{"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\/zh\/schriftlich-rechnen\/","title":{"rendered":"\u7b14\u7b97"},"content":{"rendered":"<p class=\"wp-block-paragraph\"><strong>\u4e00\u6b3e\u65e8\u5728\u5e2e\u52a9\u7528\u6237\u7406\u89e3\u5e76\u63a2\u7d22\u4e66\u9762\u52a0\u51cf\u8fd0\u7b97\u7684\u5e94\u7528\u7a0b\u5e8f\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=\"\u7b14\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=\"\u7b14\u7b97\">\u4e0b\u8f7d<\/a>\n\t\t\t<span onmouseover=\"jQuery('.wpappbox-7890478185b442ef39218ed825cd8c32 .qrcode').show();\" onmouseout=\"jQuery('.wpappbox-7890478185b442ef39218ed825cd8c32 .qrcode').hide();\">\u4e8c\u7ef4\u7801<\/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=\"\u7b14\u7b97\" aria-label=\"\u7b14\u7b97\" class=\"apptitle\">\u7b14\u7b97<\/a><\/div>\n\t\t<div class=\"developer\">\n\t\t\t<span class=\"label\">\u5f00\u53d1\u5546\uff1a <\/span>\n\t\t\t<span class=\"value\"><a target=\"_blank\" rel=\"nofollow\" href=\"https:\/\/apps.apple.com\/de\/developer\/christian-urff\/id415894463\">\u514b\u91cc\u65af\u8482\u5b89\u00b7\u4e4c\u5c14\u592b<\/a><\/span>\n\t\t<\/div>\n\t\t<div class=\"price\">\n\t\t\t<span class=\"label\">\u4ef7\u683c\uff1a <\/span>\n\t\t\t<span class=\"value\">0,99\u00a0\u20ac<\/span> \n\t\t\t<span class=\"rating\"><div title=\"0 \u661f\uff08\u6ee1\u5206 5 \u661f\uff09\" 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\">\u8be5\u5e94\u7528\u7a0b\u5e8f\u4ee5\u591a\u79cd\u5f62\u5f0f\u540c\u65f6\u663e\u793a\u6bcf\u5f20\u53d1\u7968\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u7b26\u53f7<\/strong>\uff1a\u7ecf\u5178\u7684\u4f4d\u503c\u8868\uff0c\u5305\u542b\u6570\u5b57\u3001\u8fdb\u4f4d\u548c\u51cf\u4f4d\uff0c\u5c31\u50cf\u5728\u7b14\u8bb0\u672c\u4e0a\u5199\u7684\u90a3\u6837\u3002.<\/li>\n\n\n\n<li><strong>\u76d8\u5b50<\/strong>\uff1a\u4e00\u79cd\u4e8c\u7ef4\u4f4d\u503c\u8868\uff0c\u5176\u4e2d\u6bcf\u4e2a\u4f4d\u503c\u90fd\u7528\u81ea\u5df1\u7684\u4e00\u5217\u8868\u793a\uff0c\u5e76\u4e14\u6346\u7ed1\u6216\u89e3\u7ed1\u65f6\uff0c\u65b9\u5757\u4f1a\u660e\u663e\u79fb\u52a8\u3002.<\/li>\n\n\n\n<li><strong>\u4e8c\u70ef3D<\/strong>\u8fd9\u662f\u4e00\u4e2a\u7531\u7acb\u65b9\u4f53\u3001\u68d2\u72b6\u7269\u3001\u677f\u72b6\u7269\u548c\u6570\u5343\u4e2a\u7acb\u65b9\u4f53\u7ec4\u6210\u7684\u7b49\u8ddd\u89c6\u56fe\u3002\u5b83\u4f7f\u4f4d\u503c\u4e4b\u95f4\u7684\u7a7a\u95f4\u5173\u7cfb\u4e00\u76ee\u4e86\u7136\u2014\u201410 \u662f 1 \u7684\u5341\u500d\uff0c100 \u662f 10 \u7684\u5341\u500d\u3002.<\/li>\n\n\n\n<li><strong>\u8bed\u8a00\u652f\u6301<\/strong>\u6bcf\u4e00\u6b65\u90fd\u6709\u4e66\u9762\u548c\u8bed\u97f3\u4e24\u79cd\u5f62\u5f0f\u7684\u6307\u5bfc\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b26\u53f7\u4e2d\u4efb\u4f55\u4e00\u4e2a\u6570\u5b57\u7684\u6539\u53d8\uff0c\u90fd\u4f1a\u7acb\u5373\u53cd\u6620\u5728\u5176\u4ed6\u8868\u793a\u5f62\u5f0f\u4e2d\u7684\u76f8\u5e94\u53d8\u5316\u3002\u6346\u7ed1\u548c\u89e3\u6346\u7ed1\u7684\u8fc7\u7a0b\u4e0d\u4ec5\u6709\u6587\u5b57\u63cf\u8ff0\uff0c\u8fd8\u6709\u52a8\u753b\u6f14\u793a\u3002\u5341\u4e2a\u4e00\u6346\u7ed1\u6210\u4e00\u4e2a\u5341\uff0c\u4e00\u767e\u5f20\u7eb8\u53ef\u4ee5\u89e3\u6346\u7ed1\u6210\u5341\u6839\u5341\u7684\u7eb8\u6761\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"beide-subtraktionsverfahren\">\u51cf\u6cd5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u5e94\u7528\u7a0b\u5e8f\u652f\u6301\u5fb7\u56fd\u5e38\u7528\u7684\u4e24\u79cd\u51cf\u6cd5\u65b9\u6cd5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u89e3\u7ed1<\/strong>&nbsp;\uff08\u51cf\u6cd5\uff09\uff1a\u88ab\u51cf\u6570\u7684\u6b21\u9ad8\u4f4d\u6570\u5b57\u51cf 1\uff0c\u5f53\u524d\u5217\u52a0 10 \u4e2a\u5355\u4f4d\u3002.<\/li>\n\n\n\n<li><strong>\u6269\u5f20<\/strong>&nbsp;\uff08\u586b\u7a7a\u6cd5\uff09\uff1a\u51cf\u6570\u5728\u4e0b\u4e00\u5217\u4e2d\u52a0 1\uff0c\u88ab\u51cf\u6570\u4fdd\u6301\u4e0d\u53d8\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e24\u79cd\u65b9\u6cd5\u53ef\u4ee5\u5728\u540c\u4e00\u4efb\u52a1\u60c5\u5883\u4e0b\u5207\u6362\u4f7f\u7528\uff0c\u5373\u4f7f\u662f\u6700\u56f0\u96be\u7684\u4efb\u52a1\u4e5f\u4e0d\u4f8b\u5916\u3002&nbsp;<strong>\u7ea7\u8054\u5f0f\u89e3\u7ed1<\/strong>&nbsp;\uff08\u4f8b\u5982\uff0c\u5728\uff09&nbsp;<code>900 \u2212 191<\/code>, \u5176\u4e2d\uff0c\u501f\u6765\u7684\u5355\u4f4d\u5fc5\u987b\u7a7f\u8d8a\u591a\u4e2a\u5730\u70b9\uff09\u5b8c\u5168\u7531\u52a8\u753b\u548c\u65c1\u767d\u7ec4\u6210\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"vorhersage-aufgaben\">\u9884\u6d4b\u4efb\u52a1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u5e94\u7528\u7a0b\u5e8f\u8fd8\u53ef\u4ee5\u9009\u62e9\u5728\u6bcf\u4e2a\u6b65\u9aa4\u4e4b\u524d\u63d0\u51fa\u4e00\u4e2a\u591a\u9879\u9009\u62e9\u9898\uff0c\u6216\u8005\u8981\u6c42\u5bf9\u7ed3\u679c\u8fdb\u884c\u76f4\u63a5\u64cd\u4f5c\uff1a&nbsp;<em>\u201e\u63a5\u4e0b\u6765\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f\u201c<\/em>&nbsp;\u5b69\u5b50\u9884\u6d4b\u4e0b\u4e00\u6b65\uff0c\u5e94\u7528\u7a0b\u5e8f\u624d\u4f1a\u6267\u884c\u9884\u6d4b\u540e\u7684\u6b65\u9aa4\u3002\u5e72\u6270\u9879\u6545\u610f\u63cf\u7ed8\u4e86\u5178\u578b\u7684\u9519\u8bef\u6982\u5ff5\uff0c\u4f8b\u5982\u201e\u8f83\u5927\u7684\u6570\u51cf\u53bb\u8f83\u5c0f\u7684\u6570\u201c\u6216\u5fd8\u8bb0\u8fdb\u4f4d\u3002.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"teil-2-didaktischer-hintergrund\">\u6559\u5b66\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\u6846\u67b6<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u81ea2022\u5e74\u4fee\u8ba2\u7248KMK\uff08\u6559\u80b2\u6587\u5316\u90e8\u957f\u5e38\u8bbe\u4f1a\u8bae\uff09\u6570\u5b66\u6807\u51c6\u901a\u8fc7\u4ee5\u6765\uff0c\u5bf9\u7b14\u7b97\u65b9\u6cd5\u7684\u6559\u5b66\u91cd\u70b9\u53d1\u751f\u4e86\u663e\u8457\u53d8\u5316\u30022004\u5e74\u7684\u6807\u51c6\u5c06\u7b14\u7b97\u7b97\u6cd5\u5217\u4e3a\u5c0f\u5b66\u9636\u6bb5\u7684\u6838\u5fc3\u80fd\u529b\u9886\u57df\uff0c\u800c\u65b0\u6807\u51c6\u5219\u66f4\u52a0\u5f3a\u8c03\u2026\u2026\u00a0<strong>\u534a\u4e66\u5199\u7b97\u672f<\/strong>\u00a0\u5e76\u6839\u636e\u4e66\u9762\u7a0b\u5e8f\u8d4b\u4e88\u4e00\u4e2a\u51fd\u6570\u3002\u6570\u5b66\u6559\u5b66\u5b66\u4f1a (Society for Didactics of Mathematics) \u5728\u4e00\u7bc7\u914d\u5957\u6587\u7ae0\u4e2d\u89e3\u91ca\u4e86\u8fd9\u4e9b\u91cd\u8981\u7684\u53d8\u5316\uff08Barzel \u7b49\u4eba\uff0c2023\uff09\u3002\u5176\u4e2d\u6709\u4e09\u70b9\u4e0e\u6211\u4eec\u7684\u95ee\u9898\u5c24\u4e3a\u76f8\u5173\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u534a\u4e66\u5199\u5f0f\u7b97\u672f\u8d8a\u6765\u8d8a\u666e\u904d\u3002.<\/strong>&nbsp;\u534a\u4e66\u9762\u7b56\u7565\u88ab\u8ba4\u4e3a\u662f\u513f\u7ae5\u5b66\u4e60\u6784\u5efa\u81ea\u5df1\u7684\u8ba1\u7b97\u6846\u67b6\u3001\u53ef\u89c6\u5316\u4e2d\u95f4\u6b65\u9aa4\u4ee5\u53ca\u7406\u89e3\u81ea\u8eab\u601d\u7ef4\u8fc7\u7a0b\u7684\u5148\u51b3\u6761\u4ef6\u3002\u53ea\u6709\u5728\u8fd9\u4e9b\u57fa\u7840\u7262\u56fa\u4e4b\u540e\uff0c\u624d\u4f1a\u5f15\u5165\u4e66\u9762\u7b97\u6cd5\uff08KMK 2022\uff1b\u5b9e\u65bd\u624b\u518c KMK 2023\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u7406\u89e3\u6210\u4e3a\u6307\u5bfc\u539f\u5219\u3002.<\/strong> \u201e\u5728\u81ea\u52a8\u5316\u4e4b\u524d\u8fdb\u884c\u7406\u89e3\u201c\u5df2\u4ee5\u7f16\u7a0b\u65b9\u5f0f\u7eb3\u5165\u5b9e\u65bd\u624b\u518c\u4e2d\u3002.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u5404\u8054\u90a6\u5dde\u5bf9\u6b64\u7684\u6267\u884c\u60c5\u51b5\u5e76\u4e0d\u4e00\u81f4\u3002\u5df4\u4f10\u5229\u4e9a\u5dde&nbsp;<strong>\u8bfe\u7a0bPLUS<\/strong>&nbsp;\u4f8b\u5982\uff0c\u5bf9\u4e8e\u5c0f\u5b66\u6765\u8bf4\uff0c\u51cf\u6cd5\u7684\u5177\u4f53\u5f62\u5f0f\u5982\u4e0b\uff1a&nbsp;<strong>\u6263\u9664\u6cd5<\/strong>&nbsp;\uff08= \u89e3\u6784\uff09\u5e76\u5c06\u6570\u767e\u4e2a\u76d8\u5b50\u3001\u6570\u5341\u6839\u6746\u548c\u4e00\u5217\u4e3a\u5173\u952e\u6559\u5b66\u6750\u6599\uff08\u5df4\u4f10\u5229\u4e9a\u5dde\u6559\u80b2\u548c\u6587\u5316\u4e8b\u52a1\u90e8 2024\uff09\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5317\u83b1\u8335-\u5a01\u65af\u7279\u6cd5\u4f26\u5dde\u7684\u8bfe\u7a0b\u5219\u5c06\u7a0b\u5e8f\u9009\u62e9\u6743\u7559\u7ed9\u4e86\u5b66\u6821\uff0c\u5e76\u5c06\u51b3\u5b9a\u6743\u4e0b\u653e\u7ed9\u4e86\u5b66\u6821\uff08PIKAS 2024\uff09\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u610f\u5473\u7740\u4e00\u6b3e\u53ef\u4ee5\u5728\u5168\u56fd\u8303\u56f4\u5185\u4f7f\u7528\u7684\u5b66\u4e60\u8f6f\u4ef6\u3002&nbsp;<strong>\u4e24\u79cd\u624b\u672f<\/strong>&nbsp;\u81f3\u5c11\u5fc5\u987b\u80fd\u591f\u5c06\u5176\u5448\u73b0\u51fa\u6765\uff0c\u4ee5\u4fbf\u4e0e\u76f8\u5e94\u7684\u6559\u79d1\u4e66\u8054\u7cfb\u8d77\u6765\u3002\u6b64\u5916\uff0c\u8fd9\u751a\u81f3\u53ef\u4ee5\u5bf9\u8fd9\u4e24\u79cd\u65b9\u6cd5\u8fdb\u884c\u6bd4\u8f83\u548c\u7406\u89e3\u6027\u8003\u5bdf\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"2-was-hei-t-verstehensorientierung\">\u201e\u7406\u89e3\u5bfc\u5411\u201c\u662f\u4ec0\u4e48\u610f\u601d\uff1f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u81ea2010\u5e74\u4ee3\u540e\u534a\u671f\u4ee5\u6765\uff0c\u8fd9\u4e00\u6982\u5ff5\u4e00\u76f4\u662f\u5fb7\u56fd\u6570\u5b66\u6559\u80b2\u7684\u6838\u5fc3\uff0c\u5c24\u5176\u7531\u82cf\u73ca\u5a1c\u00b7\u666e\u96f7\u8fea\u683c\u548c\u514b\u91cc\u65af\u6258\u592b\u00b7\u585e\u5c14\u7279\uff08\u591a\u7279\u8499\u5fb7\u5de5\u4e1a\u5927\u5b66\uff09\u53d1\u5c55\u5b8c\u5584\uff08Prediger &amp; Selter 2014; Selter et al. 2014\uff09\u3002\u7406\u89e3\u5bfc\u5411\u578b\u6570\u5b66\u6559\u5b66\u7684\u7279\u70b9\u662f\u4e09\u4e2a\u76f8\u4e92\u5173\u8054\u7684\u7279\u5f81\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u601d\u60f3\u4f18\u5148\u4e8e\u8ba1\u7b97\u3002.<\/strong>&nbsp;\u5728\u5f15\u5165\u6b63\u5f0f\u7684\u7b97\u672f\u89c4\u5219\u4e4b\u524d\uff0c\u5fc5\u987b\u5148\u5efa\u7acb\u5bf9\u6570\u5b57\u548c\u8fd0\u7b97\u7684\u900f\u5f7b\u7406\u89e3\u3002\u53ea\u6709\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u624d\u80fd\u5c06\u7a0b\u5e8f\u7b80\u5316\u4e3a\u6a21\u5f0f\uff08Prediger &amp; Selter 2014\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u8868\u5f81\u65b9\u5f0f\u7684\u6301\u7eed\u53d8\u5316\u3002.<\/strong>&nbsp;\u6982\u5ff5\u548c\u8fd0\u7b97\u5728\u591a\u4e2a\u8868\u5f81\u5c42\u6b21\uff08\u5177\u4f53\u3001\u56fe\u50cf\u3001\u7b26\u53f7\u3001\u8bed\u8a00\uff09\u4e0a\u76f8\u4e92\u5173\u8054\uff0c\u4f7f\u513f\u7ae5\u80fd\u591f\u5728\u4e0d\u540c\u5c42\u6b21\u4e4b\u95f4\u5207\u6362\u65f6\u68c0\u9a8c\u548c\u5b8c\u5584\u81ea\u5df1\u7684\u60f3\u6cd5\u3002.<\/li>\n\n\n\n<li><strong>\u7ed3\u6784\u6027\u7684\u3001\u6570\u5b66\u5185\u90e8\u7684\u6982\u5ff5\u3002.<\/strong> \u8be5\u63a8\u5e7f\u6d3b\u52a8\u4e0d\u4ec5\u65e8\u5728\u6fc0\u53d1\u5e94\u7528\u60c5\u5883\uff0c\u800c\u4e14\u8fd8\u65e8\u5728\u8ba4\u8bc6\u6570\u5b66\u7ed3\u6784\uff0c\u4f8b\u5982\u4f4d\u503c\u7cfb\u7edf\u7684\u6346\u7ed1\u903b\u8f91\uff08Prediger 2024\uff09\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u56e0\u6b64\uff0c\u8be5\u5e94\u7528\u7a0b\u5e8f\u88ab\u8bbe\u8ba1\u6210\u4e00\u79cd\u5de5\u5177\uff0c\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c&nbsp;<strong>\u9010\u6b65\u5f62\u6210\u60f3\u6cd5<\/strong>&nbsp;\u548c&nbsp;<strong>\u8981\u6c42\u66f4\u6362\u4ee3\u8868<\/strong>&nbsp;\u8fd9\u6709\u52a9\u4e8e\u8bed\u8a00\u652f\u6301\uff0c\u5e76\u53ef\u4f5c\u4e3a\u6c9f\u901a\u5904\u7406\u7684\u6a21\u578b\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"3-schriftliche-verfahren-als-b-ndelungs-prozeduren\">\u4e66\u9762\u7a0b\u5e8f\u4f5c\u4e3a\u6346\u7ed1\u7a0b\u5e8f<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u6240\u7f16\u5199\u7684\u7b97\u6cd5\u76f4\u63a5\u53d6\u81ea\u2026\u2026&nbsp;<strong>\u5341\u8fdb\u5236\u4f4d\u503c\u5236<\/strong>&nbsp;\u63a8\u5bfc\u8fc7\u7a0b\u3002\u4f4d\u503c\u8868\u7684\u6bcf\u4e00\u5217\u4ee3\u8868\u4e00\u4e2a\u5206\u7ec4\u7ea7\u522b\uff1b\u56e0\u6b64\uff0c\u4e66\u5199\u52a0\u6cd5\u662f\u6309\u5217\u5206\u4e24\u6b65\u8fdb\u884c\u7684\uff1a\u5148\u5c06\u5404\u5217\u6570\u5b57\u76f8\u52a0\uff0c\u5982\u679c\u8be5\u5217\u6570\u5b57\u4e4b\u548c\u5927\u4e8e\u7b49\u4e8e 10\uff0c\u5219\u5c06\u8be5\u5217\u6570\u5b57\u5206\u7ec4\u4e3a\u66f4\u9ad8\u4e00\u4f4d\u6570\u7684\u5355\u4f4d\u3002\u6284\u5199\u5c31\u662f\u7b80\u5355\u5730\u5199\u4e0b\u8fd9\u4e2a\u5206\u7ec4\uff08Padberg &amp; Benz 2021\uff0c\u7b2c 8 \u7ae0\uff09\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u7b14\u7b97\u51cf\u6cd5\u662f\u4e00\u4e2a\u4e24\u6b65\u8fc7\u7a0b\uff1a\u9996\u5148\u6bd4\u8f83\u4e0a\u4e00\u4f4d\u4e0a\u7684\u6570\u5b57\u4e2a\u4f4d\u6570\uff0c\u5982\u679c\u4e0a\u4e00\u4f4d\u4e0a\u7684\u6570\u5b57\u4e2a\u4f4d\u6570\u4e0d\u8db3\uff0c\u5219\u4ece\u4e0a\u4e00\u4f4d\u4e0a\u4e00\u4f4d\u4e0a\u79fb\u51fa\u4e00\u4e2a\u6570\u5b57\uff0c\u76f8\u5f53\u4e8e\u4ece\u5f53\u524d\u5217\u79fb\u51fa\u5341\u4e2a\u6570\u5b57\u3002\u5177\u4f53\u505a\u6cd5\u662f\u51cf\u5c11\u88ab\u51cf\u6570\uff08\u201e\u62c6\u5206\u201c\uff09\u8fd8\u662f\u589e\u52a0\u88ab\u51cf\u6570\u5e76\u52a0\u5341\uff08\u201e\u6269\u5c55\u201c\uff09\uff0c\u53d6\u51b3\u4e8e\u8fd0\u7b97\u6b65\u9aa4\uff1b\u4ece\u6570\u5b66\u89d2\u5ea6\u6765\u770b\uff0c\u4e24\u8005\u662f\u7b49\u4ef7\u7684\uff08Padberg &amp; Benz 2021\uff09\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u4e3a\u4e86\u8ba9\u5b69\u5b50\u4eec\u771f\u6b63\u7406\u89e3\u8fd9\u79cd\u903b\u8f91\uff0c\u800c\u4e0d\u4ec5\u4ec5\u662f\u673a\u68b0\u5730\u5728\u8868\u683c\u4e2d\u8ba1\u7b97\u6570\u5b57\uff0c\u4ed6\u4eec\u9700\u8981\u4e00\u4e2a&nbsp;<strong>\u7406\u89e3\u6346\u7ed1\u9500\u552e<\/strong>&nbsp;\u5728\u5177\u8eab\u8ba4\u77e5\u548c\u56fe\u50cf\u8ba4\u77e5\u5c42\u9762\uff0c\u5b83\u4eec\uff08\u7eaf\u7cb9\u5730\uff09\u4ee5\u7b26\u53f7\u7684\u65b9\u5f0f\u8fdb\u884c\u7b26\u53f7\u5316\u5de5\u4f5c\u3002. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"4-typische-verstehens-h-rden-was-die-empirie-zeigt\">\u5178\u578b\u7684\u7406\u89e3\u969c\u788d<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"4-1-addition\">\u6dfb\u52a0<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5b66\u79d1\u6559\u5b66\u6587\u732e\u4e3b\u8981\u8bb0\u5f55\u4e86\u4ee5\u4e0b\u51e0\u79cd\u4e66\u9762\u52a0\u6cd5\u9519\u8bef\u7b56\u7565\uff08<em>\u76ae\u5361\u4e18<\/em>&nbsp;(2024) \u548c Padberg &amp; Benz (2021))\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u5206\u79bb\u6216\u5b8c\u5168\u8f6c\u5f55\u9519\u8bef<\/strong>\u5b69\u5b50\u5c06\u5217\u76f8\u52a0\uff08\u4f8b\u5982\uff0c8 + 7 = 15\uff09\uff0c\u5e76\u5c06\u6574\u4e2a\u4e24\u4f4d\u6570\u5199\u5728\u4e2a\u4f4d\u4e0a\uff0c\u800c\u4e0d\u662f\u5199 5 \u5e76\u8fdb\u4f4d 1\u3002.<\/li>\n\n\n\n<li><strong>\u5fd8\u8bb0\u8f6c\u8d26\u4e86<\/strong>\u5217\u6dfb\u52a0\u6b63\u786e\uff0c\u4f46\u672a\u5305\u542b\u4e0a\u4e00\u5217\u7684\u5ef6\u7eed\u503c\u3002.<\/li>\n\n\n\n<li><strong>\u5bf9\u96f6\u7684\u5904\u7406\u4e0d\u6b63\u786e<\/strong>\uff1a\u5217&nbsp;<code>0<\/code> \u88ab\u8bef\u89e3\uff08\u4f8b\u5982\uff1a.&nbsp;<code>0 + n = 0<\/code>\uff09\uff0c\u6216\u8005\u4e0d\u6267\u884c\u8fdb\u4f4d\u5230\u96f6\u7684\u64cd\u4f5c\u3002.<\/li>\n\n\n\n<li><strong>\u4f4d\u503c\u53cd\u8f6c<\/strong>\u5f53\u64cd\u4f5c\u6570\u7684\u4f4d\u6570\u4e0d\u540c\u65f6\uff0c\u6570\u5b57\u8981\u4e0a\u4e0b\u5de6\u5bf9\u9f50\u800c\u4e0d\u662f\u53f3\u5bf9\u9f50\u3002.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"4-2-subtraktion-das-fehleranf-lligere-verfahren\">\u51cf\u6cd5<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u51cf\u6cd5\u8fd0\u7b97\u4e2d\u51fa\u73b0\u7684\u969c\u788d\u8303\u56f4\u8981\u5e7f\u6cdb\u5f97\u591a\u3002\u6700\u5e38\u89c1\u7684\u9519\u8bef\u6709\uff08KIRA 2024\uff09\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u8f6c\u4f1a\u56f0\u96be<\/strong>&nbsp;\uff08\u6ca1\u6709\u8fdb\u4f4d\uff0c\u6ca1\u6709\u8fdb\u4f4d\u5230\u7a7a\u4f4d\uff0c\u8fdb\u4f4d\u8fc7\u591a\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u9519\u8bef\u7387\u4e3a\u96f6<\/strong>&nbsp;\uff08\u201e0 \u2212 x = 0\u201e\uff0c\u201cx \u2212 0 = 0\u201d\uff0c\u65e0\u8fdb\u4f4d\u6216\u8fdb\u4f4d\u8d85\u8fc7\u96f6\u7684\u60c5\u51b5\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u8ba1\u7b97\u65b9\u5411\u8bef\u5dee<\/strong>&nbsp;\uff08\u4ece\u5de6\u5230\u53f3\u8ba1\u6570\uff09\u3002.<\/li>\n\n\n\n<li><strong>\u64cd\u4f5c\u4e92\u6362<\/strong>&nbsp;\uff08\u7528\u52a0\u6cd5\u4ee3\u66ff\u51cf\u6cd5\uff09.<\/li>\n\n\n\n<li><strong>\u6309\u5217\u8fdb\u884c\u5fae\u5206\u201e\u8f83\u5927\u503c\u51cf\u53bb\u8f83\u5c0f\u503c\u201c<\/strong>&nbsp;\u8fd9\u662f\u6700\u5e38\u89c1\u7684\u7cfb\u7edf\u8bef\u5dee\u3002.<\/li>\n\n\n\n<li><strong>\u5bf9\u91cd\u8981\u6027\u7684\u9519\u8bef\u7406\u89e3<\/strong>.<\/li>\n\n\n\n<li><strong>\u6df7\u5408\u591a\u79cd\u5de5\u827a<\/strong>&nbsp;\u2014 \u4f8b\u5982\uff0c\u5728\u540c\u4e00\u4efb\u52a1\u4e2d\u540c\u65f6\u5e94\u7528\u6269\u5c55\u548c\u89e3\u7ed1\u3002.<\/li>\n\n\n\n<li><strong>\u4e00\u52a0\u4e00\u9519\u8bef<\/strong>&nbsp;\uff08\u5217\u672c\u8eab\u7f16\u53f7\u6709\u8bef\uff09\u3002.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u9891\u7387&nbsp;<strong>\u201e\u8f83\u5927\u503c\u51cf\u53bb\u8f83\u5c0f\u503c\u201c\u7684\u8bef\u5dee<\/strong>. \u5728\u6bd4\u52d2\u8d39\u5c14\u5fb7\u5730\u533a31\u4e2a\u56db\u5e74\u7ea7\u73ed\u7ea7\u7684\u5927\u89c4\u6a21\u7814\u7a76\u4e2d\uff0cSchipper\u65e9\u57281983\u5e74\u5c31\u8bb0\u5f55\u5230\uff0c\u8fd9\u79cd\u9519\u8bef\u7ea6\u5360\u6240\u6709\u51cf\u6cd5\u9519\u8bef\u768430%\uff0c\u56e0\u6b64\u662f\u6700\u5e38\u89c1\u7684\u7cfb\u7edf\u6027\u9519\u8bef\uff08Schipper 1983\uff1b\u5f15\u81eaPadberg &amp; Benz 2021\uff09\u3002Wartha &amp; Schulz (2014)\u7684\u7814\u7a76\u8868\u660e\uff0c\u8fd9\u79cd\u9519\u8bef\u4e0e\u5b66\u751f\u5bf9\u4f4d\u503c\u7684\u7406\u89e3\u4e0d\u8db3\u5bc6\u5207\u76f8\u5173\u3002. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u57fa\u4e8e\u8fd9\u4e9b\u5e38\u89c1\u9519\u8bef\uff0c\u8be5\u5e94\u7528\u7a0b\u5e8f\u4e13\u95e8\u8c03\u6574\u4e86\u6bcf\u4e2a\u6b65\u9aa4\u7684\u8109\u51b2\u548c\u9884\u6d4b\uff0c\u5e76\u5c06\u5176\u53ef\u89c6\u5316\uff0c\u4ee5\u89e3\u51b3\u6b64\u7c7b\u9519\u8bef\u548c\u8bef\u89e3\uff0c\u5e76\u901a\u8fc7\u8868\u5f81\u7f51\u7edc\u63d0\u4f9b\u5b66\u4e60\u673a\u4f1a\u6765\u514b\u670d\u8fd9\u4e9b\u8bef\u89e3\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"4-3-verfahrens-verwechslungen\">\u7a0b\u5e8f\u4e0a\u7684\u6df7\u4e71<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5f53\u5b69\u5b50\u957f\u5927\u3001\u72ec\u7acb\u65f6\uff0c\u53c8\u4f1a\u51fa\u73b0\u53e6\u4e00\u4e2a\u96be\u9898\u3002&nbsp;<strong>\u6df7\u5408<\/strong>. \u5f53\u6559\u79d1\u4e66\u548c\u5bb6\u5ead\u8f85\u5bfc\u91c7\u7528\u4e0d\u540c\u7684\u65b9\u6cd5\u65f6\uff0c\u5c31\u4f1a\u51fa\u73b0\u8fd9\u79cd\u9519\u8bef\uff08Schipper 2009\uff09\u3002\u90e8\u5206\u539f\u56e0\u662f\u8bb8\u591a\u5bb6\u957f\u4ecd\u7136\u8bb0\u5f97\u62d3\u5c55\u6559\u5b66\u6cd5\uff0c\u800c\u4ed6\u4eec\u7684\u5b69\u5b50\u73b0\u5728\u4e3b\u8981\u5b66\u4e60\u7684\u662f\u5206\u89e3\u6559\u5b66\u6cd5\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\">\u6269\u5c55\u4e0e\u89e3\u6784\uff1a\u4e00\u573a\u5173\u4e8e\u5b66\u79d1\u6559\u5b66\u6cd5\u7684\u8fa9\u8bba<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5fb7\u56fd\u5c0f\u5b66\u5e38\u7528\u7684\u4e24\u79cd\u51cf\u6cd5\u65b9\u6cd5\u51e0\u5341\u5e74\u6765\u4e00\u76f4\u5907\u53d7\u4e89\u8bae\u3002\u76ee\u524d\u7684\u60c5\u51b5\u53ef\u4ee5\u6982\u62ec\u5982\u4e0b\uff1a<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"5-1-entb-ndeln-abziehverfahren\">\u89e3\u7ed1\uff08\u62c9\u53d6\u6cd5\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8bba\u8bc1\u903b\u8f91\uff1a<\/strong>&nbsp;\u88ab\u51cf\u6570\u7684\u4e0b\u4e00\u4e2a\u6700\u9ad8\u4f4d\u6570\u5b57\u51cf 1\uff1b\u501f\u5165\u7684\u5355\u4f4d\u4f5c\u4e3a 10 \u4e2a\u5355\u4f4d\u6dfb\u52a0\u5230\u5f53\u524d\u5217\u4e2d\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u52a0\u5f3a<\/strong>&nbsp;\uff08Padberg &amp; Benz 2021\uff1bKrauthausen 2018\uff1b\u5df4\u4f10\u5229\u4e9a\u5dde\u653f\u5e9c 2024\uff09\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e0e\u5b9e\u9645\u7269\u8d28\u6d3b\u52a8\u76f4\u63a5\u76f8\u5173\uff1a\u4e00\u6839\u5341\u6746\u88ab\u5206\u6210\u5341\u4e2a\u4e00\u7acb\u65b9\u4f53\u3002.<\/li>\n\n\n\n<li>\u903b\u8f91\u4e00\u81f4\uff1a\u53ea\u6709\u88ab\u51cf\u6570\u4f1a\u6539\u53d8\uff0c\u51cf\u6570\u4fdd\u6301\u4e0d\u53d8\u3002.<\/li>\n\n\n\n<li>\u7ea7\u8054\u501f\u8d37\u53ef\u4ee5\u8868\u73b0\u4e3a\u7a7a\u95f4\u8fd0\u52a8\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u524a\u5f31\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u79cd\u8bb0\u53f7\uff08\u201e\u5212\u6389\u5341\u4f4d\uff0c\u5728\u65c1\u8fb9\u5199\u4e0a -1\u201c\uff09\u4f1a\u8ba9\u4eba\u611f\u5230\u56f0\u60d1\uff0c\u5c24\u5176\u662f\u5728\u591a\u6b21\u501f\u4f4d\u65f6\u3002.<\/li>\n\n\n\n<li>\u5bf9\u4e8e\u8bf8\u5982\u6b64\u7c7b\u7684\u4efb\u52a1&nbsp;<code>1000 \u2212 1<\/code>&nbsp;\u4e00\u4e2a\u5355\u5143\u5fc5\u987b\u7ea7\u8054\u5230\u4e09\u4e2a\u5730\u65b9\u3002.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"5-2-erweitern-auff-llverfahren\">\u81a8\u80c0\uff08\u8865\u5145\u8fc7\u7a0b\uff09<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8bba\u8bc1\u903b\u8f91\uff1a<\/strong>&nbsp;\u5dee\u7684\u6052\u5b9a\u6027\uff1a\u5982\u679c\u5c06\u76f8\u540c\u7684\u503c\u52a0\u5230\u4e24\u4e2a\u6570\u4e0a\uff0810 \u4e2a\u4e00 = 1 \u4e2a\u5341\uff09\uff0c\u5219\u5dee\u4fdd\u6301\u4e0d\u53d8\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u52a0\u5f3a<\/strong>&nbsp;\uff08Schipper 2009\uff1bPadberg \u548c Benz 2021\uff09\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5e72\u51c0\u7684\u8bb0\u8c31\uff0c\u6ca1\u6709\u5220\u9664\u4efb\u4f55\u5185\u5bb9\u3002.<\/li>\n\n\n\n<li>\u8fde\u63a5\u5230&nbsp;<strong>\u6dfb\u52a0<\/strong>&nbsp;\uff08\u201e6 \u52a0 13 \u7b49\u4e8e\u591a\u5c11\uff1f\u201c\uff09\uff0c\u8fd9\u6bd4\u51cf\u6cd5\u66f4\u5bb9\u6613\u88ab\u8bb8\u591a\u5b69\u5b50\u7406\u89e3\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u524a\u5f31\uff1a<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5176\u539f\u7406\uff08\u201e\u6211\u4eec\u5728\u9876\u90e8\u52a0\u4e8610\uff0c\u6240\u4ee5\u5e95\u90e8\u5fc5\u987b\u8fdb\u884c\u8865\u507f\u201c\uff09\u5f88\u590d\u6742\uff0c\u800c\u4e14\u7528\u5b9e\u9645\u6750\u6599\u6765\u6f14\u793a\u4e5f\u66f4\u96be\u3002Selter (1995) \u5c06\u8fd9\u79cd\u6750\u6599\u64cd\u4f5c\u4e0e\u8bb0\u5f55\u64cd\u4f5c\u4e4b\u95f4\u7684\u5dee\u5f02\u63cf\u8ff0\u4e3a\u5178\u578b\u73b0\u8c61\u3002\u00a0<em>\u865a\u6784\u9677\u9631<\/em>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u5e94\u7528\u63d0\u4f9b\u4e86\u4e24\u79cd\u65b9\u6cd5\u7684\u53ef\u89c6\u5316\u56fe\u793a\uff0c\u4ee5\u4fbf\u4e8e\u7406\u89e3\u3002\u5728\u89e3\u7ed1\u6cd5\u4e2d\uff0c\u4ece\u66f4\u9ad8\u4f4d\u503c\u4e2d\u5212\u6389\u4e00\u4e2a\u65b9\u5757\uff0c\u5f97\u5230 10 \u4e2a\u6765\u81ea\u66f4\u4f4e\u4f4d\u503c\u7684\u65b9\u5757\u3002\u5728\u6269\u5c55\u6cd5\u4e2d\uff0c\u4f1a\u6dfb\u52a0\u4e00\u4e2a\u201e\u8d1f\u6570\u65b9\u5757\u201c\uff08\u6d88\u5931\u7684\u65b9\u5757\/\u7a7a\u4f4d\uff09\uff0c\u4e3a\u4e86\u5f25\u8865\uff0c\u4f1a\u6dfb\u52a0 10 \u4e2a\u6765\u81ea\u66f4\u4f4e\u4f4d\u503c\u7684\u65b9\u5757\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"6-umsetzung-in-der-app-didaktische-designentscheidungen\">\u5e94\u7528\u5185\u5b9e\u73b0\uff1a\u6559\u5b66\u8bbe\u8ba1\u51b3\u7b56<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u4ee5\u4e0b\u8bbe\u8ba1\u51b3\u7b56\u5747\u57fa\u4e8e\u4e0a\u8ff0\u5b66\u79d1\u7279\u5b9a\u7684\u6559\u5b66\u539f\u5219\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-1-drei-repr-sentationen-synchron-das-eis-prinzip-operationalisiert\">\u591a\u79cd\u8868\u793a\u5f62\u5f0f\u540c\u6b65<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u6838\u5fc3\u7684\u6559\u5b66\u51b3\u7b56\u662f&nbsp;<strong>\u540c\u6b65\u8026\u5408<\/strong>&nbsp;\u591a\u91cd\u8868\u5f81\u5c42\u6b21\uff1a\u6bcf\u4e2a\u52a8\u4f5c\uff08\u66f4\u6539\u6570\u5b57\u3001\u6267\u884c\u6b65\u9aa4\uff09\u90fd\u4f1a\u540c\u65f6\u5f71\u54cd\u7b26\u53f7\u3001\u4e8c\u7ef4\u56fe\u5757\u6216\u4e09\u7ef4\u56fe\u5f62\u4ee5\u53ca\u8bed\u8a00\u63cf\u8ff0\u3002\u8fd9\u6b63\u662f\u5e03\u9c81\u7eb3\uff08Bruner\uff0c1966\uff09\u6240\u63cf\u8ff0\u7684\u8868\u5f81\u8f6c\u6362\uff0c\u4e5f\u662f\u514b\u52b3\u7279\u8c6a\u68ee\uff08Krauthausen\uff0c2018\uff09\u8ba4\u4e3a\u7684\u6570\u5b57\u5b66\u4e60\u8f6f\u4ef6\u7684\u6838\u5fc3\u4efb\u52a1\uff1a\u52a8\u753b\u672c\u8eab\u5e76\u975e\u76ee\u7684\uff0c\u800c\u662f\u2026\u2026&nbsp;<em>\u7ed3\u6784\u76f8\u540c<\/em>&nbsp;\u5c06\u6570\u5b66\u5173\u7cfb\u751f\u52a8\u5730\u5c55\u73b0\u51fa\u6765\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6bcf\u4e2a\u9762\u677f\u4e0a\u65b9\u7684\u5377\u5e18\u95e8\u5141\u8bb8\u6559\u5e08\u9009\u62e9\u6027\u5730&nbsp;<strong>\u4e00<\/strong>&nbsp;\u5176\u76ee\u7684\u662f\u9690\u85cf\u4e00\u4e2a\u5c42\u6b21\uff0c\u8feb\u4f7f\u513f\u7ae5\u4ece\u5176\u4ed6\u5c42\u6b21\u8fdb\u884c\u8f6c\u6362\u3002\u8fd9\u7b26\u5408\u64cd\u4f5c\u6027\u6559\u5b66\u6cd5\uff08Wittmann &amp; M\u00fcller 1990 ff.\uff09\u7684\u8981\u6c42\uff0c\u5373\u79ef\u6781\u8981\u6c42\u5e76\u9010\u6b65\u9884\u6d4b\u8868\u5f81\u7684\u8f6c\u53d8\u3002\u8fd9\u4f7f\u5f97\u5404\u79cd\u65e2\u5b9a\u4efb\u52a1\u6210\u4e3a\u53ef\u80fd\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-2-verfahrenswahl-explizit\">\u660e\u786e\u9009\u62e9\u7a0b\u5e8f<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u7531\u4e8e\u8054\u90a6\u548c\u5dde\u8bfe\u7a0b\u8bbe\u7f6e\u504f\u597d\u4e0d\u540c\u7684\u7a0b\u5e8f\uff0c\u56e0\u6b64\u8be5\u5e94\u7528\u7a0b\u5e8f&nbsp;<strong>\u4e24\u79cd\u624b\u672f<\/strong>&nbsp;\u4f5c\u4e3a\u540c\u7b49\u6709\u6548\u7684\u9009\u62e9\u3002\u8fd9\u4e5f\u89e3\u51b3\u4e864.3\u8282\u4e2d\u63d0\u5230\u7684\u6df7\u5408\u96be\u9898\uff1a\u6559\u5e08\u53ef\u4ee5\u8bbe\u5b9a\u81ea\u5df1\u6559\u6750\u4e2d\u7684\u6559\u5b66\u6b65\u9aa4\uff0c\u540c\u65f6\u5c06\u53e6\u4e00\u79cd\u6559\u5b66\u6b65\u9aa4\u5c55\u793a\u51fa\u6765\u4ee5\u4f9b\u6bd4\u8f83\uff0c\u56e0\u4e3a\u513f\u7ae5\u901a\u5e38\u65e0\u6cd5\u6e05\u6670\u5730\u5c06\u81ea\u5df1\u7684\u601d\u7ef4\u7b56\u7565\u4e0e\u7279\u5b9a\u7684\u6559\u5b66\u6b65\u9aa4\u5bf9\u5e94\u8d77\u6765\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-3-sprachausgabe-als-modell-sprache\">\u8bed\u97f3\u8f93\u51fa\u4f5c\u4e3a\u6a21\u578b\u8bed\u8a00<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u8bed\u97f3\u8f93\u51fa\u59cb\u7ec8\u5982\u4e00&nbsp;<strong>\u6280\u672f\u4e0a\u6b63\u786e\u7684\u672f\u8bed<\/strong>\u8fd9\u91cc\u4f7f\u7528\u4e86\u201e\u6346\u7ed1\u201c\u3001\u201e\u89e3\u6346\u7ed1\u201c\u3001\u201e\u8fdb\u4f4d\u201c\u3001\u201e\u88ab\u51cf\u6570\u201c\u548c\u201e\u51cf\u6570\u201c\u8fd9\u4e9b\u8bcd\u3002\u8fd9\u4f7f\u5f97\u7b97\u6cd5\u53d8\u6210\u4e86\u4e00\u4e2a\u89e3\u91ca\u6027\u7684\u5e8f\u5217\uff0c\u5b69\u5b50\u4eec\u53ef\u4ee5\u5c06\u5176\u4f5c\u4e3a\u8bed\u8a00\u6307\u5357\u3002\u4ed6\u4eec\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u8bed\u8a00\u6a21\u578b\u4f5c\u4e3a\u6a21\u677f\uff0c\u7528\u81ea\u5df1\u7684\u8bed\u8a00\u8fdb\u884c\u7ffb\u8bd1\u3002\u8fd9\u7b26\u5408 QuaMath \u7684\u539f\u5219\u3002&nbsp;<em>\u4fc3\u8fdb\u6c9f\u901a<\/em>&nbsp;\uff08QuaMath 2024\uff09\u548c\u5176\u4e2d\u4e4b\u4e00&nbsp;<em>\u6570\u5b66\u80af\u5b9a\u6ca1\u95ee\u9898\u3002<\/em>\u4f20\u64ad\u5b9e\u8df5,&nbsp;<strong>\u53e3\u5934\u8868\u8fbe<\/strong>&nbsp;\u5c06\u5176\u89c6\u4e3a\u6570\u5b66\u7406\u89e3\u7684\u6838\u5fc3\u90e8\u5206\uff08Selter \u7b49\u4eba\uff0c2014\uff09\u3002. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-4-vorhersage-aufgaben-formatives-lernen-als-mini-diagnose\">\u9884\u6d4b\u4efb\u52a1<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u53ef\u9009\u00a0<strong>\u9884\u62a5<\/strong>\u00a0\u5728\u6bcf\u4e2a\u6b65\u9aa4\u4e4b\u524d\uff0c\u00a0<em>\u9884\u6d4b-\u89c2\u5bdf-\u89e3\u91ca<\/em>-\u79d1\u5b66\u6559\u80b2\u7684\u4e00\u79cd\u5f62\u5f0f\uff08White &amp; Gunstone 1992\uff09\u3002\u5b83\u5e76\u975e\u4ec5\u4ec5\u662f\u4e00\u6bb5\u52a8\u753b\u4f9b\u4eba\u89c2\u770b\uff0c\u800c\u662f\u6bcf\u4e2a\u6b65\u9aa4\u90fd\u914d\u6709\u76f8\u5e94\u7684\u95ee\u9898\uff1a\u00a0<em>\u8fd9\u91cc\u53d1\u751f\u4e86\u4ec0\u4e48\uff1f\u6211\u8be5\u600e\u4e48\u529e\uff1f\u54ea\u4e2a\u5e72\u6270\u9879\u770b\u4f3c\u5408\u7406\u4f46\u5374\u662f\u9519\u8bef\u7684\uff1f<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u5e94\u7528\u7a0b\u5e8f\u7684\u5e72\u6270\u9879\u523b\u610f\u53cd\u6620\u4e86\u5df2\u8bb0\u5f55\u7684\u9519\u8bef\u7b56\u7565\uff0c\u4f8b\u5982&nbsp;<em>\u201e\u8f83\u5927\u503c\u51cf\u53bb\u8f83\u5c0f\u503c\u201c<\/em>, \u6839\u636e\u9519\u8bef\u5206\u6790\u6587\u732e\uff08Schipper 1983, 2009; Padberg &amp; Benz 2021; Wartha &amp; Schulz 2014; KIRA 2024\uff09\uff0c\u9057\u5fd8\u8fdb\u4f4d\u3001\u4f4d\u503c\u98a0\u5012\u3001\u7a0b\u5e8f\u6df7\u4e71\u7b49\u90fd\u4f1a\u5bfc\u81f4\u9519\u8bef\u3002\u8fd9\u6700\u7ec8\u4f1a\u5bfc\u81f4\u2026\u2026&nbsp;<em>\u8ba4\u77e5\u6fc0\u6d3b<\/em> \uff08QuaMath 2024\uff09\u4e3e\u884c\u3002.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-5-adaptive-schwierigkeit-datengeleitete-bung\">\u4efb\u52a1\u751f\u6210\u5668\u548c\u81ea\u9002\u5e94\u96be\u5ea6<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u4efb\u52a1\u751f\u6210\u5668\u63d0\u4f9b\u591a\u4e2a\u96be\u5ea6\u7ea7\u522b\uff0c\u5e76\u4e14\u5728\u201e\u81ea\u9002\u5e94\u201c\u6a21\u5f0f\u4e0b\uff0c\u4f1a\u6839\u636e\u9884\u6d4b\u6210\u529f\u7387\u8c03\u6574\u4e0b\u4e00\u4e2a\u63d0\u4f9b\u7684\uff08\u201e\u6eda\u52a8\u201c\uff09\u4efb\u52a1\u7684\u96be\u5ea6\u3002. <\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"6-6-tipp-aufgaben-material-basierte-diagnose\">\u865a\u62df\u884c\u52a8\uff1a\u6311\u6218\u8868\u5f81\u4e4b\u95f4\u7684\u5173\u7cfb<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u67d0\u4e9b\u9636\u6bb5\uff08\u4f8b\u5982\u653e\u7f6e\u7ed3\u8f6c\u6570\u5b57\u3001\u8f93\u5165\u6269\u5c55\u4fee\u6b63\u9879\uff09\uff0c\u591a\u9879\u9009\u62e9\u9898\u4f1a\u88ab\u66ff\u6362\u4e3a&nbsp;<strong>\u63d0\u793a\u4efb\u52a1<\/strong>&nbsp;\u6750\u6599\u6216\u7b26\u53f7\u88ab\u66ff\u6362\u3002\u5b69\u5b50\u76f4\u63a5\u6307\u5411\u6b63\u786e\u7684\u5217\uff0c\u4ece\u800c\u5728\u56fe\u50cf\u7b26\u53f7\u5c42\u9762\u8fdb\u884c\u5b66\u4e60\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"7-grenzen-forschungsbedarf-und-praxis-empfehlungen\">\u5c40\u9650\u6027\u3001\u7814\u7a76\u9700\u6c42\u548c\u5b9e\u7528\u5efa\u8bae<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5c3d\u7ba1\u8be5\u5e94\u7528\u7a0b\u5e8f\u7684\u529f\u80fd\u591a\u79cd\u591a\u6837\uff0c\u4f46\u5b83\u5e76\u4e0d\u80fd\u53d6\u4ee3\u2026\u2026\u00a0<strong>\u6709\u5f62\u7269\u8d28<\/strong>\u00a0\uff08\u4f60\u53ef\u4ee5\u89e6\u6478\u7684\u8fea\u6069\u65af\u7acb\u65b9\u4f53\uff09\u00a0<strong>\u8c08\u8bba\u6570\u5b66<\/strong>\u00a0\u5728\u9636\u7ea7\u7684\u793e\u4f1a\u7a7a\u95f4\u4e2d\u3002\u514b\u52b3\u7279\u8c6a\u68ee\uff082018\uff0c\u7b2c215\u9875\u53ca\u540e\u7eed\u9875\uff09\u6307\u51fa\uff0c\u6570\u5b57\u52a8\u753b\u589e\u5f3a\u4e86\u89e6\u89c9\u4f53\u9a8c\u3002\u00a0<em>\u6dfb\u52a0<\/em>, \u5b83\u4e0d\u80fd\u53d6\u4ee3\u53e3\u5934\u6559\u5b66\u3002\u53e3\u5934\u4ea4\u6d41\u4e5f\u662f\u5982\u6b64\uff1a\u6570\u5b66\u4ea4\u6d41\u81f3\u5173\u91cd\u8981\uff0c\u4e0d\u53ef\u6216\u7f3a\uff08QuaMath 2024\uff09\u3002\u7136\u800c\uff0c\u8be5\u5e94\u7528\u7a0b\u5e8f\u53ef\u4ee5\u4f5c\u4e3a\u8f85\u52a9\u5de5\u5177\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u72ec\u7acb\u7ec3\u4e60\u548c\u7814\u7a76\u4efb\u52a1\uff08\u5e94\u7528\u7a0b\u5e8f\u4e2d\u5305\u542b\u4e00\u4e9b\u7814\u7a76\u601d\u8def\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, B.\u3001Gasteiger, H.\u3001Greefrath, G.\u3001Maritzen, N.\u3001N\u00fchrenb\u00f6rger, M. \u548c Stanat, P.<\/strong>&nbsp;\uff082023\uff09\u3002\u8fdb\u4e00\u6b65\u53d1\u5c55\u5c0f\u5b66\u548c\u521d\u4e2d\u6570\u5b66\u6559\u80b2\u6807\u51c6\u3002.&nbsp;<em>\u6570\u5b66\u6559\u5b66\u5b66\u4f1a\u901a\u8baf<\/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>\u5e03\u9c81\u7eb3\uff0cJS.<\/strong>&nbsp;(1966).&nbsp;<em>\u8fc8\u5411\u6559\u5b66\u7406\u8bba<\/em>. \u9a6c\u8428\u8bf8\u585e\u5dde\u5251\u6865\uff1a\u54c8\u4f5b\u5927\u5b66\u51fa\u7248\u793e\u3002.<\/li>\n\n\n\n<li><strong>\u514b\u52b3\u7279\u8c6a\u68ee\uff0cG.<\/strong>&nbsp;(2018).&nbsp;<em>\u5c0f\u5b66\u6570\u5b66\u6559\u5b66\u6cd5\u5bfc\u8bba<\/em>&nbsp;\uff08\u7b2c4\u7248\uff09\u3002\u67cf\u6797\/\u6d77\u5fb7\u5821\uff1a\u65bd\u666e\u6797\u683c\u5149\u8c31\u51fa\u7248\u793e\u3002.<\/li>\n\n\n\n<li><strong>Padberg, F. \u548c Benz, C.<\/strong>&nbsp;(2021).&nbsp;<em>\u7b97\u672f\u6559\u5b66\u6cd5\u2014\u2014\u7406\u8bba\u624e\u5b9e\u3001\u7528\u9014\u5e7f\u6cdb\u3001\u5b9e\u7528\u6027\u5f3a<\/em>&nbsp;\uff08\u7b2c\u4e94\u7248\uff09\u3002\u67cf\u6797\/\u6d77\u5fb7\u5821\uff1aSpringer Spektrum\u3002.<\/li>\n\n\n\n<li><strong>\u4f20\u9053\u8005\uff0cS.<\/strong>&nbsp;\uff082024\uff09\u3002\u201e\u6570\u5b66\u4e0d\u5fc5\u75db\u82e6\u3002\u201c\u53d1\u8868\u4e8e\u5fb7\u56fd\u5b66\u6821\u95e8\u6237\u7f51\u7ad9\u7684\u6587\u7ae0\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>Prediger, S. \u548c Selter, C.<\/strong>&nbsp;(2014).&nbsp;<em>\u6570\u5b66\u6559\u80b2\u6700\u65b0\u52a8\u6001\u2014\u2014\u6559\u5b66\u7814\u7a76\u4e0e\u6559\u5e08\u6559\u80b2\u7684\u6700\u65b0\u89c6\u89d2<\/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>\u5e0c\u73c0\uff0cW.<\/strong>&nbsp;(1983).&nbsp;<em>\u5b66\u751f\u5728\u4e66\u5199\u81ea\u7136\u6570\u51cf\u6cd5\u65f6\u5e38\u72af\u7684\u9519\u8bef<\/em>. \u6bd4\u52d2\u8d39\u5c14\u5fb7\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>\u5e0c\u73c0\uff0cW.<\/strong>&nbsp;(2009).&nbsp;<em>\u5c0f\u5b66\u6570\u5b66\u6559\u5b66\u624b\u518c<\/em>. \u5e03\u4f26\u745e\u514b\uff1a\u65bd\u7f57\u5fb7\u5c14\u3002.<\/li>\n\n\n\n<li><strong>\u585e\u5c14\u7279\uff0cC.<\/strong>&nbsp;\uff081995\uff09\u3002\u8bba\u65e9\u671f\u7b97\u672f\u6559\u5b66\u4e2d\u201a\u96f6\u70b9\u2018\u7684\u865a\u6784\u6027\u3002.&nbsp;<em>\u6570\u5b66\u6559\u5b66\u5b9e\u8df5<\/em>, \uff0c16(2)\uff0c11-19\u3002.<\/li>\n\n\n\n<li><strong>Selter, C.\u3001Prediger, S.\u3001N\u00fchrenb\u00f6rger, M. \u548c Hu\u00dfmann, S.\uff08\u7f16\u8f91\uff09<\/strong>&nbsp;(2014).&nbsp;<em>\u81ea\u4fe1\u638c\u63e1\u6570\u5b66\u2014\u2014\u4e00\u79cd\u786e\u4fdd\u57fa\u672c\u6570\u5b66\u6280\u80fd\u7684\u8bca\u65ad\u548c\u652f\u6301\u7406\u5ff5\u3002.<\/em>&nbsp;\u4e13\u9898\u6a21\u5757\u201e\u81ea\u7136\u6570\u201c\u3002\u67cf\u6797\uff1aCornelsen\u51fa\u7248\u793e\u3002.<\/li>\n\n\n\n<li><strong>Wartha, S. \u548c Schulz, A.<\/strong>&nbsp;(2014).&nbsp;<em>\u9632\u6b62\u8ba1\u7b97\u95ee\u9898<\/em>&nbsp;\uff08\u7b2c2\u7248\uff09\u3002\u67cf\u6797\uff1aCornelsen\u51fa\u7248\u793e\u3002.<\/li>\n\n\n\n<li><strong>\u6000\u7279\uff0cR.\u548c\u5188\u65af\u901a\uff0cR.<\/strong>&nbsp;(1992).&nbsp;<em>\u6df1\u5165\u7406\u89e3<\/em>. \u4f26\u6566\uff1aFalmer\u51fa\u7248\u793e\u3002.<\/li>\n\n\n\n<li><strong>Wittmann, E. Ch. &amp; M\u00fcller, GN.<\/strong>&nbsp;\uff081990 \u5e74\u53ca\u4ee5\u540e\uff09\u3002.&nbsp;<em>\u9ad8\u6548\u7b97\u672f\u7ec3\u4e60\u624b\u518c<\/em>, \u7b2c 1 \u5377\u548c\u7b2c 2 \u5377\u3002\u65af\u56fe\u52a0\u7279\uff1aKlett\u3002.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"bildungspolitische-dokumente\">\u6559\u80b2\u653f\u7b56\u6587\u4ef6<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"literatur\"><strong>KMK\u2014\u2014\u6559\u80b2\u548c\u6587\u5316\u4e8b\u52a1\u90e8\u957f\u5e38\u8bbe\u4f1a\u8bae<\/strong>&nbsp;(2022).&nbsp;<em>\u5c0f\u5b66\u6570\u5b66\u5b66\u79d1\u6559\u80b2\u6807\u51c6\u3002.<\/em>&nbsp;2022\u5e746\u670823\u65e5\u51b3\u5b9a\u3002\u67cf\u6797\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\u2014\u2014\u6559\u80b2\u548c\u6587\u5316\u4e8b\u52a1\u90e8\u957f\u5e38\u8bbe\u4f1a\u8bae<\/strong>&nbsp;(2023).&nbsp;<em>\u6570\u5b66\u6559\u80b2\u6807\u51c6\u3002\u5c0f\u5b66\u548c\u521d\u4e2d\u9636\u6bb5\u5b9e\u65bd\u624b\u518c\u3002.<\/em>&nbsp;\u67cf\u6797\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>\u5173\u4e8e\u4e3a\u671f\u5341\u5e74\u7684 QuaMath \u8ba1\u5212\u7684\u534f\u8bae\u3002.<\/em>&nbsp;\u65b0\u95fb\u7a3f\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>\u5df4\u4f10\u5229\u4e9a\u5dde\u6559\u80b2\u548c\u6587\u5316\u4e8b\u52a1\u90e8<\/strong>&nbsp;(2024).&nbsp;<em>CurriculumPLUS \u5c0f\u5b66\u2014\u2014\u6570\u5b66\u3002.<\/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>\u4e0b\u8428\u514b\u68ee\u5dde\u6559\u80b2\u90e8<\/strong>&nbsp;(2024).&nbsp;<em>\u5c0f\u5b66\u6838\u5fc3\u8bfe\u7a0b\u2014\u2014\u6570\u5b66\u3002.<\/em>\uff08\u97f3\u9891\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\">\u5728\u7ebf\u5e73\u53f0\u548c\u8d44\u52a9\u9879\u76ee<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"literatur\"><strong>divomath<\/strong>&nbsp;\u2014 \u591a\u7279\u8499\u5fb7\u5de5\u4e1a\u5927\u5b66\u9762\u5411 3-6 \u5e74\u7ea7\u5b66\u751f\u7684\u6570\u5b57\u5316\u6559\u5b66\u548c\u5b66\u4e60\u73af\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>\u57fa\u62c9<\/strong>&nbsp;\u2014&nbsp;<em>\u513f\u7ae5\u7684\u8ba1\u7b97\u65b9\u5f0f\u4e0e\u5e38\u4eba\u4e0d\u540c\u3002.<\/em>&nbsp;\u591a\u7279\u8499\u5fb7\u5de5\u4e1a\u5927\u5b66\/DZLM\u3002.&nbsp;<a href=\"https:\/\/kira.dzlm.de\/\">https:\/\/kira.dzlm.de<\/a>&nbsp;\uff08\u5c24\u5176\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\u80af\u5b9a\u6ca1\u95ee\u9898\u3002<\/strong>&nbsp;\u2014 \u5728\u7ebf\u8d44\u6599\u3002\u591a\u7279\u8499\u5fb7\u5de5\u4e1a\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>\u76ae\u5361\u4e18<\/strong>&nbsp;\u2014&nbsp;<em>\u8fc7\u7a0b\u76f8\u5173\u80fd\u529b\u548c\u5185\u5bb9\u76f8\u5173\u80fd\u529b\u3002.<\/em>\u591a\u7279\u8499\u5fb7\u5de5\u4e1a\u5927\u5b66\/DZLM\u3002.&nbsp;<a href=\"https:\/\/pikas.dzlm.de\/\">https:\/\/pikas.dzlm.de<\/a>&nbsp;\uff08\u5c24\u5176\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>\u548c&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>\u666e\u91cc\u9a6c\u79d1\u59c6<\/strong>&nbsp;\u2014&nbsp;<em>\u5c0f\u5b66\u6570\u5b66\u6982\u8bba\u3002.<\/em>&nbsp;\u591a\u7279\u8499\u5fb7\u5de5\u4e1a\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>\u91cf\u5b50\u6570\u5b66<\/strong>&nbsp;\u2014&nbsp;<em>\u6570\u5b66\u6559\u5b66\u8d28\u91cf\u548c\u4e13\u4e1a\u53d1\u5c55\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, [&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\/zh\/wp-json\/wp\/v2\/pages\/998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/comments?post=998"}],"version-history":[{"count":6,"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/pages\/998\/revisions"}],"predecessor-version":[{"id":1008,"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/pages\/998\/revisions\/1008"}],"wp:attachment":[{"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/media?parent=998"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}