{"id":989,"date":"2026-05-06T08:09:18","date_gmt":"2026-05-06T08:09:18","guid":{"rendered":"https:\/\/urff.app\/?page_id=989"},"modified":"2026-09-05T17:01:08","modified_gmt":"2026-09-05T17:01:08","slug":"istgleich","status":"publish","type":"page","link":"https:\/\/urff.app\/zh\/istgleich\/","title":{"rendered":"\u662f\u4e00\u6837\u7684"},"content":{"rendered":"<h3 class=\"wp-block-heading\" id=\"istgleich-die-vergleichszeichen-interaktiv-entdecken\">\u4ee5\u4e92\u52a8\u65b9\u5f0f\u63a2\u7d22\u5173\u7cfb\u7b26\u53f7<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"192\" height=\"192\" src=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/05\/favicon-192.png\" alt=\"\" class=\"wp-image-993\" srcset=\"https:\/\/urff.app\/wp-content\/uploads\/2026\/05\/favicon-192.png 192w, https:\/\/urff.app\/wp-content\/uploads\/2026\/05\/favicon-192-150x150.png 150w, https:\/\/urff.app\/wp-content\/uploads\/2026\/05\/favicon-192-12x12.png 12w\" sizes=\"auto, (max-width: 192px) 100vw, 192px\" \/><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">\u4e00\u4e2a\u4ee5\u5173\u7cfb\u7b26\u53f7\u4e3a\u91cd\u70b9\u7684\u5c0f\u5b66\u5b66\u4e60\u548c\u5b9e\u9a8c\u73af\u5883&nbsp;<code>=<\/code>,&nbsp;<code>&lt;<\/code> \u548c&nbsp;<code>&gt;<\/code>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u76f4\u63a5\u94fe\u63a5\uff1a<\/strong>\u00a0<a href=\"https:\/\/waage.urff.app\/\">https:\/\/waage.urff.app<\/a><\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u7f51\u7edc\u5e94\u7528\u7a0b\u5e8f&nbsp;<strong>\u662f\u4e00\u6837\u7684<\/strong>&nbsp;\u8fd9\u6b3e\u5e94\u7528\u6a21\u62df\u865a\u62df\u5929\u5e73\uff0c\u8ba9\u5b69\u5b50\u4eec\u901a\u8fc7\u52a8\u624b\u64cd\u4f5c\u6765\u6bd4\u8f83\u6570\u91cf\u3001\u6570\u5b57\u548c\u8868\u8fbe\u5f0f\u3002\u8ba1\u6570\u5668\u901a\u8fc7\u70b9\u51fb\u6216\u8f7b\u89e6\uff08\u652f\u6301\u591a\u70b9\u89e6\u63a7\u540c\u65f6\u70b9\u51fb\u591a\u4e2a\u8ba1\u6570\u5668\uff09\u751f\u6210\uff0c\u653e\u7f6e\u5728\u5929\u5e73\u4e24\u4fa7\u7684\u6258\u76d8\u4e2d\uff0c\u5806\u53e0\u8d77\u6765\uff0c\u81ea\u52a8\u6346\u624e\u6210\u5341\u4e2a\u4e00\u7ec4\u7684\u8ba1\u6570\u5668\u6761\uff0c\u5e76\u5b9e\u65f6\u663e\u793a\u4e3a\u7b49\u5f0f\u6216\u4e0d\u7b49\u5f0f\u3002\u8be5\u5e94\u7528\u5728\u52a8\u624b\u64cd\u4f5c\u3001\u56fe\u6807\u5f0f\u89c6\u89c9\u5448\u73b0\uff08\u5929\u5e73\u4e0a\u7684\u70b9\uff09\u548c\u7b26\u53f7\u8868\u793a\u4e4b\u95f4\u4ea4\u66ff\u8fdb\u884c\u3002<code>=<\/code>,&nbsp;<code>&lt;<\/code>,&nbsp;<code>&gt;<\/code>&nbsp;plus Zahlen und Terme) findet synchron statt. Jedes Element kann auch abgedeckt werden, sodass sich beliebige Gegeben-Gesucht-Aufgabenstellungen stellen lassen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u5e94\u7528\u7684\u8bbe\u8ba1\u5b97\u65e8\u662f\u7528\u6237\u53cb\u597d\uff1a\u65e0\u9700\u767b\u5f55\uff0c\u4e0d\u6536\u96c6\u6570\u636e\uff0c\u65e0\u5e7f\u544a\u3002\u914d\u7f6e\u4fe1\u606f\u53ef\u901a\u8fc7\u94fe\u63a5\/\u4e8c\u7ef4\u7801\u8f7b\u677e\u5206\u4eab\u3002.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"was-kinder-mit-der-waage-tun-k-nnen\">\u5b69\u5b50\u4eec\u53ef\u4ee5\u7528\u97f3\u9636\u505a\u4ec0\u4e48\uff1a<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6bd4\u8f83\u6570\u91cf\u3002.<\/strong>&nbsp;\u5c06\u76d8\u5b50\u5206\u522b\u653e\u5165\u5de6\u53f3\u4e24\u4fa7\u7684\u7897\u4e2d\u3002\u79e4\u4f1a\u7acb\u5373\u663e\u793a\u54ea\u4e00\u4fa7\u76db\u653e\u7684\u66f4\u591a\u3002.<\/li>\n\n\n\n<li><strong>\u6062\u590d\u5e73\u8861\u3002.<\/strong>&nbsp;\u901a\u8fc7\u6dfb\u52a0\u3001\u79fb\u9664\u6216\u91cd\u65b0\u5206\u914d\uff0c\u6709\u610f\u8bc6\u5730\u4f53\u9a8c\u5e76\u5b9e\u9a8c\u7b49\u53f7\u3002\u6211\u5fc5\u987b\u653e\u591a\u5c11\u4e0a\u53bb\uff0c\u5929\u5e73\u624d\u80fd\u5e73\u8861\uff1f<\/li>\n\n\n\n<li><strong>\u6bcf\u8fb9\u7528\u4e24\u4e2a\u7897\u64cd\u4f5c\u3002.<\/strong>&nbsp;\u671f\u9650\u7ed3\u6784\uff0c\u4f8b\u5982&nbsp;<code>5 + 3<\/code>&nbsp;\u76f4\u63a5\u6784\u5efa\u5b83\u5e76\u4e0e\u5176\u4ed6\u672f\u8bed\u8fdb\u884c\u6bd4\u8f83\u3002.<\/li>\n\n\n\n<li><strong>\u4f7f\u7528\u8d1f\u58f3\u5c42\u3002.<\/strong>&nbsp;\u4f8b\u5982\uff0c\u51cf\u6cd5\u5173\u7cfb&nbsp;<code>9-4<\/code>&nbsp;\u5728\u7269\u8d28\u5c42\u9762\u548c\u8c61\u5f81\u5c42\u9762\u5e76\u884c\u5448\u73b0\u3002\u88ab\u53d6\u8d70\u7684\u6570\u91cf\u88ab\u6536\u96c6\u5728\u8d1f\u6570\u76d8\u4e2d\u3002.<\/li>\n\n\n\n<li><strong>\u5806\u53e0\u548c\u6346\u7ed1\u3002.<\/strong>&nbsp;\u5728\u5806\u53e0\u6a21\u5f0f\u4e0b\uff0c\u56fe\u5757\u6392\u5217\u6210\u884c\uff1b\u6bcf 10 \u4e2a\uff08\u6216 5 \u4e2a\uff09\u56fe\u5757\u4f1a\u81ea\u52a8\u52a8\u753b\u5f62\u6210\u4e00\u4e2a\u7531 10 \u4e2a\u56fe\u5757\u7ec4\u6210\u7684\u6746\uff08\u5982\u679c\u9700\u8981\uff0c\u53ef\u4ee5\u5728\u8bbe\u7f6e\u4e2d\u66f4\u6539\uff09\u3002<\/li>\n\n\n\n<li><strong>\u63a9\u9970\u3002.<\/strong>&nbsp;\u62c9\u4e0b\u767e\u53f6\u7a97\uff0c\u76d6\u4f4f\u5355\u4e2a\u7897\u6216\u6570\u5b57\uff0c\u4ee5\u4fbf\u505a\u51fa\u731c\u6d4b\u5e76\u5728\u968f\u540e\u8fdb\u884c\u9a8c\u8bc1\u3002.<\/li>\n\n\n\n<li><strong>\u5206\u88c2\u3002.<\/strong>&nbsp;\u6bcf\u4e2a\u914d\u7f6e\u90fd\u53ef\u4ee5\u4ee5\u7b80\u77ed\u94fe\u63a5\u6216\u4e8c\u7ef4\u7801\u7684\u5f62\u5f0f\u5206\u4eab\u7ed9\u5b66\u4e60\u8005\u3002.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"aufgabenbeispiele\">\u4efb\u52a1\u793a\u4f8b\/\u4efb\u52a1\u601d\u8def\uff1a<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u627e\u51fa\u4e94\u4e2a\u5927\u4e8e 8 \u7684\u6570\u5b57\u3002.<\/li>\n\n\n\n<li>\u5728\u5de6\u8fb9\u753b 3 \u4e2a\u70b9\uff0c\u53f3\u8fb9\u753b 5 \u4e2a\u70b9\u3002\u4f60\u9700\u8981\u589e\u52a0\u6216\u51cf\u5c11\u591a\u5c11\u4e2a\u70b9\u624d\u80fd\u4f7f\u5929\u5e73\u5e73\u8861\uff1f<\/li>\n\n\n\n<li>\u5728\u5929\u5e73\u4e0a\u5c55\u793a\u201e3 + 4 = 7\u201c\uff0c\u7136\u540e\u5c55\u793a\u201e7 = 3 + 4\u201c\u3002\u6bd4\u8f83\u8fd9\u4e24\u8005\u3002\u4e3a\u4ec0\u4e48\u53ef\u4ee5\u4e92\u6362\u4e24\u8fb9\u7684\u4f4d\u7f6e\uff1f<\/li>\n\n\n\n<li>\u53cc\u65b9\u70b9\u6570\u90fd\u7ffb\u500d\u3002\u4ec0\u4e48\u65f6\u5019\u5929\u5e73\u4fdd\u6301\u5e73\u8861\uff0c\u4ec0\u4e48\u65f6\u5019\u5929\u5e73\u4e0d\u518d\u5e73\u8861\uff1f<\/li>\n\n\n\n<li>\u4e00\u8fb9\u670912\u4e2a\u70b9\uff0c\u53e6\u4e00\u8fb9\u670915\u4e2a\u70b9\u3002\u4f60\u80fd\u81ea\u5df1\u628a\u5929\u5e73\u5e73\u8861\u5417\uff1f&nbsp;<em>\u91cd\u65b0\u5206\u914d<\/em>&nbsp;\u5982\u4f55\u8fbe\u5230\u5e73\u8861\uff1f\u8bf7\u89e3\u91ca\u3002.<\/li>\n\n\n\n<li>\u4e00\u8fb9\u67098\u4e2a\u70b9\u3002\u53e6\u4e00\u8fb9\u6709\u4e24\u4e2a\u7897\uff1a\u4e00\u4e2a\u7897\u91cc\u67095\u4e2a\u70b9\uff0c\u53e6\u4e00\u4e2a\u662f\u7a7a\u7684\u3002\u8981\u4f7f\u70b9\u6570\u4e0e\u70b9\u6570\u5e73\u8861\uff0c\u7a7a\u7897\u91cc\u5fc5\u987b\u653e\u591a\u5c11\u4e2a\u70b9\uff1f<\/li>\n\n\n\n<li>Richtig oder falsch: \u201eDie Waage bleibt im Gleichgewicht, wenn ich auf jeder Seite dieselbe Anzahl dazuf\u00fcge.\u201c Begr\u00fcnde.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e94\u7528\u5185\uff08\u201e\u4fe1\u606f\u201c\u533a\u57df \u2192 \u201c\u4efb\u52a1\u793a\u4f8b\u201d\uff09\u5b58\u6709\u66f4\u4e30\u5bcc\u7684\u4efb\u52a1\u793a\u4f8b\u96c6\u5408\u3002.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"didaktischer-hintergrund\">\u6559\u5b66\u80cc\u666f<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"das-problem-operationale-deutung-des-gleichheitszeichens\">\u5c06\u7b49\u53f7\u7684\u64cd\u4f5c\u89e3\u91ca\u89c6\u4e3a\u4e00\u4e2a\u95ee\u9898<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u81ea Behr\u3001Erlwanger \u548c Nichols (1980) \u8fdb\u884c\u4e34\u5e8a\u8bbf\u8c08\u4ee5\u6765\uff0c\u7ecf\u9a8c\u5df2\u7ecf\u5145\u5206\u8bc1\u5b9e\uff0c\u5c0f\u5b66\u751f\u4e3b\u8981\u5c06\u7b49\u53f7\u89c6\u4e3a\u7b26\u53f7\u3002&nbsp;<em>\u884c\u52a8\u53f7\u53ec<\/em>&nbsp;\u4e5f\u5c31\u662f\u8bf4\uff0c\u5c06\u5176\u89e3\u91ca\u4e3a\u6267\u884c\u67d0\u9879\u64cd\u4f5c\u5e76\u8bb0\u5f55\u7ed3\u679c\u7684\u8bf7\u6c42\u3002\u5f62\u5982 \u7684\u7b49\u5f0f&nbsp;<code>3 + 4 = \u2610<\/code>&nbsp;\u5904\u7406\u8d77\u6765\u6beb\u4e0d\u8d39\u529b\uff0c\u800c\u8bf8\u5982\u6b64\u7c7b\u7684\u4efb\u52a1\u5219\u4e0d\u7136\u3002&nbsp;<code>\u2610 = 3 + 4<\/code>,&nbsp;<code>3 + 4 = 5 + \u2610<\/code>&nbsp;\u6216\u8005&nbsp;<code>5 = 5<\/code>&nbsp;\u7ecf\u5e38\u88ab\u4f5c\u4e3a\u201e\u9519\u8bef\u201c\u6216\u201e\u4e0d\u5141\u8bb8\u201c\u800c\u62d2\u7edd\uff08Behr et al., 1980; Falkner, Levi &amp; Carpenter, 1999; Knuth, Stephens, McNeil &amp; Alibali, 2006\uff09\u3002Falkner et al. (1999) \u62a5\u9053\u79f0\uff0c\u5927\u7ea6\u53ea\u6709\u56db\u5206\u4e4b\u4e00\u7684\u516d\u5e74\u7ea7\u5b66\u751f\u80fd\u591f\u5b8c\u6210\u8fd9\u9053\u9898&nbsp;<code>8 + 4 = \u2610 + 5<\/code> \u6b63\u786e\u89e3\u7b54\u3002\u5176\u4e2d\u5f88\u5927\u4e00\u90e8\u5206\u8981\u4e48\u662f&nbsp;<code>12<\/code> \u6216\u8005&nbsp;<code>17<\/code>&nbsp;\u4e00\u3001\u8fd9\u4e24\u79cd\u89e3\u51b3\u65b9\u6848\u90fd\u662f\u7eaf\u7cb9\u64cd\u4f5c\u6027\u89e3\u91ca\u7684\u5178\u578b\u7279\u5f81\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u79cd\u73b0\u8c61\u5728\u4e0d\u540c\u7684\u8bed\u8a00\u548c\u6559\u80b2\u4f53\u5236\u4e2d\u5747\u6709\u8bb0\u8f7d\uff1a\u9488\u5bf9\u5fb7\u8bed\u5b66\u4e60\u8005\uff0c\u6709 Borromeo Ferri \u548c Blum (2012)\u3001Hagemeister (2013) \u4ee5\u53ca Unteregge (2017) \u7684\u7814\u7a76\uff1b\u5728\u82f1\u8bed\u56fd\u5bb6\uff0c\u6709 Carpenter\u3001Franke \u548c Levi (2003) \u7684\u7814\u7a76\uff1b\u5728\u5176\u4ed6\u8bed\u5883\u4e2d\uff0c\u6709 Oksuz (2008)\u3001Wahyuni \u548c Herman (2019) \u4ee5\u53ca Farfan \u548c Schoen (2021) \u7684\u7814\u7a76\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Knuth\u7b49\u4eba\uff082006\uff09\u7684\u7814\u7a76\u8868\u660e\uff0c\u5bf9\u7b49\u53f7\u7684\u7406\u89e3\u662f\u2026\u2026&nbsp;<em>\u5173\u7cfb\u6216\u7b49\u4ef7\u7b26\u53f7<\/em>&nbsp;\u4e0e\u89e3\u51b3\u7b80\u5355\u65b9\u7a0b\u7684\u6210\u529f\u7387\u663e\u8457\u76f8\u5173\uff1a\u5b66\u4e60\u8005&nbsp;<code>=<\/code> \u8fdb\u884c\u5173\u7cfb\u6027\u89e3\u91ca\uff0c\u89e3\u51b3\u8bf8\u5982\u6b64\u7c7b\u7684\u4efb\u52a1&nbsp;<code>4\u7c73 + 10 = 70<\/code> \u5728\u4e2d\u5b66\u9636\u6bb5\uff0c\u4ed6\u4eec\u5728\u64cd\u4f5c\u6027\u89e3\u91ca\u65b9\u9762\u6bd4\u540c\u9f84\u4eba\u8868\u73b0\u5f97\u660e\u663e\u66f4\u597d\u3002\u95ee\u9898\u662f\uff0c\u4ed6\u4eec\u662f\u5982\u4f55\u505a\u5230\u8fd9\u4e00\u70b9\u7684\uff1f&nbsp;<code>=<\/code>&nbsp;\u56e0\u6b64\uff0c\u7406\u89e3\u8fd9\u4e00\u70b9\u662f\u5b9e\u73b0\u4ece\u7b97\u672f\u5230\u4ee3\u6570\u8fc7\u6e21\u7684\u5173\u952e\u6760\u6746\uff08Kieran\uff0c1981\uff1bSfard\uff0c1991\uff09\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"operationale-und-relationale-deutung-als-komplement-re-sichtweisen\">\u7b49\u53f7\u7684\u64cd\u4f5c\u548c\u5173\u7cfb\u89e3\u91ca<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Winter (1982) \u5df2\u7ecf\u6307\u51fa\uff0c\u8fd9\u4e24\u79cd\u89c6\u89d2\u2014\u2014\u64cd\u4f5c\u6027\u89e3\u91ca\uff08\u201e<code>=<\/code>&nbsp;\u610f\u4e3a\uff1a\u201c\u8ba1\u7b97\u201e\uff09\u4ee5\u53ca\u5173\u7cfb\u89e3\u91ca\uff08\u201e<code>=<\/code>&nbsp;\u610f\u4e3a\uff1a\u53cc\u65b9\u662f\u7b49\u4ef7\u7684\uff09\u2014\u2014\u5e94\u8be5\u5728\u5c0f\u5b66\u9636\u6bb5\u5c31\u5f00\u59cb\u57f9\u517b\u3002\u535a\u7f57\u6885\u5965-\u8d39\u91cc\u548c\u5e03\u5362\u59c6\uff08Borromeo Ferri und Blum, 2012\uff09\u4ee5\u53ca\u7fc1\u7279\u96f7\u683c\uff08Unteregge, 2017\uff09\u5f3a\u8c03\uff0c&nbsp;<em>\u7247\u9762<\/em>&nbsp;\u8fc7\u5206\u5f3a\u8c03\u4efb\u52a1\u7ed3\u679c\u7684\u89e3\u91ca\u4f1a\u5f3a\u5316\u8bef\u89e3\uff0c\u5e76\u7ed9\u4e2d\u5b66\u4ee3\u6570\u6559\u5b66\u5e26\u6765\u969c\u788d\u3002Sfard (1991) \u5728\u5176\u7406\u8bba\u4e2d\u63a2\u8ba8\u4e86\u8fd9\u79cd\u8054\u7cfb\u3002&nbsp;<em>\u8fc7\u7a0b-\u5bf9\u8c61\u4e8c\u5143\u6027<\/em> \u6570\u5b66\u6982\u5ff5\u662f\u6709\u7406\u8bba\u57fa\u7840\u7684\uff1a\u5b66\u4e60\u8005\u5fc5\u987b\u7406\u89e3\u8bf8\u5982\u201c\u6570\u5b66\u6982\u5ff5\u201d\u4e4b\u7c7b\u7684\u672f\u8bed\u3002&nbsp;<code>3 + 4<\/code>&nbsp;\u4e24\u8005\u517c\u5177&nbsp;<em>\u8fc7\u7a0b<\/em>&nbsp;\uff08\u53d1\u7968\uff09\u4ee5\u53ca&nbsp;<em>\u76ee\u7684<\/em>&nbsp;\uff08\u4e00\u4e2a\u4e0e\u5176\u4ed6\u5bf9\u8c61\u76f8\u5173\u7684\u6570\u5b57\uff09\u3002\u7b49\u53f7\u662f\u4e24\u79cd\u89e3\u91ca\u4e4b\u95f4\u7684\u63a5\u53e3\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u6559\u5b66\u8bbe\u8ba1\u4e0a\u7684\u6838\u5fc3\u7ed3\u8bba\u56e0\u6b64\u662f\uff1a\u4efb\u52a1\u5f62\u5f0f\u5e94\u8be5\u7cfb\u7edf\u5730\u517c\u987e\u8fd9\u4e24\u79cd\u89e3\u91ca\uff0c\u65e9\u5728\u5c0f\u5b66\u9636\u6bb5\u5c31\u5e94\u5982\u6b64\uff0c\u4ee5\u4fbf\u5c3d\u65e9\u7ea0\u6b63\u9519\u8bef\u89c2\u5ff5\u3002\u8fd9\u5305\u62ec\u5de6\u4fa7\u5e26\u6709\u672a\u77e5\u6570\u7684\u65b9\u7a0b\uff08<code>\u2610 = a + b<\/code>\uff09\uff0c\u6ca1\u6709\u8fd0\u7b97\u7b26\u53f7\u7684\u65b9\u7a0b\uff08<code>5 = 5<\/code>\uff09\uff0c\u672f\u8bed\u6bd4\u8f83\uff08<code>3 + 4 = 5 + 2<\/code>\uff09\u5c24\u5176\u662f&nbsp;<em>\u8bc1\u660e\u7b49\u4ef7\u6027<\/em>&nbsp;\u65e0\u8bba\u8ba1\u7b97\u7ed3\u679c\u5982\u4f55\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"die-waage-als-prototypisches-anschauungsmittel\">\u4ee5\u5929\u5e73\u4f5c\u4e3a\u89c6\u89c9\u8f85\u52a9\u5de5\u5177<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5728\u5fb7\u8bed\u533a\u548c\u82f1\u8bed\u533a\uff0c\u7b49\u81c2\u5929\u5e73\u662f\u7528\u4e8e\u5efa\u6784\u7b49\u53f7\u5173\u7cfb\u610f\u4e49\u7684\u6700\u666e\u904d\u7684\u5177\u8c61-\u56fe\u50cf\u5f0f\u6559\u5177\uff08Wittmann, 1981; Mann, 2004; Dooley &amp; Kirwan, 2014\uff09\u3002\u5b83\u5177\u6709\u4e24\u4e2a\u663e\u8457\u7684\u6559\u5b66\u4f18\u52bf\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5bf9\u79f0\u6027\u663e\u800c\u6613\u89c1\u3002.<\/strong>&nbsp;\u5904\u4e8e\u5e73\u8861\u72b6\u6001\u7684\u5929\u5e73\u4e00\u773c\u5c31\u80fd\u770b\u51fa\u662f\u5bf9\u79f0\u7684\uff1b\u5931\u8861\u7684\u5929\u5e73\u5219\u901a\u8fc7\u5176\u503e\u659c\u5ea6\u663e\u793a\u51fa\u591a\u6216\u5c11\u3002\u6b64\u5916\uff0c\u5173\u7cfb\u7b26\u53f7  \u548c = \u53ef\u4ee5\u76f4\u63a5\u4ece\u6a2a\u6881\u7684\u4f4d\u7f6e\u63a8\u5bfc\u51fa\u6765\uff0c\u56e0\u4e3a\u6a2a\u6881\u603b\u662f\u4f1a\u5411\u76f8\u5e94\u65b9\u5411\u503e\u659c\uff0c\u6216\u8005\u5728\u76f8\u7b49\u65f6\u4fdd\u6301\u6c34\u5e73\u3002.<\/li>\n\n\n\n<li><strong>\u8fd0\u8425\u65b9\u9762\u7684\u6539\u53d8\u662f\u5b8c\u5168\u53ef\u4ee5\u7406\u89e3\u7684\u3002.<\/strong>&nbsp;\u4e24\u8fb9\u540c\u65f6\u589e\u52a0\u6216\u51cf\u5c11\u7b49\u91cf\u5373\u53ef\u4fdd\u6301\u5e73\u8861\u3002\u8fd9\u79cd\u4f53\u9a8c\u662f\u884c\u52a8\u5bfc\u5411\u7684\u5148\u51b3\u6761\u4ef6\u2026\u2026&nbsp;<em>\u7b49\u4ef7\u53d8\u6362<\/em>, \u968f\u540e\u5728\u4e2d\u5b66\u6559\u80b2\u4e2d\u5f97\u5230\u6b63\u5f0f\u786e\u7acb\uff08Carpenter\u3001Franke \u548c Levi\uff0c2003\uff1bPrediger\uff0c2009\uff09\u3002.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">\u66fc\uff082004\uff09\u5c06\u8be5\u8bed\u5883\u4e0b\u7684\u7b49\u53f7\u79f0\u4e3a\u201e\u4e00\u79cd\u5e73\u8861\u884c\u4e3a\u201c\uff08a balancing act\uff09\uff0c\u5373\u5728\u73b0\u6709\u5e94\u7528\u7a0b\u5e8f\u7684\u6570\u5b57\u5b9e\u73b0\u4e2d\u88ab\u5b57\u9762\u5316\u5b9e\u73b0\u7684\u4e00\u4e2a\u9690\u55bb\uff1a\u4e00\u65e6\u6570\u91cf\u4e0d\u76f8\u7b26\uff0c\u6761\u5f62\u5c31\u4f1a\u503e\u659c\uff1b\u800c\u5728\u5efa\u7acb\u5e73\u8861\u65f6\uff0c\u5b83\u4f1a\u5b9e\u65f6\u6c34\u5e73\u5bf9\u9f50\u3002\u56e0\u6b64\uff0c\u5929\u5e73\u975e\u5e38\u9002\u5408\u4f5c\u4e3a\u5b9e\u9a8c\u73af\u5883\uff0c\u56e0\u4e3a\u6839\u636e\u64cd\u4f5c\u539f\u5219\uff0c\u8fd0\u7b97\u53ca\u5176\u5f71\u54cd\u53ef\u4ee5\u76f4\u63a5\u88ab\u4f53\u9a8c\u5230\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"stellenwertverst-ndnis-und-b-ndelung\">\u4e86\u89e3\u5176\u91cd\u8981\u6027\u53ca\u6346\u7ed1\u9500\u552e<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u5c06\u5341\u5757\uff08\u6216\u4e94\u5757\uff09\u74f7\u7816\u81ea\u52a8\u7ec4\u5408\u6210\u5341\u6839\u6746\u72b6\u7269\uff0c\u8fd9\u4e00\u53ef\u9009\u529f\u80fd\u91c7\u7528\u4e86\u8fea\u6069\u65af\u591a\u7cfb\u7edf\u79ef\u6728\u7684\u7ecf\u5178\u65b9\u6848\uff08Dienes\uff0c1960\uff09\uff0c\u800c\u65e0\u9700\u6539\u53d8\u6750\u6599\u3002\u8fd9\u91cc\u6709\u4e24\u70b9\u5728\u6559\u5b66\u4e0a\u81f3\u5173\u91cd\u8981\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u8868\u5f81\u7684\u8fde\u7eed\u6027\u3002.<\/strong>&nbsp;\u8fd9\u6839\u6746\u5b50\u4ecd\u7136\u6e05\u6670\u5730\u7531\u5341\u5757\u74f7\u7816\u7ec4\u6210\u3002\u5b66\u4e60\u8005\u4e0d\u4f1a\u5ffd\u7565\u4e00\u6bd4\u4e00\u7684\u6bd4\u4f8b\u3002\u8fd9\u4e0e Krauthausen \u548c Scherer (2007) \u7684\u5efa\u8bae\u76f8\u7b26\uff0c\u5373\u8bbe\u8ba1\u6346\u7ed1\u6750\u6599\u65f6\uff0c\u5e94\u786e\u4fdd\u6346\u7ed1\u5173\u7cfb\u5728\u4efb\u4f55\u65f6\u5019\u90fd\u53ef\u9006\u3002.<\/li>\n\n\n\n<li><strong>\u52a8\u753b\u8fde\u63a5\u548c\u89e3\u51b3\u3002.<\/strong>&nbsp;\u5f53\u79ef\u6728\u5230\u8fbe\u7b2c\u5341\u4e2a\u5355\u4f4d\u65f6\uff0c\u5b83\u4eec\u4f1a\u660e\u663e\u5730\u6ed1\u5165\u4e00\u5217\uff0c\u5e76\u7531\u4e00\u6761\u7ec6\u5fae\u7684\u8fb9\u754c\u8fde\u63a5\u8d77\u6765\u3002\u79fb\u9664\u4e00\u4e2a\u5355\u4f4d\u540e\uff0c\u8fde\u63a5\u5c31\u4f1a\u65ad\u5f00\u3002\u8fd9\u79cd\u53ef\u9006\u6027\u6709\u52a9\u4e8e\u7406\u89e3\u6346\u7ed1\u548c\u89e3\u6346\u7ed1\u662f\u4e92\u8865\u7684\u64cd\u4f5c\uff0c\u6b63\u5982\u5e15\u5fb7\u4f2f\u683c\u548c\u672c\u8328\uff082021\uff09\u6240\u5f3a\u8c03\u7684\uff0c\u8fd9\u662f\u7406\u89e3\u4f4d\u503c\u7684\u524d\u63d0\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">5\u4e2a\u88c5\u548c10\u4e2a\u88c5\u7684\u9009\u62e9\u81ea\u7531\u5ea6\u6709\u52a9\u4e8e\u8854\u63a5\u201e\u4e94\u65b9\u683c\u201c\u548c\u201e\u5341\u65b9\u683c\u201c\u6750\u6599\u7684\u6559\u5b66\u7406\u5ff5\uff08Van de Walle, Karp &amp; Bay-Williams, 2019\uff09\uff0c\u8fd9\u4e9b\u6750\u6599\u88ab\u7528\u4f5c\u76f4\u89c9\u5f0f\u6570\u91cf\u611f\u77e5\u4e0e\u4f4d\u503c\u8868\u793a\u4e4b\u95f4\u7684\u6865\u6881\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"multiple-repr-sentationen-und-wechsel-zwischen-ihnen\">\u591a\u79cd\u8868\u5f81\u53ca\u5176\u4e4b\u95f4\u7684\u5207\u6362<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8be5\u5e94\u7528\u7a0b\u5e8f\u540c\u65f6\u4ee5\u4e09\u79cd\u8868\u793a\u5f62\u5f0f\u663e\u793a\u4f53\u91cd\u79e4\u7684\u6bcf\u79cd\u72b6\u6001\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u6781\u5177\u6807\u5fd7\u6027\uff1a<\/strong>&nbsp;\u4f5c\u4e3a\u7269\u7406\u53cd\u5e94\u5c3a\u5ea6\u4e0a\u7684\u4e00\u4e2a\u76d8\u5b50\uff0c,<\/li>\n\n\n\n<li><strong>\u8c61\u5f81\u6027\u7684\uff1a<\/strong>&nbsp;\u4f5c\u4e3a\u56fe\u50cf\u4e0a\u7684\u7b49\u5f0f\u6216\u4e0d\u7b49\u5f0f\uff0c,<\/li>\n\n\n\n<li><strong>\u8bed\u8a00-\u8bed\u8a00\uff1a<\/strong>&nbsp;\u6839\u636e\u8981\u6c42\u4f5c\u4e3a\u53e3\u8bed\u53e5\u5b50\u8bfb\u51fa\uff08\u201e\u4e09\u5c0f\u4e8e\u56db\u201c\uff09\uff0c\u4e5f\u53ef\u9009\u62e9\u901a\u8fc7\u8bed\u97f3\u8f93\u51fa\u3002.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Bruner (1966) \u7684\u7ecf\u5178 EIS \u539f\u5219\uff08\u5177\u8eab\u8ba4\u77e5-\u56fe\u50cf\u8ba4\u77e5-\u7b26\u53f7\u8ba4\u77e5\uff09\u548c Ainsworth (2006) \u7684 DeFT \u6846\u67b6\uff08<em>\u591a\u79cd\u5916\u90e8\u8868\u5f81\u7684\u8bbe\u8ba1\u3001\u529f\u80fd\u548c\u4efb\u52a1<\/em>\uff09\u63d0\u4f9b\u7406\u8bba\u4f9d\u636e\uff0c\u8bf4\u660e\u4e3a\u4ec0\u4e48&nbsp;<em>\u540c\u65f6<\/em>&nbsp;\u548c&nbsp;<em>\u6301\u7eed\u7684<\/em>&nbsp;\u4e0d\u540c\u8868\u5f81\u5f62\u5f0f\u7684\u53ef\u7528\u6027\u4fc3\u8fdb\u4e86\u6982\u5ff5\u6784\u5efa\uff1a\u5b66\u4e60\u8005\u53ef\u4ee5\u79ef\u6781\u63a2\u7d22\u4e0d\u540c\u8868\u5f81\u4e4b\u95f4\u7684\u8f6c\u6362\uff0c\u800c\u4e0d\u53ea\u662f\u88ab\u52a8\u5730\u7406\u89e3\u3002\u901a\u8fc7\u5377\u5e18\u906e\u6321\u5355\u4e2a\u8868\u5f81\u7684\u529f\u80fd\uff0c\u8be5\u5e94\u7528\u7a0b\u5e8f\u6210\u4e3a\u4e00\u4e2a\u7528\u4e8e&nbsp;<em>\u7ed9\u5b9a-\u5bfb\u6c42\u4efb\u52a1<\/em>&nbsp;\u6309\u7167 Selter \u548c Spiegel (1997) \u7684\u610f\u4e49\u4e0a\u6765\u8bf4\u3002.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"konzeptionelle-designentscheidungen\">\u6982\u5ff5\u8bbe\u8ba1\u51b3\u7b56<\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u5143\u7d20<\/th><th>\u6559\u5b66\u539f\u7406<\/th><\/tr><\/thead><tbody><tr><td>\u6bcf\u8fb9\u4e00\u5230\u4e24\u4e2a\u7897<\/td><td>\u5141\u8bb8\u4f7f\u7528\u5982\u4e0b\u7684\u671f\u9650\u7ed3\u6784&nbsp;<code>(a + b) = c<\/code>&nbsp;\u6216\u8005&nbsp;<code>\uff08a + b\uff09= \uff08c + d\uff09<\/code>&nbsp;\u7531\u6b64\u53ef\u8fdb\u884c\u5173\u7cfb\u6bd4\u8f83<\/td><\/tr><tr><td>\u53ef\u9009\u7684\u8d1f\u58f3\u5c42<\/td><td>\u5c06\u51cf\u6cd5\u4f53\u9a8c\u4e3a\u201e\u62ff\u8d70\u201c\uff0c\u5176\u8fd0\u7b97\u7406\u89e3\u4e0e\u52a0\u6cd5\u76f8\u540c\uff1a\u603b\u91cf\u4fdd\u6301\u53ef\u89c1\uff0c\u4f46\u5929\u5e73\u4e0a\u8d77\u4f5c\u7528\u7684\u53ea\u6709\u5269\u4f59\u91cf\u3002.<\/td><\/tr><tr><td>\u5916\u906e\u9633\u5377\u5e18\uff0c\u9002\u7528\u4e8e\u7897\u72b6\u7269\u548c\u6570\u5b57<\/td><td>\u7ed3\u6784\u5316\u731c\u60f3\u5b66\u4e60\uff0c\u51cf\u5c11\u663e\u793a\u4ee5\u4fc3\u8fdb\u5fc3\u667a\u8fd0\u4f5c<\/td><\/tr><tr><td>\u5e26\u6bd4\u8f83\u7ebf\u7684\u5806\u53e0\u6a21\u5f0f<\/td><td>\u4e24\u4e2a\u96c6\u5408\u4e4b\u95f4\u4fdd\u6301\u987a\u5e8f\u7684\u53cc\u5c04\u7684\u6807\u5fd7\u6027\u524d\u8eab\uff0c\u5176\u7b26\u53f7\u6e90\u81ea\u9876\u90e8\u548c\u5e95\u90e8\u4e24\u6761\u6a2a\u7ebf\u7684\u89c6\u89c9\u5448\u73b0\u3002.<\/td><\/tr><tr><td>\u9650\u5236\u74f7\u7816\u6570\u91cf<\/td><td>\u6309\u6570\u5b57\u8303\u56f4\u533a\u5206\uff08\u4e00\u5e74\u7ea7\uff1a10-20\uff1b\u4e8c\u5e74\u7ea7\uff1a100\uff1b\u4e09\u5e74\u7ea7\u53ca\u4ee5\u4e0a\uff1a\u81f3500\uff09<\/td><\/tr><tr><td>\u901a\u8fc7\u94fe\u63a5\/\u4e8c\u7ef4\u7801\u5206\u4eab<\/td><td>\u6559\u5e08\u4e0e\u5b66\u4e60\u8005\u4e4b\u95f4\u4f4e\u95e8\u69db\u7684\u4efb\u52a1\u8fc1\u79fb\uff0c\u4e5f\u9002\u7528\u4e8e\u8fdc\u7a0b\u5b66\u4e60<\/td><\/tr><tr><td>\u65e0\u9700\u6ce8\u518c\uff0c\u4e0d\u8ddf\u8e2a\u6570\u636e\uff0c\u4ec5\u6536\u96c6\u672c\u5730\u6570\u636e<\/td><td>\u5728\u5b66\u6821\u73af\u5883\u4e2d\u5b9e\u73b0\u7b26\u5408 GDPR \u6807\u51c6\u7684\u4f7f\u7528\uff0c\u65e0\u9700\u989d\u5916\u7684\u7ec4\u7ec7\u5de5\u4f5c<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"einsatzempfehlung\">\u63a8\u8350\u7528\u9014<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u6b3e\u5e94\u7528\u7a0b\u5e8f\u7279\u522b\u9002\u5408\u5c0f\u5b66\u548c\u521d\u4e2d\u4f4e\u5e74\u7ea7\u5b66\u751f\u4f7f\u7528\uff0c\u5c24\u5176\u9002\u7528\u4e8e\u90a3\u4e9b\u5728\u7406\u89e3\u7b49\u53f7\u5173\u7cfb\u65b9\u9762\u5b58\u5728\u56f0\u96be\u7684\u5b66\u751f\uff08Prediger\uff0c2009\uff09\u3002\u5b83\u5e76\u975e\u53d6\u4ee3\u5b9e\u4f53\u5b66\u4e60\u6750\u6599\uff0c\u800c\u662f\u5bf9\u5176\u8fdb\u884c\u8865\u5145\uff1a\u6839\u636e\u87ba\u65cb\u5f0f\u5b66\u4e60\u539f\u5219\uff08Bruner\uff0c1966\uff1bWittmann\uff0c1981\uff09\uff0c\u8fd9\u79cd\u63a2\u7d22\u673a\u4f1a\u53ef\u4ee5\u53cd\u590d\u4f7f\u7528\u5e76\u4e0d\u65ad\u79ef\u7d2f\u3002\u8be5\u7f51\u9875\u5e94\u7528\u7a0b\u5e8f\u63d0\u4f9b\u4e86\u4f7f\u7528\u76f8\u540c\u5b66\u4e60\u7ed3\u6784\u7684\u53ef\u80fd\u6027\u3002&nbsp;<em>\u4e4b\u95f4<\/em>&nbsp;\u91cd\u590d\u3001\u53d8\u4f53\u548c\u5206\u4eab\u6750\u6599\u76f8\uff0c\u8fd9\u662f\u7528\u7269\u7406\u6750\u6599\u65e0\u6cd5\u5b9e\u73b0\u7684\u3002.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"literatur\">\u6587\u5b66<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Ainsworth, S. (2006). DeFT\uff1a\u8003\u8651\u5177\u6709\u591a\u79cd\u8868\u5f81\u7684\u5b66\u4e60\u7684\u6982\u5ff5\u6846\u67b6\u3002.&nbsp;<em>\u5b66\u4e60\u4e0e\u6559\u5b66<\/em>, \uff0c16(3)\uff0c183\u2013198\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Behr, M.\u3001Erlwanger, S. \u548c Nichols, E. (1980)\u3002\u513f\u7ae5\u5982\u4f55\u770b\u5f85\u7b49\u53f7\u3002.&nbsp;<em>\u6570\u5b66\u6559\u5b66<\/em>, \uff0c92\uff0c13-15\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Borromeo Ferri, R., &amp; Blum, W. (2012). \u5c0f\u5b66\u548c\u4e2d\u5b66\u8854\u63a5\u6559\u80b2\u4e2d\u5b66\u4e60\u8005\u5bf9\u7b49\u53f7\u7528\u6cd5\u7684\u7406\u89e3\u3002.&nbsp;<em>2012\u5e74\u6570\u5b66\u6559\u80b2\u8d21\u732e<\/em>, \uff0c127\u2013130\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bruner, JS (1966)\u3002.&nbsp;<em>\u8fc8\u5411\u6559\u5b66\u7406\u8bba<\/em>. \u54c8\u4f5b\u5927\u5b66\u51fa\u7248\u793e\u8d1d\u5c14\u7eb3\u666e\u51fa\u7248\u793e\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Carpenter, T.P.\u3001Franke, M.L. \u548c Levi, L. (2003)\u3002.&nbsp;<em>\u6570\u5b66\u601d\u7ef4\uff1a\u5c0f\u5b66\u7b97\u672f\u4e0e\u4ee3\u6570\u7684\u878d\u5408<\/em>. \u6d77\u6d85\u66fc\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dienes, ZP (1960)\u3002.&nbsp;<em>\u6784\u5efa\u6570\u5b66<\/em>. \u54c8\u94a6\u68ee\u6559\u80b2\u96c6\u56e2\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u675c\u5229\uff0cT.\uff0c\u548c\u57fa\u5c14\u4e07\uff0cA.\uff082014\uff09\u3002. <em>\u5e2e\u52a9\u5e7c\u513f\u7406\u89e3\u201a\u7b49\u53f7\u2018<\/em>. \u6f14\u8bb2\u4e8e2014\u5e7411\u670824\u65e5\u5728\u90fd\u67cf\u6797NCCA\u6570\u5b66\u4f1a\u8bae\u3002https:\/\/www.ncca.ie\/media\/2006\/ncca-maths-conf_equal-sign_24-11-14-2.pdf<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Falkner, KP, Levi, L., &amp; Carpenter, T.P. (1999). \u513f\u7ae5\u5bf9\u7b49\u5f0f\u7684\u7406\u89e3\uff1a\u4ee3\u6570\u7684\u57fa\u7840\u3002.&nbsp;<em>\u6559\u5b69\u5b50\u6570\u5b66<\/em>, \uff0c6(4)\uff0c232\u2013236\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Farfan, G. \u548c Schoen, R.C. (2021)\u3002\u5c0f\u5b66\u751f\u5bf9\u7b49\u53f7\u7684\u7406\u89e3\uff1a\u4f5b\u7f57\u91cc\u8fbe\u5dde\u7684\u5b66\u751f\u662f\u5426\u4f18\u4e8e\u540c\u9f84\u4eba\uff1f&nbsp;<em>\u6570\u5b66\u4e2d\u7684\u7ef4\u5ea6<\/em>, \uff0c41(1), 27\u201338\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hagemeister, V. (2013). \u5c0f\u5b66\u7b49\u53f7\u95ee\u9898\u3002.&nbsp;<em>\u8499\u5927\u62ff\u5927\u5b66<\/em>, \uff0c66(7), 393\u2013398\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Kieran, C. (1981). \u4e0e\u7b49\u53f7\u76f8\u5173\u7684\u6982\u5ff5\u3002.&nbsp;<em>\u6570\u5b66\u6559\u80b2\u7814\u7a76<\/em>, \uff0c12(3)\uff0c317\u2013326\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Knuth, EJ, Stephens, AC, McNeil, NM, &amp; Alibali, MW (2006). \u7406\u89e3\u7b49\u53f7\u91cd\u8981\u5417\uff1f\u6765\u81ea\u89e3\u65b9\u7a0b\u7684\u8bc1\u636e\u3002.&nbsp;<em>\u6570\u5b66\u6559\u80b2\u7814\u7a76\u6742\u5fd7<\/em>, \uff0c37(4), 297\u2013312\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Krauthausen, G. \u548c Scherer, P. (2007)\u3002.&nbsp;<em>\u6570\u5b66\u6559\u5b66\u6cd5\u5bfc\u8bba<\/em>&nbsp;\uff08\u7b2c\u4e09\u7248\uff09\u3002 Spektrum Akademischer Verlag\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mann, R.L. (2004). \u5e73\u8861\u4e4b\u9053\uff1a\u7b49\u53f7\u80cc\u540e\u7684\u771f\u76f8\u3002.&nbsp;<em>\u6559\u5b69\u5b50\u6570\u5b66<\/em>, \uff0c11(3)\uff0c65-69\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Oksuz, C. (2008). \u513f\u7ae5\u5bf9\u5e73\u7b49\u548c\u7b49\u53f7\u7684\u7406\u89e3\u3002.&nbsp;<em>\u56fd\u9645\u6570\u5b66\u6559\u5b66\u4e0e\u5b66\u4e60\u671f\u520a<\/em>, \uff0c \u516b\u6708\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u5e15\u5fb7\u4f2f\u683c\uff0cF. \u548c\u672c\u8328\uff0cC. (2021)\u3002.&nbsp;<em>\u7b97\u672f\u6559\u5b66\u6cd5<\/em>&nbsp;\uff08\u7b2c5\u7248\uff09\u3002\u65bd\u666e\u6797\u683c\u5149\u8c31\u51fa\u7248\u793e\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Prediger, S. (2009). \u201e\u2026 nee, so darf man das Gleich doch nicht denken!\u201c \u2014 Lehramtsstudierende auf dem Weg zur fachdidaktisch fundierten diagnostischen Kompetenz. In B. Barzel et al. (Hrsg.),&nbsp;<em>\u4ee3\u6570\u601d\u7ef4\u3002\u4e3d\u838e\u00b7\u8d6b\u82ac\u5fb7\u5c14-\u8d6b\u8d1d\u514b\u5c14\u8282\u6587<\/em>&nbsp;\uff08\u7b2c 89-99 \u9875\uff09\u3002\u5f17\u6717\u8328\u8d1d\u514b\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Selter, C. \u548c Spiegel, H. (1997)\u3002.&nbsp;<em>\u513f\u7ae5\u5982\u4f55\u8ba1\u6570<\/em>. \u9b54\u672f\u8d34\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sfard, A. (1991). \u8bba\u6570\u5b66\u6982\u5ff5\u7684\u4e8c\u5143\u6027\uff1a\u5bf9\u8fc7\u7a0b\u548c\u5bf9\u8c61\u4f5c\u4e3a\u540c\u4e00\u679a\u786c\u5e01\u4e24\u9762\u7684\u53cd\u601d\u3002.&nbsp;<em>\u6570\u5b66\u6559\u80b2\u7814\u7a76<\/em>, \uff0c22(1)\uff0c1-36\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Unteregge, S. (2017). \u5c0f\u5b66\u7b97\u672f\u6559\u5b66\u4e2d\u7684\u4ee3\u6570\u7b49\u5f0f\u5173\u7cfb\u3002.&nbsp;<em>2017\u5e74\u6570\u5b66\u6559\u80b2\u8d21\u732e<\/em>, \uff0c1009\u20131012 \u5e74\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Van de Walle, JA\u3001Karp, KS \u548c Bay-Williams, JM (2019)\u3002.&nbsp;<em>\u5c0f\u5b66\u548c\u521d\u4e2d\u6570\u5b66\uff1a\u5faa\u5e8f\u6e10\u8fdb\u6559\u5b66<\/em>&nbsp;\uff08\u7b2c10\u7248\uff09\u3002\u57f9\u751f\u96c6\u56e2\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wahyuni, R., &amp; Herman, T. (2019). \u5b66\u751f\u5bf9\u7b49\u53f7\u7684\u7406\u89e3\uff1a\u4ee5\u90ca\u533a\u5b66\u6821\u4e3a\u4f8b\u3002.&nbsp;<em>\u7b2c\u4e00\u5c4a\u56fd\u9645\u6559\u80b2\u79d1\u5b66\u4f1a\u8bae\u8bba\u6587\u96c6<\/em>, \uff0c351\u2013355\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Winter, H. (1982). \u5c0f\u5b66\u6570\u5b66\u6559\u5b66\u4e2d\u7684\u7b49\u53f7\u3002.&nbsp;<em>\u6570\u5b66\u6559\u5b66<\/em>, \uff0c5(4), 185\u2013211\u3002.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wittmann, EC (1981)\u3002.&nbsp;<em>\u6570\u5b66\u6559\u5b66\u7684\u57fa\u672c\u95ee\u9898<\/em>&nbsp;\uff08\u7b2c6\u7248\uff09\u3002Vieweg\u3002.<\/p>","protected":false},"excerpt":{"rendered":"<p>Die Relationszeichen interaktiv entdecken Eine Lern- und Experimentierumgebung f\u00fcr die Grundschule rund um die Relationszeichen&nbsp;=,&nbsp;&lt; und&nbsp;&gt;. Direktlink:\u00a0https:\/\/waage.urff.app Die Webapp&nbsp;Istgleich&nbsp;simuliert eine virtuelle Balkenwaage, mit der Kinder Mengen, Zahlen und Terme handelnd vergleichen. Pl\u00e4ttchen werden per Tipp oder Klick (per Multitouch gleichzeitig mehrere) erzeugt, in Schalen auf beide Seiten der Waage gelegt, gestapelt, automatisch zu Zehnerstangen geb\u00fcndelt [&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-989","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/pages\/989","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=989"}],"version-history":[{"count":7,"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/pages\/989\/revisions"}],"predecessor-version":[{"id":1357,"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/pages\/989\/revisions\/1357"}],"wp:attachment":[{"href":"https:\/\/urff.app\/zh\/wp-json\/wp\/v2\/media?parent=989"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}