionsverfahren\">\u6e1b\u7b97\u6cd5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30a2\u30d7\u30ea\u306f\u3001\u30c9\u30a4\u30c4\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u3066\u3044\u308b2\u3064\u306e\u5f15\u304d\u7b97\u65b9\u6cd5\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0<\/strong>&nbsp;\uff08\u6e1b\u7b97\u65b9\u6cd5\uff09\uff1a\u88ab\u6e1b\u6570\u306e\u6b21\u306e\u6841\u304b\u30891\u3092\u5f15\u3044\u3066\u3001\u73fe\u5728\u306e\u6841\u306b10\u3092\u52a0\u7b97\u3057\u307e\u3059\u3002.<\/li>\n\n\n\n<li><strong>\u62e1\u5927\u3059\u308b<\/strong>&nbsp;\uff08\u7a74\u57cb\u3081\u65b9\u5f0f\uff09\uff1a\u6b21\u306e\u6841\u306e\u6e1b\u6570\u306b1\u3092\u52a0\u3048\u3001\u88ab\u6e1b\u6570\u306f\u5909\u66f4\u3057\u307e\u305b\u3093\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3069\u3061\u3089\u306e\u65b9\u6cd5\u3082\u3001\u540c\u3058\u30bf\u30b9\u30af\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u5185\u3067\u5207\u308a\u66ff\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u96e3\u3057\u3044\u65b9\u306e\u65b9\u6cd5\u3067\u3082\u540c\u69d8\u3067\u3059\u3002&nbsp;<strong>\u30ab\u30b9\u30b1\u30fc\u30c9\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0<\/strong>&nbsp;\uff08\u4f8b\u3048\u3070\u3001at\uff09&nbsp;<code>900 \u2212 191<\/code>, \uff08\u501f\u308a\u305f\u30e6\u30cb\u30c3\u30c8\u304c\u8907\u6570\u306e\u5834\u6240\u3092\u79fb\u52d5\u3057\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff09\u306f\u5b8c\u5168\u306b\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u5316\u3055\u308c\u3001\u30ca\u30ec\u30fc\u30b7\u30e7\u30f3\u3082\u4ed8\u3044\u3066\u3044\u307e\u3059\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"vorhersage-aufgaben\">\u4e88\u6e2c\u30bf\u30b9\u30af<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30aa\u30d7\u30b7\u30e7\u30f3\u3068\u3057\u3066\u3001\u30a2\u30d7\u30ea\u306f\u5404\u30b9\u30c6\u30c3\u30d7\u306e\u524d\u306b\u8907\u6570\u9078\u629e\u5f0f\u306e\u8cea\u554f\u3092\u8868\u793a\u3057\u305f\u308a\u3001\u8868\u73fe\u306b\u5bfe\u3057\u3066\u76f4\u63a5\u7684\u306a\u30a2\u30af\u30b7\u30e7\u30f3\u3092\u8981\u6c42\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002&nbsp;<em>\u201e\u300c\u6b21\u306b\u4f55\u304c\u8d77\u3053\u308b\u306e\u304b\uff1f\u300d\u201c<\/em>&nbsp;\u5b50\u3069\u3082\u306f\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u4e88\u6e2c\u3057\u307e\u3059\u3002\u30a2\u30d7\u30ea\u306f\u305d\u306e\u5f8c\u306b\u306e\u307f\u305d\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u610f\u56f3\u7684\u306b\u3001\u6ce8\u610f\u3092\u305d\u3089\u3059\u8981\u7d20\u3068\u3057\u3066\u3001\u300c\u5927\u304d\u3044\u6570\u304b\u3089\u5c0f\u3055\u3044\u6570\u3092\u5f15\u304f\u300d\u3068\u3044\u3063\u305f\u5178\u578b\u7684\u306a\u8aa4\u89e3\u3084\u3001\u7e70\u308a\u4e0a\u304c\u308a\u306e\u8a08\u7b97\u3092\u5fd8\u308c\u3066\u3057\u307e\u3046\u3068\u3044\u3063\u305f\u4f8b\u304c\u7528\u3044\u3089\u308c\u3066\u3044\u307e\u3059\u3002.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"teil-2-didaktischer-hintergrund\">\u6559\u80b2\u7684\u80cc\u666f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"1-bildungspolitischer-rahmen-was-sich-seit-2022-ge-ndert-hat\">\u6559\u80b2\u653f\u7b56\u306e\u67a0\u7d44\u307f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">2022\u5e74\u306b\u6539\u8a02\u3055\u308c\u305fKMK\uff08\u6559\u80b2\u6587\u5316\u5927\u81e3\u5e38\u8a2d\u4f1a\u8b70\uff09\u6570\u5b66\u57fa\u6e96\u306e\u63a1\u629e\u4ee5\u6765\u3001\u7b46\u7b97\u65b9\u6cd5\u306b\u5bfe\u3059\u308b\u6559\u80b2\u4e0a\u306e\u91cd\u70b9\u306f\u5927\u304d\u304f\u5909\u5316\u3057\u305f\u30022004\u5e74\u306e\u57fa\u6e96\u3067\u306f\u7b46\u7b97\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5c0f\u5b66\u6821\u306b\u304a\u3051\u308b\u4e2d\u5fc3\u7684\u306a\u80fd\u529b\u9818\u57df\u3068\u3057\u3066\u4f4d\u7f6e\u3065\u3051\u3089\u308c\u3066\u3044\u305f\u304c\u3001\u65b0\u3057\u3044\u57fa\u6e96\u3067\u306f\u2026\u00a0<strong>\u534a\u7b46\u7b97\u8853<\/strong>\u00a0\u305d\u3057\u3066\u3001\u8a18\u8ff0\u3055\u308c\u305f\u624b\u9806\u306b\u57fa\u3065\u3044\u3066\u95a2\u6570\u3092\u5272\u308a\u5f53\u3066\u307e\u3059\u3002\u91cd\u8981\u306a\u5909\u66f4\u70b9\u306f\u3001\u6570\u5b66\u6559\u80b2\u5b66\u4f1a\u306b\u3088\u308b\u4ed8\u968f\u8a18\u4e8b\uff08Barzel et al. 2023\uff09\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u79c1\u305f\u3061\u306e\u8cea\u554f\u306b\u7279\u306b\u95a2\u9023\u3059\u308b\u70b9\u306f\u6b21\u306e3\u3064\u3067\u3059\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u534a\u7b46\u7b97\u304c\u307e\u3059\u307e\u3059\u666e\u53ca\u3057\u3064\u3064\u3042\u308b\u3002.<\/strong>&nbsp;\u534a\u6587\u66f8\u5316\u3055\u308c\u305f\u6226\u7565\u306f\u3001\u5b50\u3069\u3082\u305f\u3061\u304c\u8a08\u7b97\u3092\u69cb\u9020\u5316\u3057\u3001\u4e2d\u9593\u6bb5\u968e\u3092\u8996\u899a\u5316\u3057\u3001\u81ea\u8eab\u306e\u601d\u8003\u30d7\u30ed\u30bb\u30b9\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u524d\u63d0\u6761\u4ef6\u3068\u3057\u3066\u7406\u89e3\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6587\u66f8\u5316\u3055\u308c\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u3053\u306e\u57fa\u790e\u304c\u3057\u3063\u304b\u308a\u3068\u78ba\u7acb\u3055\u308c\u3066\u304b\u3089\u521d\u3081\u3066\u5c0e\u5165\u3055\u308c\u307e\u3059\uff08KMK 2022; \u5b9f\u65bd\u8981\u65e8 KMK 2023\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u7406\u89e3\u3053\u305d\u304c\u6307\u91dd\u3068\u306a\u308b\u3002.<\/strong> \u201e\u300c\u81ea\u52d5\u5316\u3059\u308b\u524d\u306b\u7406\u89e3\u3059\u308b\u300d\u3068\u3044\u3046\u539f\u5247\u306f\u3001\u5c0e\u5165\u306b\u95a2\u3059\u308b\u30d1\u30f3\u30d5\u30ec\u30c3\u30c8\u306b\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u3057\u3066\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u307e\u3059\u3002.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u9023\u90a6\u5dde\u306f\u3053\u308c\u3092\u4e00\u8cab\u6027\u306a\u304f\u5b9f\u65bd\u3057\u3066\u3044\u308b\u3002\u30d0\u30a4\u30a8\u30eb\u30f3\u5dde&nbsp;<strong>\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u30d7\u30e9\u30b9<\/strong>&nbsp;\u4f8b\u3048\u3070\u3001\u5c0f\u5b66\u6821\u3067\u306f\u3001\u5f15\u304d\u7b97\u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u660e\u793a\u7684\u306b\u8a18\u8ff0\u3055\u308c\u3066\u3044\u307e\u3059\u3002&nbsp;<strong>\u6f14\u7e79\u6cd5<\/strong>&nbsp;\uff08\uff1d\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0\uff09\u3057\u3001\u767e\u306e\u30d7\u30ec\u30fc\u30c8\u3001\u5341\u306e\u68d2\u3001\u4e00\u306e\u68d2\u3092\u4e3b\u8981\u306a\u6559\u6750\u3068\u3057\u3066\u6319\u3052\u3066\u3044\u308b\uff08\u30d0\u30a4\u30a8\u30eb\u30f3\u5dde\u6559\u80b2\u6587\u5316\u7701 2024\uff09\u3002\u4e00\u65b9\u3001\u30ce\u30eb\u30c8\u30e9\u30a4\u30f3\uff1d\u30f4\u30a7\u30b9\u30c8\u30d5\u30a1\u30fc\u30ec\u30f3\u5dde\u306e\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u3067\u306f\u3001\u624b\u9806\u306e\u9078\u629e\u306f\u81ea\u7531\u3067\u3042\u308a\u3001\u6c7a\u5b9a\u306f\u5b66\u6821\u306b\u59d4\u306d\u3089\u308c\u3066\u3044\u308b\uff08PIKAS 2024\uff09\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u306f\u3001\u5168\u56fd\u7684\u306b\u4f7f\u7528\u3067\u304d\u308b\u5b66\u7fd2\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u3092\u610f\u5473\u3057\u307e\u3059\u3002&nbsp;<strong>\u4e21\u65b9\u306e\u624b\u9806<\/strong>&nbsp;\u305d\u308c\u305e\u308c\u306e\u6559\u79d1\u66f8\u3068\u95a2\u9023\u4ed8\u3051\u308b\u305f\u3081\u306b\u306f\u3001\u5c11\u306a\u304f\u3068\u3082\u305d\u308c\u3092\u8868\u73fe\u3067\u304d\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u3055\u3089\u306b\u3001\u3053\u308c\u306b\u3088\u308a\u30012\u3064\u306e\u65b9\u6cd5\u3092\u6bd4\u8f03\u691c\u8a0e\u3057\u3001\u7406\u89e3\u3092\u6df1\u3081\u308b\u3053\u3068\u3082\u53ef\u80fd\u306b\u306a\u308b\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2-was-hei-t-verstehensorientierung\">\u300c\u7406\u89e3\u91cd\u8996\u300d\u3068\u306f\u3069\u3046\u3044\u3046\u610f\u5473\u3067\u3059\u304b\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u6982\u5ff5\u306f2010\u5e74\u4ee3\u5f8c\u534a\u304b\u3089\u30c9\u30a4\u30c4\u306e\u6570\u5b66\u6559\u80b2\u306e\u4e2d\u5fc3\u3068\u306a\u3063\u3066\u304a\u308a\u3001\u7279\u306b\u30b9\u30b6\u30f3\u30cd\u30fb\u30d7\u30ec\u30c7\u30a3\u30ac\u30fc\u3068\u30af\u30ea\u30b9\u30c8\u30d5\u30fb\u30bb\u30eb\u30bf\u30fc\uff08\u30c9\u30eb\u30c8\u30e0\u30f3\u30c8\u5de5\u79d1\u5927\u5b66\uff09\u306b\u3088\u3063\u3066\u767a\u5c55\u3055\u305b\u3089\u308c\u305f\uff08Prediger &amp; Selter 2014; Selter et al. 2014\uff09\u3002\u7406\u89e3\u91cd\u8996\u306e\u6570\u5b66\u6559\u80b2\u306f\u3001\u76f8\u4e92\u306b\u95a2\u9023\u3059\u308b3\u3064\u306e\u7279\u5fb4\u306b\u3088\u3063\u3066\u7279\u5fb4\u3065\u3051\u3089\u308c\u308b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8a08\u7b97\u3088\u308a\u3082\u30a2\u30a4\u30c7\u30a2\u3092\u512a\u5148\u3059\u308b\u3002.<\/strong>&nbsp;\u6b63\u5f0f\u306a\u7b97\u8853\u898f\u5247\u3092\u5c0e\u5165\u3059\u308b\u524d\u306b\u3001\u6570\u3068\u6f14\u7b97\u306b\u95a2\u3059\u308b\u78ba\u304b\u306a\u7406\u89e3\u3092\u78ba\u7acb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3002\u3053\u306e\u57fa\u790e\u304c\u3042\u3063\u3066\u521d\u3081\u3066\u3001\u624b\u9806\u3092\u4f53\u7cfb\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff08Prediger &amp; Selter 2014\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u4ee3\u8868\u8005\u306e\u4ea4\u4ee3\u304c\u983b\u7e41\u306b\u7e70\u308a\u8fd4\u3055\u308c\u308b\u3002.<\/strong>&nbsp;\u6982\u5ff5\u3068\u64cd\u4f5c\u306f\u3001\u8907\u6570\u306e\u8868\u73fe\u30ec\u30d9\u30eb\uff08\u5177\u4f53\u7269\u3001\u56f3\u50cf\u3001\u8c61\u5fb4\u3001\u8a00\u8a9e\uff09\u306b\u308f\u305f\u3063\u3066\u76f8\u4e92\u306b\u95a2\u9023\u3057\u3066\u304a\u308a\u3001\u5b50\u3069\u3082\u305f\u3061\u306f\u30ec\u30d9\u30eb\u3092\u5207\u308a\u66ff\u3048\u308b\u969b\u306b\u3001\u81ea\u8eab\u306e\u8003\u3048\u3092\u691c\u8a3c\u3057\u3001\u6d17\u7df4\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002.<\/li>\n\n\n\n<li><strong>\u69cb\u9020\u7684\u3001\u6570\u5b66\u5185\u90e8\u306e\u6982\u5ff5\u3002.<\/strong> \u3053\u306e\u63a8\u9032\u306f\u3001\u5fdc\u7528\u5834\u9762\u3092\u5968\u52b1\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u4f8b\u3048\u3070\u4f4d\u53d6\u308a\u8a18\u6570\u6cd5\u306e\u675f\u306d\u8ad6\u7406\uff08Prediger 2024\uff09\u306e\u3088\u3046\u306a\u6570\u5b66\u7684\u69cb\u9020\u306e\u8a8d\u8b58\u3082\u76ee\u7684\u3068\u3057\u3066\u3044\u308b\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u30a2\u30d7\u30ea\u306f\u3001&nbsp;<strong>\u30a2\u30a4\u30c7\u30a2\u3092\u69cb\u7bc9\u3059\u308b<\/strong>&nbsp;\u305d\u3057\u3066&nbsp;<strong>\u4ee3\u8868\u8005\u306e\u5909\u66f4\u3092\u8981\u6c42\u3059\u308b<\/strong>&nbsp;\u3053\u308c\u306f\u52a9\u3051\u3068\u306a\u308a\u3001\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u51e6\u7406\u306e\u30e2\u30c7\u30eb\u3068\u306a\u308b\u8a00\u8a9e\u7684\u30b5\u30dd\u30fc\u30c8\u3092\u3082\u305f\u3089\u3059\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"3-schriftliche-verfahren-als-b-ndelungs-prozeduren\">\u6587\u66f8\u5316\u3055\u308c\u305f\u624b\u9806\u3092\u30d0\u30f3\u30c9\u30eb\u624b\u9806\u3068\u3057\u3066\u6271\u3046<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8a18\u8ff0\u3055\u308c\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001&nbsp;<strong>\u5c0f\u6570\u70b9\u4ee5\u4e0b\u306e\u4f4d\u53d6\u308a\u30b7\u30b9\u30c6\u30e0<\/strong>&nbsp;\u6d3e\u751f\u3002\u4f4d\u53d6\u308a\u8868\u306e\u5404\u5217\u306f\u30b0\u30eb\u30fc\u30d7\u5316\u306e\u30ec\u30d9\u30eb\u3092\u8868\u3057\u307e\u3059\u3002\u7b46\u7b97\u306b\u3088\u308b\u52a0\u7b97\u306f\u3001\u5217\u3054\u3068\u306b2\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u884c\u308f\u308c\u307e\u3059\u3002\u307e\u305a\u5408\u8a08\u3092\u8db3\u3057\u5408\u308f\u305b\u3001\u5217\u306e\u5408\u8a08\u304c10\u4ee5\u4e0a\u306b\u306a\u3063\u305f\u5834\u5408\u306f\u3001\u6b21\u306e\u9ad8\u3044\u4f4d\u306e\u5358\u4f4d\u306b\u30b0\u30eb\u30fc\u30d7\u5316\u3057\u307e\u3059\u3002\u30b3\u30d4\u30fc\u3068\u306f\u3001\u3053\u306e\u30b0\u30eb\u30fc\u30d7\u5316\u3092\u66f8\u304d\u7559\u3081\u308b\u3053\u3068\u3067\u3059\uff08Padberg &amp; Benz 2021\u3001\u7b2c8\u7ae0\uff09\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b46\u7b97\u306b\u3088\u308b\u5f15\u304d\u7b97\u306f2\u6bb5\u968e\u306e\u30d7\u30ed\u30bb\u30b9\u3067\u3059\u3002\u307e\u305a\u3001\u6700\u4e0a\u4f4d\u306e\u4f4d\u306e\u5358\u4f4d\u3092\u6bd4\u8f03\u3057\u3001\u6700\u4e0a\u4f4d\u306e\u4f4d\u306e\u5358\u4f4d\u304c\u4e0d\u8db3\u3057\u3066\u3044\u308b\u5834\u5408\u306f\u3001\u6b21\u306e\u4e0a\u4f4d\u306e\u4f4d\u306e\u5358\u4f4d\u3092\u73fe\u5728\u306e\u6841\u306e10\u306e\u5358\u4f4d\u3068\u3057\u3066\u5229\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002\u3053\u306e\u64cd\u4f5c\u3092\u88ab\u6e1b\u6570\u3092\u6e1b\u3089\u3059\uff08\u300c\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0\u300d\uff09\u304b\u3001\u6e1b\u6570\u3092\u5897\u3084\u3057\u3066\u88ab\u6e1b\u6570\u306b10\u3092\u52a0\u3048\u308b\uff08\u300c\u62e1\u5f35\u300d\uff09\u304b\u306f\u624b\u9806\u306e\u554f\u984c\u3067\u3059\u304c\u3001\u6570\u5b66\u7684\u306b\u306f\u3069\u3061\u3089\u3082\u540c\u7b49\u3067\u3059\uff08Padberg &amp; Benz 2021\uff09\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b50\u4f9b\u305f\u3061\u304c\u3053\u306e\u8ad6\u7406\u3092\u771f\u306b\u7406\u89e3\u3057\u3001\u5358\u306b\u5217\u306e\u6570\u5b57\u3067\u7121\u601d\u616e\u306b\u8a08\u7b97\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001&nbsp;<strong>\u30d0\u30f3\u30c9\u30eb\u306b\u95a2\u3059\u308b\u7406\u89e3<\/strong>&nbsp;\u8a18\u53f7\u3092\u7528\u3044\u3066\uff08\u7d14\u7c8b\u306b\uff09\u8c61\u5fb4\u7684\u306b\u4f5c\u696d\u3059\u308b\u524d\u306b\u3001\u80fd\u52d5\u7684\u304b\u3064\u8c61\u5fb4\u7684\u306a\u30ec\u30d9\u30eb\u3067\u4f5c\u696d\u3092\u884c\u3046\u3002. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"4-typische-verstehens-h-rden-was-die-empirie-zeigt\">\u5178\u578b\u7684\u306a\u7406\u89e3\u306e\u969c\u58c1<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"4-1-addition\">\u8ffd\u52a0<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u79d1\u76ee\u5225\u306e\u6559\u6388\u6cd5\u306b\u95a2\u3059\u308b\u6587\u732e\u3067\u306f\u3001\u7b46\u7b97\u306e\u8db3\u3057\u7b97\u306b\u95a2\u3059\u308b\u4ee5\u4e0b\u306e\u8aa4\u308a\u8a02\u6b63\u6226\u7565\u304c\u4e3b\u306b\u8a18\u9332\u3055\u308c\u3066\u3044\u307e\u3059\uff08<em>\u30d4\u30ab\u30b9<\/em>&nbsp;(2024) \u304a\u3088\u3073\u30d1\u30c9\u30d9\u30eb\u30b0 &amp; \u30d9\u30f3\u30c4 (2021)):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u96e2\u30a8\u30e9\u30fc\u307e\u305f\u306f\u5b8c\u5168\u306a\u8ee2\u5199\u30a8\u30e9\u30fc<\/strong>\u5b50\u4f9b\u306f\u3001\u6841\u3092\u8db3\u3057\u7b97\u3057\uff08\u4f8b\uff1a8 + 7 = 15\uff09\u30015\u3068\u66f8\u3044\u30661\u3092\u7e70\u308a\u4e0a\u3052\u308b\u306e\u3067\u306f\u306a\u304f\u30012\u6841\u306e\u6570\u5b57\u5168\u4f53\u30921\u306e\u4f4d\u306b\u66f8\u304d\u307e\u3059\u3002.<\/li>\n\n\n\n<li><strong>\u9001\u91d1\u3092\u5fd8\u308c\u305f<\/strong>\u5217\u306f\u6b63\u3057\u304f\u8ffd\u52a0\u3055\u308c\u307e\u3059\u304c\u3001\u524d\u306e\u5217\u304b\u3089\u306e\u7e70\u308a\u8d8a\u3057\u5024\u304c\u542b\u307e\u308c\u307e\u305b\u3093\u3002.<\/li>\n\n\n\n<li><strong>\u30bc\u30ed\u306e\u4e0d\u9069\u5207\u306a\u51e6\u7406<\/strong>: \u5217&nbsp;<code>0<\/code> \u8aa4\u89e3\u3055\u308c\u3066\u3044\u308b (\u4f8b:.&nbsp;<code>0 + n = 0<\/code>)\u3001\u307e\u305f\u306f\u30bc\u30ed\u3078\u306e\u7e70\u308a\u4e0a\u304c\u308a\u306f\u884c\u308f\u308c\u307e\u305b\u3093\u3002.<\/li>\n\n\n\n<li><strong>\u4f4d\u53d6\u308a\u306e\u9006\u8ee2<\/strong>\u30aa\u30da\u30e9\u30f3\u30c9\u306e\u6841\u6570\u304c\u7570\u306a\u308b\u5834\u5408\u3001\u6841\u306f\u53f3\u63c3\u3048\u3067\u306f\u306a\u304f\u5de6\u63c3\u3048\u3067\u4e0a\u4e0b\u306b\u4e26\u3079\u3066\u8868\u793a\u3055\u308c\u307e\u3059\u3002.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"4-2-subtraktion-das-fehleranf-lligere-verfahren\">\u5f15\u304d\u7b97<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f15\u304d\u7b97\u3067\u306f\u3001\u969c\u5bb3\u3068\u306a\u308b\u3082\u306e\u306e\u7bc4\u56f2\u304c\u8457\u3057\u304f\u5e83\u304f\u306a\u308a\u307e\u3059\u3002\u6700\u3082\u4e00\u822c\u7684\u306a\u8aa4\u308a\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\uff08KIRA 2024\uff09\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u9001\u91d1\u306b\u95a2\u3059\u308b\u554f\u984c<\/strong>&nbsp;\uff08\u7e70\u308a\u8d8a\u3057\u306f\u5165\u529b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3001\u7a7a\u6b04\u3078\u306e\u7e70\u308a\u8d8a\u3057\u306f\u3042\u308a\u307e\u305b\u3093\u3001\u7e70\u308a\u8d8a\u3057\u304c1\u3064\u591a\u3059\u304e\u307e\u3059\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u30bc\u30ed\u306b\u3088\u308b\u30a8\u30e9\u30fc<\/strong>&nbsp;\uff08\u300c0 \u2212 x = 0\u300d\u3001\u300cx \u2212 0 = 0\u300d\u30010 \u3092\u8d85\u3048\u308b\u7e70\u308a\u4e0a\u304c\u308a\u3084\u7e70\u308a\u4e0a\u304c\u308a\u306a\u3057\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u8a08\u7b97\u65b9\u5411\u306e\u8aa4\u5dee<\/strong>&nbsp;\uff08\u5de6\u304b\u3089\u53f3\u3078\u6570\u3048\u308b\uff09.<\/li>\n\n\n\n<li><strong>\u4f5c\u6226\u9006\u8ee2<\/strong>&nbsp;\uff08\u5f15\u304d\u7b97\u3067\u306f\u306a\u304f\u8db3\u3057\u7b97\uff09.<\/li>\n\n\n\n<li><strong>\u5217\u3054\u3068\u306e\u5dee\u5206\u300c\u5927\u304d\u3044\u5024\u30de\u30a4\u30ca\u30b9\u5c0f\u3055\u3044\u5024\u300d\u201e<\/strong>&nbsp;\u6700\u3082\u4e00\u822c\u7684\u306a\u7cfb\u7d71\u8aa4\u5dee\u3068\u3057\u3066\u3002.<\/li>\n\n\n\n<li><strong>\u91cd\u8981\u6027\u306e\u8aa4\u3063\u305f\u7406\u89e3<\/strong>.<\/li>\n\n\n\n<li><strong>\u8907\u6570\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u7d44\u307f\u5408\u308f\u305b\u308b<\/strong>&nbsp;\u4f8b\u3048\u3070\u3001\u540c\u3058\u30bf\u30b9\u30af\u5185\u3067\u62e1\u5f35\u3068\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0\u3092\u540c\u6642\u306b\u9069\u7528\u3059\u308b\u5834\u5408\u306a\u3069\u3002.<\/li>\n\n\n\n<li><strong>1+1\u30a8\u30e9\u30fc<\/strong>&nbsp;\uff08\u5217\u81ea\u4f53\u306b\u756a\u53f7\u306e\u8aa4\u308a\u304c\u3042\u308a\u307e\u3059\u3002\uff09.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u983b\u5ea6&nbsp;<strong>\u201e\u300c\u5927\u304d\u3044\u5024\u304b\u3089\u5c0f\u3055\u3044\u5024\u3092\u5f15\u304f\u300d\u8aa4\u5dee<\/strong>. \u30d3\u30fc\u30ec\u30d5\u30a7\u30eb\u30c8\u5730\u65b9\u306e31\u306e4\u5e74\u751f\u30af\u30e9\u30b9\u3092\u5bfe\u8c61\u3068\u3057\u305f\u5927\u898f\u6a21\u306a\u8abf\u67fb\u3067\u3001Schipper\u306f1983\u5e74\u306e\u6642\u70b9\u3067\u3001\u3053\u306e\u30a8\u30e9\u30fc\u304c\u6e1b\u7b97\u30a8\u30e9\u30fc\u5168\u4f53\u306e\u7d0430%\u3092\u5360\u3081\u3001\u6700\u3082\u983b\u7e41\u306b\u767a\u751f\u3059\u308b\u7cfb\u7d71\u7684\u30a8\u30e9\u30fc\u3067\u3042\u308b\u3053\u3068\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3057\u305f\uff08Schipper 1983; Padberg &amp; Benz 2021\u306b\u5f15\u7528\uff09\u3002Wartha &amp; Schulz\uff082014\uff09\u306f\u3001\u3053\u306e\u30a8\u30e9\u30fc\u304c\u4f4d\u53d6\u308a\u306e\u7406\u89e3\u306e\u5f31\u3055\u3068\u78ba\u5b9f\u306b\u76f8\u95a2\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u308c\u3089\u306e\u3088\u304f\u3042\u308b\u8aa4\u308a\u306b\u57fa\u3065\u3044\u3066\u3001\u30a2\u30d7\u30ea\u306f\u5404\u30b9\u30c6\u30c3\u30d7\u306e\u30a4\u30f3\u30d1\u30eb\u30b9\u3068\u4e88\u6e2c\u3092\u5177\u4f53\u7684\u306b\u8abf\u6574\u3057\u3001\u3055\u3089\u306b\u305d\u308c\u3089\u3092\u8996\u899a\u5316\u3059\u308b\u3053\u3068\u3067\u3001\u305d\u306e\u3088\u3046\u306a\u8aa4\u308a\u3084\u8aa4\u89e3\u306b\u5bfe\u51e6\u3057\u3001\u8868\u73fe\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3092\u901a\u3058\u3066\u3053\u308c\u3089\u306e\u8aa4\u89e3\u3092\u514b\u670d\u3059\u308b\u305f\u3081\u306e\u5b66\u7fd2\u6a5f\u4f1a\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"4-3-verfahrens-verwechslungen\">\u624b\u7d9a\u304d\u4e0a\u306e\u6df7\u4e71<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b50\u4f9b\u305f\u3061\u304c\u6210\u9577\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u500b\u6027\u3092\u89e3\u304d\u653e\u3064\u3068\u304d\u3001\u307e\u305f\u5225\u306e\u969c\u5bb3\u304c\u751f\u3058\u308b\u3002&nbsp;<strong>\u30df\u30c3\u30af\u30b9<\/strong>. \u3053\u306e\u30a8\u30e9\u30fc\u306f\u3001\u6559\u79d1\u66f8\u3068\u5bb6\u5ead\u5b66\u7fd2\u652f\u63f4\u3067\u7570\u306a\u308b\u65b9\u6cd5\u304c\u7528\u3044\u3089\u308c\u308b\u5834\u5408\u306b\u7d4c\u9a13\u7684\u306b\u767a\u751f\u3057\u307e\u3059\uff08Schipper 2009\uff09\u3002\u3053\u308c\u306f\u3001\u591a\u304f\u306e\u89aa\u304c\u4f9d\u7136\u3068\u3057\u3066\u62e1\u5f35\u5b66\u7fd2\u6cd5\u3092\u899a\u3048\u3066\u3044\u308b\u4e00\u65b9\u3067\u3001\u5b50\u4f9b\u305f\u3061\u306f\u73fe\u5728\u3001\u4e3b\u306b\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0\u5b66\u7fd2\u6cd5\u3092\u6559\u3048\u3089\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u4e00\u56e0\u3067\u3059\uff08Padberg &amp; Benz 2021\uff09\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"5-erweitern-vs-entb-ndeln-stand-der-fachdidaktischen-debatte\">\u62e1\u5f35\u304b\u5206\u5272\u304b\uff1a\u6559\u79d1\u5225\u6559\u80b2\u6cd5\u8ad6\u4e89<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30c9\u30a4\u30c4\u306e\u5c0f\u5b66\u6821\u3067\u4e00\u822c\u7684\u306b\u7528\u3044\u3089\u308c\u3066\u3044\u308b2\u3064\u306e\u5f15\u304d\u7b97\u306e\u65b9\u6cd5\u306f\u3001\u6570\u5341\u5e74\u306b\u308f\u305f\u308a\u8b70\u8ad6\u306e\u7684\u3068\u306a\u3063\u3066\u304d\u305f\u3002\u73fe\u72b6\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8981\u7d04\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"5-1-entb-ndeln-abziehverfahren\">\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0\uff08\u30d7\u30eb\u65b9\u5f0f\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6b63\u5f53\u5316\u306e\u8ad6\u7406\uff1a<\/strong>&nbsp;\u88ab\u6e1b\u6570\u306e\u6b21\u306e\u6841\u304b\u30891\u3092\u5f15\u3044\u305f\u6570\u3002\u501f\u308a\u305f\u5358\u4f4d\u3092\u73fe\u5728\u306e\u6841\u306b10\u5358\u4f4d\u3068\u3057\u3066\u52a0\u7b97\u3059\u308b\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f37\u5316\u3059\u308b<\/strong>&nbsp;\uff08\u30d1\u30c9\u30d9\u30eb\u30af\uff06\u30d9\u30f3\u30c4 2021; \u30af\u30e9\u30a6\u30c8\u30cf\u30a6\u30bc\u30f3 2018; \u30d0\u30a4\u30a8\u30eb\u30f3\u5dde\u653f\u5e9c 2024\uff09<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7269\u8cea\u7684\u306a\u6d3b\u52d5\u306b\u76f4\u63a5\u7d50\u3073\u3064\u304f\u4f8b\uff1a10\u672c\u306e\u68d2\u309210\u500b\u306e1\u7acb\u65b9\u4f53\u306b\u5206\u5272\u3059\u308b\u3002.<\/li>\n\n\n\n<li>\u8ad6\u7406\u7684\u306b\u4e00\u8cab\u3057\u3066\u3044\u308b\u3002\u6e1b\u6570\u3060\u3051\u304c\u5909\u5316\u3057\u3001\u6e1b\u6570\u306f\u540c\u3058\u307e\u307e\u3067\u3042\u308b\u3002.<\/li>\n\n\n\n<li>\u9023\u9396\u7684\u306a\u501f\u5165\u306f\u3001\u7a7a\u9593\u7684\u306a\u79fb\u52d5\u3068\u3057\u3066\u8868\u73fe\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f31\u3081\u308b\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u300c\u5341\u306e\u4f4d\u3092\u6d88\u3057\u3066\u3001\u305d\u306e\u6a2a\u306b-1\u3092\u66f8\u304f\u300d\u3068\u3044\u3046\u8868\u8a18\u306f\u3001\u7279\u306b\u8907\u6570\u56de\u7e70\u308a\u4e0b\u304c\u308a\u3092\u884c\u3046\u5834\u5408\u306b\u6df7\u4e71\u3092\u62db\u304f\u3002.<\/li>\n\n\n\n<li>\u6b21\u306e\u3088\u3046\u306a\u30bf\u30b9\u30af\u306e\u5834\u5408&nbsp;<code>1000 \u2212 1<\/code>&nbsp;\u30e6\u30cb\u30c3\u30c8\u306f3\u7b87\u6240\u306b\u307e\u305f\u304c\u3063\u3066\u914d\u7f6e\u3055\u308c\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u3002.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"5-2-erweitern-auff-llverfahren\">\u62e1\u5f35\uff08\u88dc\u5145\u30d7\u30ed\u30bb\u30b9\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u6b63\u5f53\u5316\u306e\u8ad6\u7406\uff1a<\/strong>&nbsp;\u5dee\u306e\u4e0d\u5909\u6027\uff1a\u4e21\u65b9\u306e\u6570\u306b\u540c\u3058\u5024\u3092\u52a0\u3048\u308b\u3068\uff0810\u500b\u306e1\uff1d1\u500b\u306e10\uff09\u3001\u5dee\u306f\u5909\u308f\u308a\u307e\u305b\u3093\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f37\u5316\u3059\u308b<\/strong>&nbsp;(\u30b7\u30c3\u30d1\u30fc 2009; \u30d1\u30c9\u30d9\u30eb\u30b0 &amp; \u30d9\u30f3\u30c4 2021):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6574\u7136\u3068\u3057\u305f\u8868\u8a18\u3001\u524a\u9664\u306a\u3057\u3002.<\/li>\n\n\n\n<li>\u63a5\u7d9a\u5148&nbsp;<strong>\u306b\u8ffd\u52a0<\/strong>&nbsp;\uff08\u300c6\u306b\u8db3\u3059\u306813\u306f\u3044\u304f\u3064\uff1f\u300d\uff09\u306f\u3001\u591a\u304f\u306e\u5b50\u4f9b\u306b\u3068\u3063\u3066\u5f15\u304d\u7b97\u3088\u308a\u3082\u8a8d\u77e5\u7684\u306b\u7406\u89e3\u3057\u3084\u3059\u3044\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u5f31\u3081\u308b\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u300c\u4e0a\u90e8\u306b10\u3092\u52a0\u3048\u308b\u306e\u3067\u3001\u4e0b\u90e8\u3067\u305d\u306e\u5206\u3092\u88dc\u308f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u300d\u3068\u3044\u3046\u8ad6\u7406\u306f\u8907\u96d1\u3067\u3001\u5b9f\u969b\u306e\u6750\u6599\u3092\u4f7f\u3063\u3066\u5b9f\u8a3c\u3059\u308b\u306e\u306f\u3088\u308a\u56f0\u96e3\u3067\u3059\u3002\u30bb\u30eb\u30bf\u30fc\uff081995\uff09\u306f\u3001\u6750\u6599\u306e\u64cd\u4f5c\u3068\u8a18\u9332\u3055\u308c\u305f\u64cd\u4f5c\u3068\u306e\u9593\u306e\u3053\u306e\u4e0d\u4e00\u81f4\u3092\u5178\u578b\u7684\u306a\u3082\u306e\u3068\u3057\u3066\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u00a0<em>\u30d5\u30a3\u30af\u30b7\u30e7\u30f3\u306e\u7f60<\/em>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u3053\u306e\u30a2\u30d7\u30ea\u306f\u3001\u4e21\u65b9\u306e\u65b9\u6cd5\u3092\u7406\u89e3\u3057\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u306b\u3001\u8996\u899a\u7684\u306a\u8868\u793a\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u3059\u3002\u30a2\u30f3\u30d0\u30f3\u30c9\u30ea\u30f3\u30b0\u65b9\u5f0f\u3067\u306f\u3001\u6b21\u306e\u9ad8\u3044\u4f4d\u306e\u30bf\u30a4\u30eb\u304c\u6d88\u3055\u308c\u3001\u6b21\u306e\u4f4e\u3044\u4f4d\u306e\u30bf\u30a4\u30eb\u304c10\u500b\u6b8b\u308a\u307e\u3059\u3002\u62e1\u5f35\u65b9\u5f0f\u3067\u306f\u3001\u300c\u30de\u30a4\u30ca\u30b9\u30bf\u30a4\u30eb\u300d\uff08\u6d88\u3048\u308b\u30bf\u30a4\u30eb\uff0f\u7a74\uff09\u304c\u8ffd\u52a0\u3055\u308c\u3001\u305d\u306e\u5206\u3001\u4f4e\u3044\u4f4d\u306e\u30bf\u30a4\u30eb\u304c10\u500b\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"6-umsetzung-in-der-app-didaktische-designentscheidungen\">\u30a2\u30d7\u30ea\u3078\u306e\u5b9f\u88c5\uff1a\u6559\u80b2\u8a2d\u8a08\u4e0a\u306e\u6c7a\u5b9a<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u306e\u8a2d\u8a08\u4e0a\u306e\u6c7a\u5b9a\u306f\u3001\u4e0a\u8a18\u3067\u6982\u8aac\u3057\u305f\u6559\u79d1\u56fa\u6709\u306e\u6559\u80b2\u539f\u5247\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-1-drei-repr-sentationen-synchron-das-eis-prinzip-operationalisiert\">\u8907\u6570\u306e\u8868\u73fe\u304c\u540c\u671f\u7684\u306b<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e2d\u5fc3\u7684\u306a\u6559\u8a13\u7684\u6c7a\u5b9a\u306f&nbsp;<strong>\u540c\u671f\u7d50\u5408<\/strong>&nbsp;\u8907\u6570\u306e\u8868\u73fe\u30ec\u30d9\u30eb: \u3059\u3079\u3066\u306e\u30a2\u30af\u30b7\u30e7\u30f3 (\u6570\u5b57\u306e\u5909\u66f4\u3001\u30b9\u30c6\u30c3\u30d7\u306e\u5b9f\u884c) \u306f\u3001\u8868\u8a18\u6cd5\u30012D \u30bf\u30a4\u30eb\u307e\u305f\u306f 3D \u30c7\u30a3\u30fc\u30f3\u3001\u304a\u3088\u3073\u8a00\u8a9e\u7684\u8a18\u8ff0\u306b\u540c\u6642\u306b\u5f71\u97ff\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u307e\u3055\u306b\u30d6\u30eb\u30fc\u30ca\u30fc (1966) \u304c\u8868\u73fe\u30b7\u30d5\u30c8\u3068\u8868\u73fe\u3057\u3001\u30af\u30e9\u30a6\u30c8\u30cf\u30a6\u30bc\u30f3 (2018) \u304c\u30c7\u30b8\u30bf\u30eb\u5b66\u7fd2\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u306e\u4e2d\u5fc3\u7684\u306a\u30bf\u30b9\u30af\u3068\u3057\u3066\u7279\u5b9a\u3057\u3066\u3044\u308b\u3082\u306e\u3067\u3059\u3002\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u81ea\u4f53\u304c\u76ee\u7684\u3067\u306f\u306a\u304f\u3001&nbsp;<em>\u69cb\u9020\u7684\u306b\u540c\u4e00<\/em>&nbsp;\u6570\u5b66\u7684\u306a\u95a2\u4fc2\u6027\u3092\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u5316\u3059\u308b\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5404\u30d1\u30cd\u30eb\u306e\u4e0a\u306b\u3042\u308b\u30ed\u30fc\u30e9\u30fc\u30b7\u30e3\u30c3\u30bf\u30fc\u306b\u3088\u308a\u3001\u6559\u5e2b\u306f\u9078\u629e\u7684\u306b&nbsp;<strong>1\u3064<\/strong>&nbsp;\u305d\u306e\u76ee\u7684\u306f\u3001\u3042\u308b\u30ec\u30d9\u30eb\u3092\u96a0\u853d\u3057\u3001\u5b50\u3069\u3082\u305f\u3061\u306b\u4ed6\u306e\u30ec\u30d9\u30eb\u304b\u3089\u7ffb\u8a33\u3055\u305b\u308b\u3053\u3068\u306b\u3042\u308b\u3002\u3053\u308c\u306f\u3001\u80fd\u52d5\u7684\u306b\u8868\u73fe\u306e\u5909\u5316\u3092\u8981\u6c42\u3057\u3001\u307e\u3059\u307e\u3059\u4e88\u6e2c\u3057\u3066\u3044\u304f\u3068\u3044\u3046\u3001\u64cd\u4f5c\u7684\u6559\u80b2\u5b66\uff08Wittmann &amp; M\u00fcller 1990 ff.\uff09\u306e\u8981\u6c42\u306b\u5408\u81f4\u3059\u308b\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u591a\u69d8\u306a\u65e2\u77e5\u8ab2\u984c\u3068\u8981\u6c42\u8ab2\u984c\u304c\u53ef\u80fd\u3068\u306a\u308b\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-2-verfahrenswahl-explizit\">\u624b\u7d9a\u304d\u306e\u660e\u793a\u7684\u306a\u9078\u629e<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u9023\u90a6\u5dde\u306e\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0\u306f\u7570\u306a\u308b\u624b\u9806\u3092\u597d\u3080\u305f\u3081\u3001\u30a2\u30d7\u30ea&nbsp;<strong>\u4e21\u65b9\u306e\u624b\u9806<\/strong>&nbsp;\u3053\u308c\u3089\u3092\u540c\u7b49\u306b\u6709\u52b9\u306a\u9078\u629e\u80a2\u3068\u3057\u3066\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u30014.3\u3067\u8ff0\u3079\u305f\u6df7\u5408\u306e\u30cf\u30fc\u30c9\u30eb\u306b\u3082\u5bfe\u51e6\u3057\u307e\u3059\u3002\u6559\u5e2b\u306f\u72ec\u81ea\u306e\u6559\u79d1\u66f8\u306e\u624b\u9806\u3092\u8a2d\u5b9a\u3059\u308b\u3068\u540c\u6642\u306b\u3001\u6bd4\u8f03\u306e\u305f\u3081\u306b\u4ee3\u66ff\u306e\u624b\u9806\u3082\u53ef\u80fd\u6027\u3068\u3057\u3066\u793a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u5b50\u3069\u3082\u306f\u81ea\u5206\u306e\u601d\u8003\u6226\u7565\u3092\u7279\u5b9a\u306e\u624b\u9806\u306b\u660e\u78ba\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u306a\u3044\u3053\u3068\u304c\u591a\u3044\u304b\u3089\u3067\u3059\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-3-sprachausgabe-als-modell-sprache\">\u97f3\u58f0\u51fa\u529b\u3092\u30e2\u30c7\u30eb\u8a00\u8a9e\u3068\u3057\u3066\u7528\u3044\u308b<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u97f3\u58f0\u51fa\u529b\u306f\u4e00\u8cab\u3057\u3066&nbsp;<strong>\u6280\u8853\u7684\u306b\u6b63\u3057\u3044\u7528\u8a9e<\/strong>\u300c\u307e\u3068\u3081\u308b\u300d\u300c\u53d6\u308a\u51fa\u3059\u300d\u300c\u7e70\u308a\u4e0a\u304c\u308a\u300d\u300c\u88ab\u6e1b\u6570\u300d\u300c\u6e1b\u6570\u300d\u3068\u3044\u3063\u305f\u8a00\u8449\u304c\u4f7f\u308f\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5b50\u3069\u3082\u305f\u3061\u304c\u8a00\u8a9e\u7684\u306a\u624b\u5f15\u304d\u3068\u3057\u3066\u4f7f\u3048\u308b\u8aac\u660e\u7684\u306a\u624b\u9806\u3078\u3068\u5909\u63db\u3055\u308c\u307e\u3059\u3002\u5b50\u3069\u3082\u305f\u3061\u306f\u3053\u306e\u8a00\u8a9e\u30e2\u30c7\u30eb\u3092\u30c6\u30f3\u30d7\u30ec\u30fc\u30c8\u3068\u3057\u3066\u3001\u81ea\u5206\u306e\u8a00\u8449\u3067\u7ffb\u8a33\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306fQuaMath\u306e\u539f\u7406\u306b\u5408\u81f4\u3057\u3066\u3044\u307e\u3059\u3002&nbsp;<em>\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u306e\u4fc3\u9032<\/em>&nbsp;\uff08QuaMath 2024\uff09\u3068&nbsp;<em>\u6570\u5b66\u306f\u9593\u9055\u3044\u306a\u304f\u3067\u304d\u308b<\/em>\u666e\u53ca\u3057\u305f\u5b9f\u8df5,&nbsp;<strong>\u8a00\u8a9e\u5316<\/strong>&nbsp;\u6570\u5b66\u7684\u7406\u89e3\u306e\u4e2d\u5fc3\u7684\u306a\u90e8\u5206\u3068\u3057\u3066\u6271\u3046\uff08Selter et al. 2014\uff09\u3002. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-4-vorhersage-aufgaben-formatives-lernen-als-mini-diagnose\">\u4e88\u6e2c\u30bf\u30b9\u30af<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u30aa\u30d7\u30b7\u30e7\u30f3\u00a0<strong>\u4e88\u5831<\/strong>\u00a0\u5404\u30b9\u30c6\u30c3\u30d7\u306e\u524d\u306b\u3001\u00a0<em>\u4e88\u6e2c\u30fb\u89b3\u5bdf\u30fb\u8aac\u660e<\/em>\u79d1\u5b66\u6559\u80b2\u306e\u5f62\u5f0f\uff08\u30db\u30ef\u30a4\u30c8\uff06\u30ac\u30f3\u30b9\u30c8\u30fc\u30f3 1992\uff09\u3002\u5358\u306b\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3092\u898b\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u5404\u30b9\u30c6\u30c3\u30d7\u306f\u9069\u5207\u306a\u8cea\u554f\u306b\u3088\u3063\u3066\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u00a0<em>\u3053\u3053\u3067\u4f55\u304c\u8d77\u3053\u3063\u3066\u3044\u308b\u306e\u3067\u3059\u304b\uff1f\u3053\u3053\u3067\u4f55\u3092\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3059\u304b\uff1f\u3069\u308c\u304c\u3082\u3063\u3068\u3082\u3089\u3057\u304f\u898b\u3048\u308b\u304c\u3001\u5b9f\u969b\u306b\u306f\u9593\u9055\u3063\u3066\u3044\u308b\u9078\u629e\u80a2\u3067\u3059\u304b\uff1f<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u30a2\u30d7\u30ea\u306e\u59a8\u5bb3\u8981\u7d20\u306f\u3001\u4f8b\u3048\u3070\u3001\u6587\u66f8\u5316\u3055\u308c\u305f\u30a8\u30e9\u30fc\u6226\u7565\u3092\u610f\u56f3\u7684\u306b\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002&nbsp;<em>\u201e\u300c\u5927\u304d\u3044\u65b9\u304b\u3089\u5c0f\u3055\u3044\u65b9\u3092\u5f15\u304f\u300d\u201c<\/em>, \u30a8\u30e9\u30fc\u5206\u6790\u6587\u732e\u306b\u57fa\u3065\u304f\u3068\u3001\u7e70\u308a\u4e0a\u304c\u308a\u306e\u5fd8\u308c\u3001\u4f4d\u53d6\u308a\u306e\u53cd\u8ee2\u3001\u624b\u7d9a\u304d\u4e0a\u306e\u6df7\u4e71\u306a\u3069\u304c\u751f\u3058\u308b\u3002(Schipper 1983, 2009; Padberg &amp; Benz 2021; Wartha &amp; Schulz 2014; KIRA 2024)\u3002&nbsp;<em>\u8a8d\u77e5\u6d3b\u6027\u5316<\/em> \uff08QuaMath 2024\uff09\u304c\u958b\u50ac\u3055\u308c\u307e\u3059\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-5-adaptive-schwierigkeit-datengeleitete-bung\">\u30bf\u30b9\u30af\u751f\u6210\u5668\u3068\u9069\u5fdc\u578b\u96e3\u6613\u5ea6<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u30bf\u30b9\u30af\u751f\u6210\u6a5f\u80fd\u306f\u8907\u6570\u306e\u96e3\u6613\u5ea6\u30ec\u30d9\u30eb\u3092\u63d0\u4f9b\u3057\u3001\u300c\u9069\u5fdc\u578b\u300d\u30e2\u30fc\u30c9\u3067\u306f\u3001\u4e88\u6e2c\u6210\u529f\u7387\u306b\u57fa\u3065\u3044\u3066\u6b21\u306b\u63d0\u793a\u3055\u308c\u308b\uff08\u300c\u30ed\u30fc\u30eb\u30a2\u30a6\u30c8\u3055\u308c\u308b\u300d\uff09\u30bf\u30b9\u30af\u306e\u96e3\u6613\u5ea6\u3092\u8abf\u6574\u3057\u307e\u3059\u3002. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-6-tipp-aufgaben-material-basierte-diagnose\">\u4eee\u60f3\u30a2\u30af\u30b7\u30e7\u30f3\uff1a\u8868\u73fe\u9593\u306e\u95a2\u4fc2\u6027\u3078\u306e\u6311\u6226<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u7279\u5b9a\u306e\u30d5\u30a7\u30fc\u30ba\uff08\u7e70\u308a\u8d8a\u3057\u3001\u62e1\u5f35\u4fee\u6b63\u306e\u5165\u529b\uff09\u3067\u306f\u3001\u591a\u80a2\u9078\u629e\u554f\u984c\u306f&nbsp;<strong>\u30d2\u30f3\u30c8\u30bf\u30b9\u30af<\/strong>&nbsp;\u6559\u6750\u3084\u8868\u8a18\u6cd5\u304c\u7f6e\u304d\u63db\u3048\u3089\u308c\u307e\u3059\u3002\u5b50\u3069\u3082\u306f\u6b63\u3057\u3044\u5217\u3092\u76f4\u63a5\u6307\u3057\u793a\u3059\u3053\u3068\u3067\u3001\u56f3\u50cf\u7684\u30fb\u8a18\u53f7\u7684\u306a\u30ec\u30d9\u30eb\u3067\u5b66\u7fd2\u3092\u9032\u3081\u307e\u3059\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"7-grenzen-forschungsbedarf-und-praxis-empfehlungen\">\u9650\u754c\u3001\u7814\u7a76\u30cb\u30fc\u30ba\u3001\u304a\u3088\u3073\u5b9f\u8df5\u7684\u306a\u63d0\u8a00<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u30a2\u30d7\u30ea\u306e\u53ef\u80fd\u6027\u306f\u591a\u5c90\u306b\u308f\u305f\u308b\u304c\u3001\u00a0<strong>\u6709\u5f62\u7269<\/strong>\u00a0\uff08\u89e6\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u30c7\u30a3\u30fc\u30f3\u30ba\u30ad\u30e5\u30fc\u30d6\uff09\u305d\u3057\u3066\u00a0<strong>\u6570\u5b66\u306b\u3064\u3044\u3066\u8a71\u3059<\/strong>\u00a0\u6388\u696d\u3068\u3044\u3046\u793e\u4f1a\u7684\u7a7a\u9593\u306b\u304a\u3044\u3066\u3001\u30af\u30e9\u30a6\u30c8\u30cf\u30a6\u30bc\u30f3\uff082018\u5e74\u3001215\u9801\u4ee5\u964d\uff09\u306f\u3001\u30c7\u30b8\u30bf\u30eb\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u304c\u89e6\u899a\u4f53\u9a13\u3092\u5411\u4e0a\u3055\u305b\u308b\u3068\u6307\u6458\u3057\u3066\u3044\u308b\u3002\u00a0<em>\u306b\u8ffd\u52a0<\/em>, \u53e3\u982d\u6307\u5c0e\u306b\u53d6\u3063\u3066\u4ee3\u308f\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u53e3\u982d\u3067\u306e\u5b66\u7fd2\u306b\u3064\u3044\u3066\u3082\u540c\u69d8\u3067\u3001\u6570\u5b66\u306b\u95a2\u3059\u308b\u30b3\u30df\u30e5\u30cb\u30b1\u30fc\u30b7\u30e7\u30f3\u306f\u4e0d\u53ef\u6b20\u3067\u3042\u308a\u3001\u59d4\u4efb\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\uff08QuaMath 2024\uff09\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u30a2\u30d7\u30ea\u306f\u88dc\u52a9\u6559\u6750\u3068\u3057\u3066\u3001\u7279\u306b\u81ea\u4e3b\u5b66\u7fd2\u3084\u7814\u7a76\u8ab2\u984c\u306e\u67a0\u7d44\u307f\u306e\u4e2d\u3067\u6d3b\u7528\u3067\u304d\u307e\u3059\uff08\u30a2\u30d7\u30ea\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u30a2\u30a4\u30c7\u30a2\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\uff09\u3002.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"literaturverzeichnis\">\u6587\u5b66<\/h3>\n\n\n\n<ul class=\"wp-block-list literatur\">\n<li><strong>Barzel\u3001B.\u3001Gasteiger\u3001H.\u3001Greefrath\u3001G.\u3001Maritzen\u3001N.\u3001N\u00fchrenb\u00f6rger\u3001M.\u3001\u30b9\u30bf\u30ca\u30c3\u30c8\u3001P.<\/strong>&nbsp;\uff082023\u5e74\uff09\u521d\u7b49\u6559\u80b2\u304a\u3088\u3073\u524d\u671f\u4e2d\u7b49\u6559\u80b2\u306b\u304a\u3051\u308b\u6570\u5b66\u306e\u6559\u80b2\u57fa\u6e96\u306e\u3055\u3089\u306a\u308b\u767a\u5c55\u3002.&nbsp;<em>\u6570\u5b66\u6559\u6388\u5b66\u4f1a\u901a\u4fe1<\/em>.&nbsp;<a href=\"https:\/\/ojs.didaktik-der-mathematik.de\/index.php\/mgdm\/article\/view\/1113\">https:\/\/ojs.didaktik-der-mathematik.de\/index.php\/mgdm\/article\/view\/1113<\/a><\/li>\n\n\n\n<li><strong>\u30d6\u30eb\u30fc\u30ca\u30fc\u3001JS.<\/strong>&nbsp;(1966).&nbsp;<em>\u6307\u5c0e\u7406\u8ad6\u306b\u5411\u3051\u3066<\/em>. \u30b1\u30f3\u30d6\u30ea\u30c3\u30b8\u3001\u30de\u30b5\u30c1\u30e5\u30fc\u30bb\u30c3\u30c4\u5dde\uff1a\u30cf\u30fc\u30d0\u30fc\u30c9\u5927\u5b66\u51fa\u7248\u5c40\u3002.<\/li>\n\n\n\n<li><strong>\u30af\u30e9\u30a6\u30c8\u30cf\u30a6\u30bc\u30f3\u3001G.<\/strong>&nbsp;(2018).&nbsp;<em>\u6570\u5b66\u6559\u80b2\u6cd5\u5165\u9580 \u2015 \u5c0f\u5b66\u6821<\/em>&nbsp;\uff08\u7b2c4\u7248\uff09\u3002\u30d9\u30eb\u30ea\u30f3\uff0f\u30cf\u30a4\u30c7\u30eb\u30d9\u30eb\u30af\uff1a\u30b7\u30e5\u30d7\u30ea\u30f3\u30ac\u30fc\u30fb\u30b9\u30da\u30af\u30c8\u30e9\u30e0\u3002.<\/li>\n\n\n\n<li><strong>\u30d1\u30c9\u30d0\u30fc\u30b0\u3001F. &amp; \u30d9\u30f3\u30c4\u3001C.<\/strong>&nbsp;(2021).&nbsp;<em>\u7b97\u8853\u306e\u6559\u6388\u6cd5 \u2015 \u3057\u3063\u304b\u308a\u3068\u3057\u305f\u6839\u62e0\u306b\u57fa\u3065\u304d\u3001\u591a\u7528\u9014\u3067\u3001\u5b9f\u8df5\u7684<\/em>&nbsp;\uff08\u7b2c5\u7248\uff09\u3002\u30d9\u30eb\u30ea\u30f3\/\u30cf\u30a4\u30c7\u30eb\u30d9\u30eb\u30af: Springer Spektrum\u3002.<\/li>\n\n\n\n<li><strong>\u8aac\u6559\u8005\u3001S.<\/strong>&nbsp;\uff082024\u5e74\uff09\u300c\u6570\u5b66\u306f\u82e6\u75db\u3067\u3042\u308b\u5fc5\u8981\u306f\u306a\u3044\u300d\u3002\u30c9\u30a4\u30c4\u306e\u5b66\u6821\u30dd\u30fc\u30bf\u30eb\u30b5\u30a4\u30c8\u306b\u63b2\u8f09\u3055\u308c\u305f\u8a18\u4e8b\u3002.&nbsp;<a href=\"https:\/\/deutsches-schulportal.de\/expertenstimmen\/susanne-prediger-didaktik-mathematik-muss-nicht-wehtun\/\">https:\/\/deutsches-schulportal.de\/expertenstimmen\/susanne-prediger-didaktik-mathematik-muss-nicht-wehtun\/<\/a><\/li>\n\n\n\n<li><strong>\u30d7\u30ec\u30c7\u30a3\u30ac\u30fc\u3001S. &amp; \u30bb\u30eb\u30bf\u30fc\u3001C.<\/strong>&nbsp;(2014).&nbsp;<em>\u6570\u5b66\u6559\u80b2\u6700\u65b0\u60c5\u5831 \u2015 \u6559\u80b2\u3068\u5b66\u7fd2\u7814\u7a76\u304a\u3088\u3073\u6559\u54e1\u990a\u6210\u306b\u95a2\u3059\u308b\u6700\u65b0\u306e\u8996\u70b9<\/em>.&nbsp;<a href=\"https:\/\/wwwold.mathematik.tu-dortmund.de\/%3Csub%3Eprediger\/veroeff\/14-FuCo-Prediger-Selter.pdf\">https:\/\/wwwold.mathematik.tu-dortmund.de\/prediger\/veroeff\/14-FuCo-Prediger-Selter.pdf<\/a><\/li>\n\n\n\n<li><strong>\u30b7\u30c3\u30d1\u30fc\u3001W.<\/strong>&nbsp;(1983).&nbsp;<em>\u81ea\u7136\u6570\u306e\u7b46\u7b97\u306b\u3088\u308b\u5f15\u304d\u7b97\u306b\u304a\u3051\u308b\u5178\u578b\u7684\u306a\u751f\u5f92\u306e\u8aa4\u308a<\/em>. \u30d3\u30fc\u30ec\u30d5\u30a7\u30eb\u30c8\u5927\u5b66\u3002.&nbsp;<a href=\"https:\/\/pub.uni-bielefeld.de\/record\/1775198\">https:\/\/pub.uni-bielefeld.de\/record\/1775198<\/a><\/li>\n\n\n\n<li><strong>\u30b7\u30c3\u30d1\u30fc\u3001W.<\/strong>&nbsp;(2009).&nbsp;<em>\u5c0f\u5b66\u6821\u306b\u304a\u3051\u308b\u6570\u5b66\u6307\u5c0e\u306e\u305f\u3081\u306e\u30cf\u30f3\u30c9\u30d6\u30c3\u30af<\/em>. \u30d6\u30e9\u30a6\u30f3\u30b7\u30e5\u30f4\u30a1\u30a4\u30af\uff1a\u30b7\u30e5\u30ec\u30fc\u30c7\u30eb\u3002.<\/li>\n\n\n\n<li><strong>\u30bb\u30eb\u30bf\u30fc\u3001C.<\/strong>&nbsp;\uff081995\u5e74\uff09\u521d\u671f\u7b97\u6570\u6559\u80b2\u306b\u304a\u3051\u308b\u300c\u30bc\u30ed\u6642\u9593\u300d\u306e\u865a\u69cb\u6027\u306b\u3064\u3044\u3066\u3002.&nbsp;<em>\u6570\u5b66\u6559\u80b2\u5b9f\u8df5<\/em>, \u300116(2)\u300111\u201319\u3002.<\/li>\n\n\n\n<li><strong>\u30bb\u30eb\u30bf\u30fc\u3001C.\u3001\u30d7\u30ec\u30c7\u30a3\u30ac\u30fc\u3001S.\u3001\u30cb\u30e5\u30fc\u30ec\u30f3\u30d9\u30eb\u30ac\u30fc\u3001M.\u3001\u30d5\u30b9\u30de\u30f3\u3001S. (\u7de8\u8457)<\/strong>&nbsp;(2014).&nbsp;<em>\u81ea\u4fe1\u3092\u6301\u3063\u3066\u6570\u5b66\u3092\u30de\u30b9\u30bf\u30fc\u3059\u308b \u2015 \u57fa\u672c\u7684\u306a\u6570\u5b66\u30b9\u30ad\u30eb\u3092\u78ba\u5b9f\u306b\u8eab\u306b\u3064\u3051\u308b\u305f\u3081\u306e\u8a3a\u65ad\u3068\u30b5\u30dd\u30fc\u30c8\u306e\u6982\u5ff5\u3002.<\/em>&nbsp;\u30c6\u30fc\u30de\u5225\u30e2\u30b8\u30e5\u30fc\u30eb\u300c\u81ea\u7136\u6570\u300d\u3002\u30d9\u30eb\u30ea\u30f3\uff1a\u30b3\u30eb\u30cd\u30eb\u30bc\u30f3\u3002.<\/li>\n\n\n\n<li><strong>\u30ef\u30eb\u30bf\u3001S. &amp; \u30b7\u30e5\u30eb\u30c4\u3001A.<\/strong>&nbsp;(2014).&nbsp;<em>\u8a08\u7b97\u4e0a\u306e\u554f\u984c\u3092\u9632\u6b62\u3059\u308b<\/em>&nbsp;\uff08\u7b2c2\u7248\uff09\u3002\u30d9\u30eb\u30ea\u30f3\uff1a\u30b3\u30eb\u30cd\u30eb\u30bc\u30f3\u3002.<\/li>\n\n\n\n<li><strong>\u30db\u30ef\u30a4\u30c8\u3001R. &amp; \u30ac\u30f3\u30b9\u30c8\u30fc\u30f3\u3001R.<\/strong>&nbsp;(1992).&nbsp;<em>\u7406\u89e3\u3092\u6df1\u3081\u308b<\/em>. \u30ed\u30f3\u30c9\u30f3\uff1a\u30d5\u30a1\u30eb\u30de\u30fc\u30fb\u30d7\u30ec\u30b9\u3002.<\/li>\n\n\n\n<li><strong>\u30a6\u30a3\u30c3\u30c8\u30de\u30f3\u3001E. Ch. \u304a\u3088\u3073\u30df\u30e5\u30e9\u30fc\u3001GN.<\/strong>&nbsp;\uff081990\u5e74\u4ee5\u964d\uff09.&nbsp;<em>\u751f\u7523\u7684\u306a\u7b97\u8853\u6f14\u7fd2\u30cf\u30f3\u30c9\u30d6\u30c3\u30af<\/em>, \u7b2c 1 \u5dfb\u3068\u7b2c 2 \u5dfb\u3002\u30b7\u30e5\u30c4\u30c3\u30c8\u30ac\u30eb\u30c8: \u30af\u30ec\u30c3\u30c8\u3002.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"bildungspolitische-dokumente\">\u6559\u80b2\u653f\u7b56\u6587\u66f8<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"literatur\"><strong>KMK \u2015 \u6559\u80b2\u6587\u5316\u5927\u81e3\u5e38\u8a2d\u4f1a\u8b70<\/strong>&nbsp;(2022).&nbsp;<em>\u6570\u5b66\u306e\u6559\u80b2\u57fa\u6e96\u3002\u5c0f\u5b66\u6821\u30ec\u30d9\u30eb\u3002.<\/em>&nbsp;2022\u5e746\u670823\u65e5\u306e\u6c7a\u5b9a\u3002\u30d9\u30eb\u30ea\u30f3\u3002.&nbsp;<a href=\"https:\/\/www.kmk.org\/fileadmin\/Dateien\/veroeffentlichungen_beschluesse\/2022\/2022_06_23-Bista-Primarbereich-Mathe.pdf\">https:\/\/www.kmk.org\/fileadmin\/Dateien\/veroeffentlichungen_beschluesse\/2022\/2022_06_23-Bista-Primarbereich-Mathe.pdf<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>KMK \u2015 \u6559\u80b2\u6587\u5316\u5927\u81e3\u5e38\u8a2d\u4f1a\u8b70<\/strong>&nbsp;(2023).&nbsp;<em>\u6570\u5b66\u306e\u6559\u80b2\u57fa\u6e96\u3002\u5c0f\u5b66\u6821\u304a\u3088\u3073\u4e2d\u5b66\u6821\u524d\u671f\u6559\u80b2\u306b\u304a\u3051\u308b\u5b9f\u65bd\u8981\u89a7\u3002.<\/em>&nbsp;\u30d9\u30eb\u30ea\u30f3\u3002.&nbsp;<a href=\"https:\/\/www.kmk.org\/fileadmin\/Dateien\/pdf\/Bildung\/Qualitaet\/ImplBroschu__re_BiSta_MATHEMATIK_2023-03-23.pdf\">https:\/\/www.kmk.org\/fileadmin\/Dateien\/pdf\/Bildung\/Qualitaet\/ImplBroschu__re_BiSta_MATHEMATIK_2023-03-23.pdf<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>KMK &amp; DZLM<\/strong>&nbsp;(2023).&nbsp;<em>10\u5e74\u9593\u306eQuaMath\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u95a2\u3059\u308b\u5408\u610f\u3002.<\/em>&nbsp;\u30d7\u30ec\u30b9\u30ea\u30ea\u30fc\u30b9\u3002.&nbsp;<a href=\"https:\/\/dzlm.de\/aktuelles\/kmk_dzlm_quamath\">https:\/\/dzlm.de\/aktuelles\/kmk_dzlm_quamath<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>\u30d0\u30a4\u30a8\u30eb\u30f3\u5dde\u6559\u80b2\u6587\u5316\u7701<\/strong>&nbsp;(2024).&nbsp;<em>CurriculumPLUS \u5c0f\u5b66\u6821 - \u7b97\u6570.<\/em><a href=\"https:\/\/www.lehrplanplus.bayern.de\/fachlehrplan\/grundschule\/3\/mathematik\">https:\/\/www.lehrplanplus.bayern.de\/fachlehrplan\/grundschule\/3\/mathematik<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>\u30cb\u30fc\u30c0\u30fc\u30b6\u30af\u30bb\u30f3\u5dde\u6559\u80b2\u7701<\/strong>&nbsp;(2024).&nbsp;<em>\u5c0f\u5b66\u6821\u306e\u4e3b\u8981\u30ab\u30ea\u30ad\u30e5\u30e9\u30e0 \u2015 \u6570\u5b66\u3002.<\/em>\uff08\u97f3\u58f0\u7248\uff09.&nbsp;<a href=\"https:\/\/www.mk.niedersachsen.de\/download\/211766\/KC_Mathematik_fuer_die_Grundschule.pdf\">https:\/\/www.mk.niedersachsen.de\/download\/211766\/KC_Mathematik_fuer_die_Grundschule.pdf<\/a><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"online-plattformen-und-f-rderprogramme\">\u30aa\u30f3\u30e9\u30a4\u30f3\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u3068\u8cc7\u91d1\u63d0\u4f9b\u30d7\u30ed\u30b0\u30e9\u30e0<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"literatur\"><strong>\u30c7\u30a3\u30dc\u30de\u30b9<\/strong>&nbsp;\u2014 \u30c9\u30eb\u30c8\u30e0\u30f3\u30c8\u5de5\u79d1\u5927\u5b66\u306b\u3088\u308b\u3001\u5c0f\u5b663\u5e74\u751f\u304b\u30896\u5e74\u751f\u5411\u3051\u306e\u30c7\u30b8\u30bf\u30eb\u6559\u80b2\u30fb\u5b66\u7fd2\u74b0\u5883\u3002.&nbsp;<a href=\"https:\/\/www.schulministerium.nrw\/divomath-mathematische-basiskompetenzen-digital-und-verstehensorientiert-foerdern\">https:\/\/www.schulministerium.nrw\/divomath-mathematische-basiskompetenzen-digital-und-verstehensorientiert-foerdern<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>\u30ad\u30e9<\/strong>&nbsp;\u2014&nbsp;<em>\u5b50\u3069\u3082\u305f\u3061\u306e\u8a08\u7b97\u65b9\u6cd5\u306f\u305d\u308c\u305e\u308c\u7570\u306a\u308b\u3002.<\/em>&nbsp;\u30c9\u30eb\u30c8\u30e0\u30f3\u30c8\u5de5\u79d1\u5927\u5b66 \/ DZLM\u3002.&nbsp;<a href=\"https:\/\/kira.dzlm.de\/\">https:\/\/kira.dzlm.de<\/a>&nbsp;\uff08\u7279\u306b\uff09.&nbsp;<a href=\"https:\/\/kira.dzlm.de\/zahlen-und-operationen\/schriftliches-rechnen\/typische-fehler-bei-der-schriftlichen-subtraktion\">https:\/\/kira.dzlm.de\/zahlen-und-operationen\/schriftliches-rechnen\/typische-fehler-bei-der-schriftlichen-subtraktion<\/a>)<\/li>\n\n\n\n<li class=\"literatur\"><strong>\u6570\u5b66\u306f\u9593\u9055\u3044\u306a\u304f\u3067\u304d\u308b<\/strong>&nbsp;\u2014 \u30aa\u30f3\u30e9\u30a4\u30f3\u8cc7\u6599\u3002\u30c9\u30eb\u30c8\u30e0\u30f3\u30c8\u5de5\u79d1\u5927\u5b66 \/ DZLM\u3002.&nbsp;<a href=\"https:\/\/mathe-sicher-koennen.dzlm.de\/\">https:\/\/mathe-sicher-koennen.dzlm.de<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>\u30d4\u30ab\u30b9<\/strong>&nbsp;\u2014&nbsp;<em>\u30d7\u30ed\u30bb\u30b9\u304a\u3088\u3073\u30b3\u30f3\u30c6\u30f3\u30c4\u306b\u95a2\u9023\u3059\u308b\u80fd\u529b\u3002.<\/em>\u30c9\u30eb\u30c8\u30e0\u30f3\u30c8\u5de5\u79d1\u5927\u5b66 \/ DZLM\u3002.&nbsp;<a href=\"https:\/\/pikas.dzlm.de\/\">https:\/\/pikas.dzlm.de<\/a>&nbsp;\uff08\u7279\u306b\uff09.&nbsp;<a href=\"https:\/\/pikas.dzlm.de\/unterricht\/zahlen-und-operationen\/zahlenraum-bis-1000\/schriftliche-addition\">https:\/\/pikas.dzlm.de\/unterricht\/zahlen-und-operationen\/zahlenraum-bis-1000\/schriftliche-addition<\/a>\u305d\u3057\u3066&nbsp;<a href=\"https:\/\/pikas.dzlm.de\/unterricht\/zahlen-und-operationen\/zahlenraum-bis-1000\/schriftliche-subtraktion\">https:\/\/pikas.dzlm.de\/unterricht\/zahlen-und-operationen\/zahlenraum-bis-1000\/schriftliche-subtraktion<\/a>)<\/li>\n\n\n\n<li class=\"literatur\"><strong>\u30d7\u30ea\u30de\u30b3\u30e0<\/strong>&nbsp;\u2014&nbsp;<em>\u5c0f\u5b66\u6821\u306e\u7b97\u6570\u3092\u7c21\u6f54\u306b\u307e\u3068\u3081\u308b\u3068\u3053\u3046\u306a\u308a\u307e\u3059\u3002.<\/em>&nbsp;\u30c9\u30eb\u30c8\u30e0\u30f3\u30c8\u5de5\u79d1\u5927\u5b66 \/ DZLM\u3002.&nbsp;<a href=\"https:\/\/primakom.dzlm.de\/\">https:\/\/primakom.dzlm.de<\/a><\/li>\n\n\n\n<li class=\"literatur\"><strong>\u30af\u30a2\u30de\u30b9<\/strong>&nbsp;\u2014&nbsp;<em>\u6570\u5b66\u306b\u304a\u3051\u308b\u6559\u80b2\u306e\u8cea\u3068\u5c02\u9580\u80fd\u529b\u958b\u767a\u3002.<\/em>&nbsp;DZLM \/ IPN\u3002.&nbsp;<a href=\"https:\/\/quamath.de\/\">https:\/\/quamath.de\/<\/a><\/li>\n<\/ul>","protected":false},"excerpt":{"rendered":"<p>Eine App f\u00fcr die verst\u00e4ndnisorientierte Erkundung der schriftliche Addition und Subtraktion. Die App zeigt jede Rechnung gleichzeitig in mehreren Repr\u00e4sentationen: Wer in der Notation eine Ziffer \u00e4ndert, sieht in den anderen Darstellungen sofort, was sich ver\u00e4ndert. Der B\u00fcndelungs- und Entb\u00fcndelungs\u00adprozess wird nicht nur beschrieben, sondern animiert sichtbar. Zehn Einer b\u00fcndeln sich in einen einzelnen Zehner, eine Hundertplatte wird entb\u00fcndelt in zehn Zehnerstangen. Subtraktionsverfahren Die App beherrscht beide in Deutschland verbreiteten Subtraktionsverfahren: Beide Verfahren sind im selben Aufgabenkontext umschaltbar. Auch das schwierige&nbsp;kaskadierte Entb\u00fcndeln&nbsp;(etwa bei&nbsp;900 \u2212 191, wo eine geborgte Einheit \u00fcber mehrere Stellen wandern muss) wird vollst\u00e4ndig animiert und sprachlich begleitet. Vorhersage-Aufgaben Optional kann die App vor jedem Schritt eine Multiple-Choice-Frage [&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-998","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/pages\/998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/comments?post=998"}],"version-history":[{"count":6,"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/pages\/998\/revisions"}],"predecessor-version":[{"id":1008,"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/pages\/998\/revisions\/1008"}],"wp:attachment":[{"href":"https:\/\/urff.app\/ja\/wp-json\/wp\/v2\/media?parent=998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}