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\u8a2a\u554f\u9019\u88e1\u95b1\u8b80\u66f4\u591a\u95dc\u65bc120\u79d2\u4e2d\u6709\u591a\u5c11\u5206\u9418\u7684\u4fe1\u606f\uff01<br \/><br \/>\u6578\u5b78\u5bb6\u4e00\u76f4\u90fd\u660e\u767d\uff0c\u89e3\u6c7a\u554f\u984c\u662f\u4ed6\u5011\u5b78\u79d1\u7684\u6838\u5fc3\uff0c\u56e0\u70ba\u6c92\u6709\u554f\u984c\u5c31\u6c92\u6709\u6578\u5b78\u3002\u81ea 1945 \u5e74 P\u00f3lya \u7684\u300a\u5982\u4f55\u6253\u7834\u5b83\u300b\u4e00\u66f8\u51fa\u7248\u4ee5\u4f86\uff0c\u89e3\u6c7a\u554f\u984c\u4e00\u76f4\u5728\u6559\u80b2\u652f\u6301\u8005\u7684\u601d\u60f3\u4e2d\u767c\u63ee\u6838\u5fc3\u4f5c\u7528\u3002\u5168\u570b\u6578\u5b78\u5c0e\u5e2b\u59d4\u54e1\u6703 (NCTM) \u4e00\u76f4\u5728\u5021\u5c0e\u89e3\u6c7a\u554f\u984c\u8fd1 40 \u500d\uff0c\u800c\u5f9e 1990 \u5e74\u4ee3\u521d\u958b\u59cb\uff0c\u6578\u5b78\u8f14\u5c0e\u7684\u8de8\u570b\u8da8\u52e2\u986f\u793a\u51fa\u8d8a\u4f86\u8d8a\u95dc\u6ce8\u554f\u984c\u89e3\u6c7a\u548c\u7cbe\u7d30\u5efa\u6a21\u3002<br \/><br \/>\u96a8\u8457\u570b\u969b\u4e0a\u7684\u5c0e\u5e2b\u8d8a\u4f86\u8d8a\u64d4\u5fc3\uff0c\u5982\u679c\u5b78\u8005\u8981\u9069\u5408\u4ee5\u6709\u610f\u7fa9\u7684\u65b9\u5f0f\u4f7f\u7528\u548c\u61c9\u7528\u7cbe\u7d30\u77e5\u8b58\uff0c\u63d0\u4f9b\u554f\u984c\u89e3\u6c7a\u65b9\u6848\u81f3\u95dc\u91cd\u8981\uff08Wu and Zhang 2006\uff09\u5728\u7f8e\u570b\u7684\u5b78\u8853\u5730\u4f4d\u5e7e\u4e4e\u6c92\u6709\u8b8a\u5316\u3002<br \/>\u201c\u89e3\u6c7a\u554f\u984c\u4e0d\u50c5\u662f\u5b78\u7fd2\u6578\u5b78\u7684\u4e8b\u60c5\uff0c\u4e5f\u662f\u5b78\u7fd2\u6578\u5b78\u7684\u4e3b\u8981\u624b\u6bb5\u3002\u201d<br \/><br \/>2011 \u5e74\uff0c\u901a\u7528\u6838\u5fc3\u5dde\u898f\u7bc4\u5c07\u554f\u984c\u89e3\u6c7a\u3001\u908f\u8f2f\u548c\u8b49\u64da\u3001\u6e9d\u901a\u3001\u8868\u793a\u548c\u9023\u63a5\u7684 NCTM \u904e\u7a0b\u898f\u7bc4\u7d0d\u5165\u6578\u5b78\u5be6\u8e10\u898f\u7bc4\u3002\u5c0d\u65bc\u8a31\u591a\u6578\u5b78\u5c0e\u5e2b\u4f86\u8aaa\uff0c\u9019\u662f\u4ed6\u5011\u7b2c\u4e00\u6b21\u88ab\u671f\u671b\u5c07\u5b78\u751f\u5408\u4f5c\u548c\u8207\u554f\u984c\u8655\u7406\u76f8\u7d50\u5408\u3002<br \/><br \/>\u9019\u7a2e\u505a\u6cd5\u9700\u8981\u4ee5\u622a\u7136\u4e0d\u540c\u7684\u65b9\u5f0f\u9032\u884c\u8f14\u5c0e\uff0c\u56e0\u70ba\u795e\u5b78\u9662\u5f9e\u6559\u5e2b\u8f49\u8b8a\u70ba\u66f4\u5177\u5c0d\u8a71\u6027\u7684\u8f14\u5c0e\u548c\u8b58\u5b57\u65b9\u6cd5\u3002\u5c0e\u5e2b\u9762\u81e8\u7684\u6311\u6230\u662f\u6559\u80b2\u5b78\u8005\u4e0d\u50c5\u8981\u89e3\u6c7a\u554f\u984c\uff0c\u9084\u8981\u901a\u904e\u89e3\u6c7a\u554f\u984c\u4f86\u5b78\u7fd2\u6578\u5b78\u3002\u96d6\u7136\u8a31\u591a\u5b78\u8005\u53ef\u80fd\u6703\u767c\u5c55\u51fa\u7a0b\u5e8f\u4e0a\u7684\u7121\u77e5\uff0c\u4f46\u4ed6\u5011\u7d93\u5e38\u4fdd\u8b49\u6253\u7834\u65b0\u554f\u984c\u6216\u5728\u597d\u60f3\u6cd5\u4e4b\u9593\u5efa\u7acb\u806f\u7e6b\u6240\u5fc5\u9700\u7684\u6df1\u523b\u62bd\u8c61\u7406\u89e3\u3002<br \/>\u4e00\u500b\u554f\u984c\u5de5\u4f5c\u73ed\uff0c\u4ecd\u7136\u9700\u8981\u8207\u6559\u5e2b\u4e0d\u540c\u7684\u90e8\u5206\u3002\u6559\u5e2b\u9700\u8981\u7d66\u5b78\u751f\u6642\u9593\u4f86\u89e3\u6c7a\u554f\u984c\uff0c\u81ea\u5df1\u5c0b\u627e\u7b56\u7565\u548c\u7d50\u679c\uff0c\u4e26\u5b78\u6703\u4f30\u8a08\u81ea\u5df1\u7684\u7d50\u679c\uff0c\u800c\u4e0d\u662f\u6307\u5c0e\u4f5c\u696d\u3002\u5118\u7ba1\u6559\u5e2b\u9700\u8981\u5728\u5834\u4e0a\u975e\u5e38\u91cd\u8981\uff0c\u4f46\u8ab2\u5802\u4e0a\u7684\u4e3b\u8981\u91cd\u9ede\u9700\u8981\u653e\u5728\u5b78\u8005\u5141\u8a31\u7684\u904e\u7a0b\u4e0a\u3002\u201d<br \/><br \/>\u5b78\u6703\u89e3\u6c7a\u554f\u984c<br \/>\u8981\u4e86\u89e3\u5b78\u8005\u5982\u4f55\u6210\u70ba\u554f\u984c\u89e3\u6c7a\u8005\uff0c\u6211\u5011\u9700\u8981\u770b\u770b\u90a3\u4e9b\u63d0\u9ad8\u6578\u5b78\u7d20\u990a\u7684\u547d\u984c\u3002\u5176\u4e2d\u5305\u62ec\u5c0d\u8b80\u5beb\u80fd\u529b\u7684\u5be6\u9a57\u65b9\u9762\u7684\u8a8d\u8b58\uff0c\u4ee5\u53ca\u5b78\u8005\u5011\u901a\u904e\u201c\u505a\u3001\u8aaa\u3001\u53cd\u601d\u3001\u6fc0\u52d5\u3001\u89c0\u5bdf\u3001\u63a2\u7d22\u3001\u50be\u807d\u548c\u908f\u8f2f\u201d\u52aa\u529b\u5b78\u7fd2\u6578\u5b78\u9019\u4e00\u57fa\u672c\u4e8b\u5be6\uff08Copley\uff0c2000\uff0c\u7b2c 29 \u9801\uff09\u3002\u8b58\u5b57\u5171\u69cb\u89c0\u662f\u547d\u984c\u7684\u57fa\u790e\u3002\u6b64\u5916\uff0c\u6211\u5011\u77e5\u9053\u6bcf\u500b\u5b78\u751f\u90fd\u5728\u4ed6\u5011\u7368\u7279\u7684\u767c\u5c55\u9053\u8def\u4e0a\u3002<br \/><br \/>\u5b69\u5b50\u5011\u5e36\u8457\u76f4\u89ba\u7684\u7cbe\u7d30\u7406\u89e3\u9032\u5165\u5b78\u9662\u3002\u6559\u5e2b\u9700\u8981\u901a\u904e\u8b93\u5b78\u8005\u63a2\u7d22\u6578\u5b78\u4e26\u5728\u8207\u6559\u5e2b\u548c\u4ed6\u5011\u7684\u540c\u9f61\u4eba\u9032\u884c\u6709\u610f\u7fa9\u7684\u5c0d\u8a71\u4e2d\u4ea4\u6d41\u4ed6\u5011\u7684\u60f3\u6cd5\u7684 gestes \u8207\u9019\u4e9b\u7406\u89e3\u5efa\u7acb\u806f\u7e6b\u4e26\u505a\u51fa\u7406\u89e3\u3002<br \/><br \/>\u8b58\u5b57\u767c\u751f\u5728\u793e\u6703\u74b0\u5883\u4e2d\uff08Vygotsky\uff0c1978\uff09\u3002\u5b78\u8005\u5011\u901a\u904e\u5728\u9019\u4e9b\u689d\u4ef6\u53cd\u5c04\u4e2d\u8655\u7406\u554f\u984c\u548c\u8207\u4ed6\u4eba\u9032\u884c\u4ea4\u6613\u4f86\u69cb\u5efa\u7406\u89e3\u3002\u901a\u904e\u9019\u4e9b\u793e\u6703\u95dc\u4fc2\uff0c\u5b78\u8005\u5011\u89ba\u5f97\u4ed6\u5011\u53ef\u4ee5\u6293\u4f4f\u9677\u9631\uff0c\u5617\u8a66\u65b0\u7684\u7b56\u7565\uff0c\u4e26\u7d66\u4e88\u548c\u627f\u8a8d\u53cd\u994b\u3002\u7576\u4ed6\u5011\u5206\u4eab\u4e00\u7cfb\u5217\u89c0\u9ede\u6216\u89e3\u6c7a\u554f\u984c\u7684\u5404\u7a2e\u65b9\u6cd5\u6642\uff0c\u4ed6\u5011\u6703\u5408\u4f5c\u5b78\u7fd2\u3002\u6b63\u662f\u901a\u904e\u8ac7\u8ad6\u554f\u984c\u548c\u6fc0\u767c\u4ed6\u5011\u7684\u60f3\u6cd5\uff0c\u5b69\u5b50\u5011\u69cb\u5efa\u77e5\u8b58\u4e26\u7372\u5f97\u8a9e\u8a00\u4f86\u7406\u89e3 gests\u3002<br \/><br \/>\u5b78\u8005\u5011\u901a\u904e\u89e3\u6c7a\u554f\u984c\u800c\u4e0d\u662f\u76f4\u63a5\u63a5\u53d7\u8f14\u5c0e\uff0c\u5f9e\u800c\u7372\u5f97\u5c0d\u6578\u5b78\u7684\u7406\u89e3\u4e26\u57f9\u990a\u89e3\u6c7a\u554f\u984c\u7684\u80fd\u529b\uff08Hiebert1997\uff09\u3002\u6559\u5e2b\u7684\u8077\u8cac\u662f\u69cb\u5efa\u554f\u984c\u548c\u5448\u73fe\u60c5\u5883\uff0c\u70ba\u554f\u984c\u5de5\u4f5c\u63d0\u4f9b\u4e00\u500b\u8ad6\u58c7\u3002<br \/><br \/>\u70ba\u4ec0\u9ebc\u554f\u984c\u5de5\u4f5c\u5f88\u91cd\u8981\uff1f<br \/>\u6211\u5011\u7684\u5b78\u8005\u751f\u6d3b\u5728\u4e00\u500b\u4ee5\u4fe1\u606f\u548c\u6280\u8853\u70ba\u57fa\u790e\u7684\u793e\u6703\u4e2d\uff0c\u4ed6\u5011\u9700\u8981\u9069\u5408\u5c0d\u8907\u96dc\u554f\u984c\u9032\u884c\u6279\u5224\u6027\u5047\u8a2d\uff0c\u4e26\u4e14\u201c\u5c0d\u65b0\u60c5\u6cc1\u9032\u884c\u908f\u8f2f\u5256\u6790\u548c\u5047\u8a2d\uff0c\u7de8\u9020\u672a\u77e5\u7684\u7d50\u679c\u7a0b\u5e8f\uff0c\u4e26\u5c07\u5176\u7d50\u679c\u8f15\u9b06\u800c\u4ee4\u4eba\u4fe1\u670d\u5730\u50b3\u9054\u7d66\u4ed6\u4eba\u201d\u3002\u5df4\u9b6f\u8fea\uff0c1998\uff09\u3002\u6578\u5b78\u6559\u80b2\u4e4b\u6240\u4ee5\u91cd\u8981\uff0c\u4e0d\u50c5\u662f\u56e0\u70ba\u201c\u6578\u5b78\u5728\u5b78\u8005\u7372\u5f97\u6559\u80b2\u548c\u6709\u5229\u53ef\u5716\u7684\u6a5f\u6703\u65b9\u9762\u767c\u63ee\u4e86\u628a\u95dc\u4f5c\u7528\u201d\uff0c\u800c\u4e14\u9084\u56e0\u70ba\u89e3\u6c7a\u554f\u984c\u7684\u904e\u7a0b\u548c\u89e3\u6c7a\u554f\u984c\u7684\u7b56\u7565\u7684\u52a0\u5165\u70ba\u5b78\u8005\u5011\u63d0\u4f9b\u4e86\u8d85\u8d8a\u5b78\u9662\u7684\u751f\u6d3b\uff08\u79d1\u5e03, 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