{"id":9753,"date":"2026-07-22T21:07:02","date_gmt":"2026-07-22T13:07:02","guid":{"rendered":"https:\/\/www.coletree.com\/weblog\/?p=9753"},"modified":"2026-07-26T16:52:03","modified_gmt":"2026-07-26T08:52:03","slug":"mathematical-thinking-learning-for-children","status":"publish","type":"post","link":"https:\/\/www.coletree.com\/weblog\/studio\/children-programming\/mathematical-thinking-learning-for-children\/","title":{"rendered":"\u5b69\u5b50\u7684\u6570\u7406\u601d\u7ef4\u5b66\u4e60"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u7f16\u7a0b\u60f3\u5b66\u597d\u4e00\u70b9\uff0c\u5c31\u4e0d\u53ea\u662f\u5b66\u4e60\u7f16\u7a0b\u8bed\u8a00\u76f8\u5173\u77e5\u8bc6\u3002\u4e0d\u7ba1\u5b66\u4ec0\u4e48\u8bed\u8a00\uff0c\u6709\u6bd4\u8f83\u597d\u7684\u6570\u5b66\u57fa\u7840\u90fd\u80fd\u4e8b\u534a\u529f\u500d\u3002\u81ea\u4ece\u5c0f\u9c7c\u4e00\u5e74\u7ea7\u5f00\u59cb\u5b66\u4e60\u6570\u5b66\uff0c\u6211\u4eec\u4e70\u8fc7\u76f8\u5173\u5b66\u4e60\u4e66\u7c4d\uff0c\u4e5f\u5c1d\u8bd5\u8fc7\u62a5\u57f9\u8bad\u673a\u6784\uff08\u5c1d\u8bd5\u4e00\u671f\u540e\u653e\u5f03\uff09\u3002\u51e0\u4e2a\u5e74\u7ea7\u7684\u5b66\u4e60\u7ecf\u5386\u4e0b\u6765\uff0c\u81ea\u5df1\u611f\u89c9\u6bd4\u8f83\u6709\u7528\u7684\u6709\u4ee5\u4e0b\u8fd9\u4e9b\u8d44\u6e90\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">1. \u5b66\u79d1\u5185\u6559\u8f85\u4e66&amp;\u8d44\u6e90<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6559\u8f85\u4e66\uff1a\u300a\u65b0\u52a0\u5761\u6570\u5b66\u5efa\u6a21\u300b\u8fd9\u4e2a\u662f\u4f4e\u5e74\u7ea7\u65f6\u5019\u4e70\u7684\u65b0\u52a0\u5761\u7684\u6570\u5b66\u4e66\uff0c\u91cc\u9762\u7684\u56fe\u793a\u633a\u597d\u7684\u3002\u6211\u89c9\u5f97\u7279\u522b\u9002\u5408\u5b69\u5b50\u7406\u89e3\u57fa\u7840\u6982\u5ff5\u3002\u7b97\u662f\u4e70\u5f97\u6bd4\u8f83\u6ee1\u610f\u7684\u6559\u8f85\u4e66\u3002<\/li>\n\n\n\n<li>\u6559\u8f85\u4e66\uff1a\u300a\u4e3e\u4e00\u53cd\u4e09\u300b\u8fd9\u4e2a\u662f\u56fd\u5185\u4e66\u5e97\u7684\u70ed\u95e8\u6559\u8f85\u4e66\uff0c\u91cc\u9762\u662f\u4e00\u4e9b\u6d45\u5965\u8d5b\u7684\u9898\u76ee\uff0c\u91cd\u70b9\u4f3c\u4e4e\u4e5f\u662f\u591a\u7ec3\u4e60\u591a\u5237\u9898\uff0c\u4e66\u672c\u8eab\u5e76\u6ca1\u6709\u8bb2\u89e3\u592a\u591a\u3002\u6240\u4ee5\u6211\u89c9\u5f97\u4e00\u822c\uff0c\u6700\u540e\u4e5f\u4e0d\u4e70\u4e86\u3002<\/li>\n\n\n\n<li>\u89c6\u9891\u8d44\u6e90\uff1a<a href=\"https:\/\/www.bilibili.com\/video\/BV1mjSjBJEkE\/?spm_id_from=333.337.search-card.all.click&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\" data-type=\"link\" data-id=\"https:\/\/www.bilibili.com\/video\/BV1mjSjBJEkE\/?spm_id_from=333.337.search-card.all.click&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\">\u6e05\u534e\u9644\u5c0f\u6570\u5b66\u89c6\u9891\uff081-6\u5e74\u7ea7\uff09<\/a>\u3002\u8fd9\u4e2a\u7cfb\u5217\u89c6\u9891\u7279\u522b\u9002\u5408\u7528\u4f5c\u65b0\u5b66\u671f\u7684\u9884\u4e60\uff0c\u4e00\u4e2a\u662f\u7279\u522b\u6d45\u663e\u6613\u61c2\uff0c\u90fd\u662f\u8bfe\u672c\u57fa\u7840\u77e5\u8bc6\uff1b\u7b2c\u4e8c\u662f\u8bed\u901f\u4e0d\u5feb\uff0c\u7279\u522b\u5408\u9002\uff1b\u6700\u540e\u52a8\u753b\u505a\u5f97\u77ed\u5c0f\u6613\u61c2\u3002\u975e\u5e38\u63a8\u8350\u9884\u4e60\u4f7f\u7528\u3002<\/li>\n\n\n\n<li>\u89c6\u9891\u8d44\u6e90\uff1a<a href=\"https:\/\/www.bilibili.com\/video\/BV1evS1YnEpV\/?spm_id_from=333.1387.favlist.content.click\" data-type=\"link\" data-id=\"https:\/\/www.bilibili.com\/video\/BV1evS1YnEpV\/?spm_id_from=333.1387.favlist.content.click\">\u9ad8\u65af\u6570\u5b661-6\u5e74\u7ea7\u52a8\u753b\u7248 &#8211; \u5965\u6570\u601d\u7ef4\u63d0\u5347<\/a>\u3002\u8fd9\u4e2a\u7cfb\u5217\u6bd4\u8bfe\u672c\u77e5\u8bc6\u96be\u4e00\u70b9\u70b9\uff0c\u7a0d\u5fae\u591a\u8bb2\u4e00\u4e9b\u6280\u5de7\uff0c\u7f3a\u70b9\u662f\u6211\u89c9\u5f97\u8bed\u901f\u592a\u5feb\u4e86\uff0c\u6574\u5f97\u50cf\u662f\u52a8\u753b\u7247\u4e00\u6837\uff0c\u4e0d\u591f\u53cb\u597d\u3002<\/li>\n\n\n\n<li><a href=\"https:\/\/zh.khanacademy.org\">\u53ef\u6c57\u5b66\u9662<\/a>\uff1a\u53ef\u6c57\u5b66\u9662\u91cc\u6709\u5c0f\u5b66\u5230\u521d\u4e2d\u7684\u57fa\u672c\u6570\u5b66\u6559\u7a0b\uff0c\u548c\u56fd\u5185\u6570\u5b66\u6559\u6750\u8fdb\u5ea6\u57fa\u672c\u4e5f\u80fd\u5bf9\u5f97\u4e0a\uff0c\u5e76\u4e14\u90fd\u662f\u514d\u8d39\u7684\u3002\u6bd4\u8f83\u9002\u5408\u7ed9\u5b69\u5b50\u7528\u6765\u505a\u6570\u5b66\u8bfe\u7a0b\u9884\u4e60\uff0c\u90fd\u662f\u8bfe\u672c\u4e0a\u7684\u77e5\u8bc6\uff0c\u6ca1\u6709\u4ec0\u4e48\u96be\u7684\u77e5\u8bc6\u70b9\u3002<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">2. \u8bfe\u5916\u62d3\u5c55\u8bfe\u7a0b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8bfe\u5916\u62d3\u5c55\u65b9\u9762\uff0c\u6211\u4eec\u8fd8\u662f\u5e0c\u671b\u953b\u70bc\u5b69\u5b50\u7684\u6570\u7406\u601d\u7ef4\uff0c\u903b\u8f91\u601d\u7ef4\u4e3a\u4e3b\u3002\u5e76\u6ca1\u6709\u60f3\u8981\u53c2\u52a0\u56fd\u5185\u7684\u5965\u8d5b\u57f9\u8bad\uff0c\u603b\u89c9\u673a\u6784\u7684\u5f88\u591a\u5965\u8d5b\u57f9\u8bad\u90fd\u662f\u5b66\u4e60\u4e00\u4e9b\u8ba1\u7b97\u7684\u5947\u6280\u6deb\u5de7\uff0c\u5f88\u591a\u90fd\u4e0d\u8bb2\u201c\u6240\u4ee5\u7136\u201d\uff0c\u4f8b\u5982\u8bb2\u4e00\u7b14\u753b\u95ee\u9898\u7684\u65f6\u5019\uff0c\u5c31\u662f\u8ba9\u5b69\u5b50\u80cc\u7ed3\u8bba\u3002\u4f46\u80cc\u540e\u7684\u63a8\u7406\u5206\u6790\u662f\u5f88\u5c11\u8bb2\uff0c\u6240\u4ee5\u4e0d\u662f\u5f88\u559c\u6b22\u3002\u4e07\u4e00\u540e\u9762\u5b69\u5b50\u6ca1\u6709\u5929\u4efd\u80fd\u51b2\u6bd4\u8d5b\u540d\u6b21\uff0c\u90a3\u4e9b\u5b66\u8fc7\u7684\u77e5\u8bc6\u3001\u82b1\u8d39\u7684\u65f6\u95f4\uff0c\u4f3c\u4e4e\u5bf9\u5176\u4ed6\u65b9\u9762\u6ca1\u4ec0\u4e48\u5b9e\u8d28\u4f5c\u7528\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u5c1d\u8bd5\u4e00\u4e0b AMC8 \u6bd4\u8d5b\u4f3c\u4e4e\u6210\u672c\u662f\u76f8\u5bf9\u80fd\u63a5\u53d7\u7684\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u7f57\u535a\u6df1\u6559\u6388\u8bfe\u7a0b<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u7f57\u535a\u6df1\u662f\u524d\u7f8e\u56fd\u5965\u6570\u961f\u603b\u6559\u7ec3\uff0c\u4ed6\u7684\u8bb2\u89e3\u98ce\u683c\u6781\u5177\u542f\u53d1\u6027\uff0c\u5584\u4e8e\u7528\u7b80\u5355\u7684\u56fe\u5f62\u548c\u903b\u8f91\u628a AMC 8 \u7ea7\u522b\u7684\u96be\u9898\u8bb2\u5f97\u751f\u52a8\u6709\u8da3\u3002\u4ed6\u5728\u6cb9\u7ba1\u6709\u4e13\u95e8\u6559\u5b66\u9891\u9053\uff1b\u5728\u5b98\u7f51\u4e0a\u4e5f\u6709 <a href=\"https:\/\/daily.poshenloh.com\/\" data-type=\"link\" data-id=\"https:\/\/daily.poshenloh.com\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u7f57\u535a\u6df1\u6559\u6388\u7684\u6bcf\u65e5\u6311\u6218<\/a> \u7cfb\u5217\uff0c\u4f46\u90fd\u662f\u82f1\u6587\u7684\u3002B\u7ad9\u6709\u4ed6\u7684 ACM8 \u7684\u6559\u5b66\u89c6\u9891\u7ffb\u8bd1\uff0c\u8fd9\u91cc\u6309\u7167\u4ece\u6613\u5230\u96be\u7684\u987a\u5e8f\uff0c\u5217\u4e3e\u4e00\u4e9b\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2705 <a href=\"https:\/\/www.bilibili.com\/video\/BV1gG2gYBE99?spm_id_from=333.788.videopod.episodes&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\" target=\"_blank\" rel=\"noreferrer noopener\">\u7f57\u535a\u6df1\u5c0f\u5b66\u6570\u611f\u8bad\u7ec3\uff082-4\u5e74\u7ea7\uff09<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.bilibili.com\/video\/BV1Ut421571T?spm_id_from=333.788.videopod.episodes&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\" target=\"_blank\" rel=\"noreferrer noopener\">\u7f57\u535a\u6df1\u5c0f\u5b66\u6570\u5b66\u9752\u5c11\u5e74\u6570\u5b66\u601d\u7ef4\u5206\u7ea7\u8bfe\u7a0b &#8211; 24\u96c6\u5168\uff083-4\u5e74\u7ea7\uff09<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.bilibili.com\/video\/BV1TF4m177pp\/?spm_id_from=333.1387.favlist.content.click&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\">\u7f57\u535a\u6df1\u5c0f\u5b66\u6570\u5b66\u601d\u7ef4\u5165\u95e8\u8bfe\uff08\u6392\u5217\u7ec4\u5408+\u9b54\u6cd5\u7b97\u672f\uff09<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.bilibili.com\/video\/BV1Fk4y1D7nL\/?spm_id_from=333.1387.favlist.content.click&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\" target=\"_blank\" rel=\"noreferrer noopener\">\u7f57\u535a\u6df1\u5c0f\u5b66\u6570\u5b66\u601d\u7ef4\uff08\u5e73\u9762\u51e0\u4f55\u57fa\u7840\uff09- 13\u96c6\u5168<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.bilibili.com\/video\/BV16z4y1w7wU\/?spm_id_from=333.788.recommend_more_video.1&amp;trackid=web_related_0.router-related-2479604-dplt2.1784723775934.325&amp;vd_source=6a50a0924a25c3b16d2998930d6ef24b\" target=\"_blank\" rel=\"noreferrer noopener\">\u5168\u7f8e\u6570\u5b66\u7ade\u8d5bAMC8\/10\u7ea7\u5165\u95e8\u7cbe\u8bb2 &#8211; \u601d\u7ef4\u57f9\u517b<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">ACM \u8d44\u6599<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.omegalearn.org\/\">OmegaLearn<\/a>\uff1a\u7cfb\u7edf\u7684 AMC 8 \u5907\u8003\u8d44\u6599\uff0c\u6cb9\u7ba1\u6709\u89c6\u9891\uff0c\u4f46\u662f\u662f\u82f1\u8bed\u7684\u3002<\/li>\n\n\n\n<li>AoPS Wiki\uff1a\u5386\u5e74\u771f\u9898\u5e93\uff0c\u514d\u8d39\u5237\u9898\u4e0e\u89e3\u6790\u7f51\u7ad9\uff0c\u8fd9\u662f\u6700\u6743\u5a01\u7684\u514d\u8d39\u8d44\u6e90\u3002\u6536\u5f55\u4e86\u4ece 1985 \u5e74\u81f3\u4eca\u6240\u6709\u7684 AMC 8 \u771f\u9898\u3002\u6bcf\u9053\u9898\u90fd\u7531\u5168\u7403\u7684\u6570\u5b66\u6559\u7ec3\u548c\u5b66\u9738\u63d0\u4f9b\u4e86\u591a\u79cd\u4e0d\u540c\u7684\u89e3\u9898\u601d\u8def\u3002\u641c\u7d22 &#8220;AoPS Wiki AMC 8 Problems and Solutions&#8221; \u5373\u53ef\u3002<\/li>\n\n\n\n<li>ZIML\uff1aZoom International Math League \u514d\u8d39\u5237\u9898\u4e0e\u89e3\u6790\u7f51\u7ad9\uff0c\u4e00\u4e2a\u63d0\u4f9b\u514d\u8d39\u6570\u5b66\u7ade\u8d5b\u7ec3\u4e60\u7684\u5e73\u53f0\u3002\u62e5\u6709\u4e13\u95e8\u7684 AMC 8 \u6bcf\u65e5\u4e00\u9898\u548c\u6a21\u62df\u6d4b\u8bd5\u7cfb\u7edf\uff0c\u652f\u6301\u81ea\u52a8\u9605\u5377\uff0c\u53ef\u4ee5\u7528\u6765\u5e2e\u5b69\u5b50\u4fdd\u6301\u624b\u611f\u548c\u8fdb\u884c\u9650\u65f6\u8bad\u7ec3\u3002<\/li>\n\n\n\n<li>AoPS Volume 1 The Basics\uff1aAMC \u5b98\u65b9\u673a\u6784 Art of Problem Solving \u51fa\u7248\u7684\u6559\u6750\uff0c\u5b8c\u7f8e\u8986\u76d6\u4e86 AMC 8 \u6240\u9700\u7684\u5168\u90e8\u77e5\u8bc6\u4f53\u7cfb\uff0c\u9002\u5408\u4f5c\u4e3a\u5e95\u5b50\u6559\u6750\u3002<\/li>\n\n\n\n<li>American Mathematics Competitions 8 Preparation\uff1a\u9488\u5bf9 AMC 8 \u6700\u7cfb\u7edf\u7684\u4e13\u9879\u8bad\u7ec3\u4e66\u4e4b\u4e00\uff0c\u6309\u77e5\u8bc6\u70b9\u5206\u7c7b\uff0c\u5305\u542b\u5927\u91cf\u7684\u4f8b\u9898\u548c\u8be6\u5c3d\u7684\u6b65\u9aa4\u89e3\u6790\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Brilliant<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/brilliant.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">Brilliant<\/a> \u662f\u4e00\u4e2a\u542f\u53d1\u5f0f\u7684\u6570\u7406\u601d\u7ef4\u5b66\u4e60\u5e73\u53f0\uff0c\u6709\u70b9\u50cf\u6570\u7406\u9886\u57df\u7684\u591a\u90bb\u56fd\u3002\u91c7\u7528\u7531\u6d45\u5165\u6df1\u7684\u89c6\u89c9\u5316\u4e92\u52a8\u6559\u5b66\uff0c\u8bbe\u8ba1\u548c\u4ea4\u4e92\u8bbe\u8ba1\u90fd\u6bd4\u8f83\u597d\uff0c\u7b80\u5355\u6709\u8da3\u5473\u3002\u53ea\u662f\u4e0d\u652f\u6301\u4e2d\u6587\uff0c\u5e76\u4e14\u514d\u8d39\u5e10\u53f7\u6bcf\u5929\u53ea\u80fd\u73a9 2 \u4e2a\u5355\u5143\u7684\u8bfe\uff1b\u6536\u8d39\u5e10\u53f7\u5219\u4e0d\u53d7\u9650\u5236\u3002\u4ed8\u8d39\u4ef7\u683c\u662f\u6bcf\u6708 30 \u7f8e\u5143\u5de6\u53f3\uff0c\u6bd4\u8f83\u8d35\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">3. \u6559\u5b66\u5de5\u5177\u5e73\u53f0<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u6709\u65f6\u5019\u5728\u6559\u5b66\u65f6\uff0c\u6211\u4eec\u9700\u8981\u753b\u4e00\u4e9b\u56fe\u793a\uff0c\u5e0c\u671b\u66f4\u76f4\u89c2\u5730\u5411\u5b69\u5b50\u5c55\u793a\u3002\u8fd9\u65f6\u9700\u8981\u4e00\u4e9b\u753b\u56fe\u5de5\u5177\uff0c\u5982\u679c\u80fd\u4ea4\u4e92\u90a3\u66f4\u597d\u3002\u4f46\u6211\u4eec\u4e0d\u5927\u5e0c\u671b\u4ec5\u56e0\u4e3a\u8fd9\u4e2a\u7406\u7531\uff0c\u53bb\u5b89\u88c5\u6216\u5b66\u4e60\u4e00\u4e2a\u4e13\u4e1a\u7684\u7ed8\u56fe\u8f6f\u4ef6\u3002\u5e76\u4e14\u8fd9\u4e9b\u56fe\u6709\u65f6\u5019\u7528 AI \u753b\u4e5f\u4e0d\u662f\u592a\u51c6\u786e\u3002\u90a3\u4ee5\u4e0b\u8fd9\u4e9b\u5de5\u5177\u662f\u6211\u5c1d\u8bd5\u8fc7\uff0c\u6bd4\u8f83\u65b9\u4fbf\u4e14\u597d\u7528\u7684\uff0c\u6bcf\u4e2a\u90fd\u63a8\u8350\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">GeoGebra<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.geogebra.org\/?lang=zh-CN\" target=\"_blank\" rel=\"noreferrer noopener\">GeoGebra<\/a> \u6700\u4e3a\u63a8\u8350\uff0c\u652f\u6301\u7f51\u9875\u7248\u5728\u7ebf\u4f7f\u7528\uff0c\u4e5f\u6709\u7535\u8111\u7aef\u548c\u624b\u673a\u7aefApp\u3002GeoGebra \u662f\u5168\u7403\u6700\u53d7\u6b22\u8fce\u7684\u514d\u8d39\u6570\u5b66\u7ed8\u56fe\u8f6f\u4ef6\uff0c\u529f\u80fd\u6700\u5168\u9762\uff0c\u5b8c\u7f8e\u652f\u6301\u4e2d\u6587\u3002\u975e\u5e38\u9002\u5408\u7ed8\u5236\u5305\u542b\u5706\u3001\u5207\u7ebf\u3001\u52a8\u6001\u6f14\u793a\u7684\u51e0\u4f55\u9898\u3002\u62e5\u6709\u4e13\u95e8\u7684\u51e0\u4f55\u5de5\u5177\u680f\uff0c\u70b9\u9009\u5373\u53ef\u8f7b\u677e\u753b\u51fa\u5706\u3001\u5706\u5fc3\u3001\u534a\u5f84\u3001\u5207\u7ebf\u53ca\u5782\u7ebf\u3002\u652f\u6301\u4e00\u952e\u6dfb\u52a0\u9634\u5f71\u3001\u989c\u8272\u586b\u5145\u4ee5\u53ca\u8be6\u7ec6\u7684\u51e0\u4f55\u6807\u6ce8\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Desmos<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.desmos.com\/geometry\" target=\"_blank\" rel=\"noreferrer noopener\">Desmos<\/a> \u662f\u4e00\u6b3e\u754c\u9762\u7cbe\u7f8e\u3001\u6781\u7b80\u7684\u5728\u7ebf\u51e0\u4f55\u7ed8\u56fe\u5de5\u5177\uff0c\u4e0a\u624b\u5feb\u3002\u540c\u6837\u652f\u6301\u7f51\u9875\u7aef\u5728\u7ebf\u64cd\u4f5c\u3002\u867d\u7136\u529f\u80fd\u6bd4 GeoGebra \u7565\u5c11\uff0c\u4f46\u5bf9\u4e8e\u7ed8\u5236\u57fa\u7840\u7684\u5706\u53ca\u7ebf\u6bb5\u5207\u7ebf\u7ef0\u7ef0\u6709\u4f59\uff0c\u4e14\u81ea\u5e26\u9ad8\u7ea7\u7ed8\u56fe\u5f15\u64ce\uff0c\u753b\u51fa\u7684\u56fe\u5f62\u975e\u5e38\u6e05\u6670\u7f8e\u89c2\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Mathigon<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/mathigon.org\/\" target=\"_blank\" rel=\"noreferrer noopener\">Mathigon<\/a> \u53f7\u79f0\u6570\u5b66\u6e38\u4e50\u573a\uff0c\u662f\u4e00\u6b3e\u514d\u8d39\u7684\u6570\u5b66\u5de5\u5177\u3001\u8bfe\u7a0b\u548c\u6559\u5177\u3002\u5176\u6838\u5fc3\u4eae\u70b9\u662f\u5c06\u6570\u5b66\u77e5\u8bc6\u505a\u6210\u4e86\u50cf\u89e3\u8c1c\u6e38\u620f\u4e00\u6837\u7684\u4e92\u52a8\u8bfe\u672c\uff08Polypad \u7ed8\u56fe\u677f\uff09\u3002\u5b69\u5b50\u53ef\u4ee5\u7528\u624b\u6307\u62d6\u52a8\u865a\u62df\u7684\u201c\u51e0\u4f55\u74f7\u7816\u201d\u3001\u6298\u53e0\u4e09\u7ef4\u5c55\u5f00\u56fe\u3001\u65cb\u8f6c\u5706\u548c\u5207\u7ebf\uff0c\u6240\u6709\u7684\u51e0\u4f55\u5b9a\u7406\u548c\u5206\u6570\u6982\u5ff5\u90fd\u80fd\u901a\u8fc7\u52a8\u6001\u64cd\u4f5c\u77ac\u95f4\u770b\u61c2\u3002\u7b80\u5355\u8bf4\u5c31\u662f\u5b83\u5185\u7f6e\u4e86\u5f88\u591a\u53ef\u4ea4\u4e92\u7684\u7ec4\u4ef6\uff0c\u633a\u65b9\u4fbf\u52a8\u624b\u64cd\u4f5c\u4f53\u9a8c\u7684\u3002\u4f46\u662f\u81ea\u5b9a\u4e49\u7684\u7ed8\u56fe\u529f\u80fd\u5c31\u597d\u50cf\u5f31\u4e00\u70b9\uff0c\u6216\u8005\u8bf4\u4e0d\u662f\u5f88\u987a\u624b\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Wolfram&nbsp;Demonstrations Project<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/demonstrations.wolfram.com\">https:\/\/demonstrations.wolfram.com<\/a> Wolfram \u521b\u7acb\u7684\u7f51\u7ad9\uff0c\u8fd9\u91cc\u6709\u5927\u91cf\u7684\u6570\u5b66\u6982\u5ff5\u7684\u53ef\u64cd\u4f5c\u6a21\u578b\uff0c\u53ef\u4ee5\u67e5\u627e\u6765\u505a\u6f14\u793a\u3002\u9664\u4e86\u6570\u5b66\uff0c\u8fd8\u6709\u5927\u91cf\u7684\u5176\u4ed6\u9886\u57df\u7684\u6a21\u578b\uff0c\u4f8b\u5982\u8ba1\u7b97\u673a\u7684\uff0c\u751a\u81f3\u8fde\u5e73\u9762\u8bbe\u8ba1\u90fd\u6709\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">4. \u6570\u5b66\u5174\u8da3\u79d1\u666e\u4e66<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8001\u5e08\u4eec\u7ecf\u5e38\u5728\u5bd2\u6691\u5047\u4f1a\u5e03\u7f6e\u4f5c\u4e1a\uff0c\u8ba9\u5b69\u5b50\u53bb\u770b\u4e00\u4e9b\u6570\u5b66\u7684\u79d1\u666e\u4e66\u3001\u5174\u8da3\u4e66\u3002\u8fd9\u7c7b\u4e66\u4e3b\u8981\u76ee\u7684\u662f\u63d0\u5347\u5174\u8da3\uff0c\u5927\u540c\u5c0f\u5f02\uff0c\u4e70\u8fc7\u4e00\u4e9b\u540e\u53d1\u73b0\u5176\u5b9e\u90fd\u4e0d\u5927\u503c\u5f97\u3002\u6700\u540e\u81ea\u5df1\u7559\u4e0b\u7684\u89c9\u5f97\u4e0d\u9519\u7684\u6709\u4ee5\u4e0b\u8fd9\u4e9b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/book.douban.com\/subject\/2270743\/\">\u6211\u7684\u7b2c\u4e00\u672c\u6570\u5b66\u4e66<\/a>\uff1a\u8fd9\u4e2a\u6bd4\u8f83\u7b80\u5355\uff0c\u9002\u5408\u5b69\u5b50\u81ea\u5df1\u770b<\/li>\n\n\n\n<li><a href=\"https:\/\/www.douban.com\/personage\/37403474\/\">\u201c\u70c2\u63d2\u753b\u201d\u7684\u5feb\u4e50\u6570\u5b66\u542f\u8499\u4e66\u7cfb\u5217<\/a>\uff1a\u8fd9\u5957\u4e66\u5012\u662f\u633a\u6709\u8da3\u7684\uff0c\u4f46\u662f\u5e74\u7eaa\u5c0f\u7684\u5b69\u5b50\u9700\u8981\u7236\u6bcd\u966a\u8bfb<\/li>\n\n\n\n<li><a href=\"https:\/\/book.douban.com\/subject\/4182774\/\">\u8981\u547d\u7684\u6570\u5b66\u7cfb\u5217<\/a>\uff1a\u8f7b\u677e\u5e7d\u9ed8<\/li>\n\n\n\n<li><a href=\"https:\/\/book.douban.com\/subject\/26148739\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u6570\u5b66\u4e0e\u751f\u6d3b\u7cfb\u5217 &#8211; \u8fdc\u5c71\u542f<\/a>\uff1a\u65e5\u672c\u4eba\u5199\u7684\uff0c\u8fd8\u6ca1\u8bfb\u5462<\/li>\n\n\n\n<li>\u6570\u5b66\u7684\u96e8\u4f1e\u4e0b<\/li>\n\n\n\n<li>\u7528\u6570\u5b66\u7684\u8bed\u8a00\u770b\u4e16\u754c<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u9664\u4e86\u4e0a\u9762\u8fd9\u4e9b\uff0c\u6211\u8fd8\u4f7f\u7528 Codex \u7ed9\u5b69\u5b50\u505a\u4e86\u4e00\u5957\u6570\u5b66\u5b66\u4e60\u7684\u7cfb\u7edf\uff0c\u6b63\u51c6\u5907\u5728\u8fd9\u4e2a\u6691\u5047\u6295\u5165\u4f7f\u7528 \ud83d\ude04<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"1156\" src=\"https:\/\/www.coletree.com\/weblog\/wp-content\/uploads\/2026\/07\/math-learning-system-scaled.png\" alt=\"\" class=\"wp-image-9766\" srcset=\"https:\/\/www.coletree.com\/weblog\/wp-content\/uploads\/2026\/07\/math-learning-system-scaled.png 2560w, https:\/\/www.coletree.com\/weblog\/wp-content\/uploads\/2026\/07\/math-learning-system-768x347.png 768w, https:\/\/www.coletree.com\/weblog\/wp-content\/uploads\/2026\/07\/math-learning-system-1536x693.png 1536w, https:\/\/www.coletree.com\/weblog\/wp-content\/uploads\/2026\/07\/math-learning-system-2048x925.png 2048w\" sizes=\"auto, (max-width: 2560px) 100vw, 2560px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>\u7f16\u7a0b\u60f3\u5b66\u597d\u4e00\u70b9\uff0c\u5c31\u4e0d\u53ea\u662f\u5b66\u4e60\u7f16\u7a0b\u8bed\u8a00\u76f8\u5173\u77e5\u8bc6\u3002\u4e0d\u7ba1\u5b66\u4ec0\u4e48\u8bed\u8a00\uff0c\u6709\u6bd4\u8f83\u597d\u7684\u6570\u5b66\u57fa\u7840\u90fd\u80fd\u4e8b\u534a\u529f\u500d\u3002\u81ea\u4ece\u5c0f\u9c7c\u4e00\u5e74\u7ea7\u5f00 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[194],"tags":[],"series":[],"class_list":["post-9753","post","type-post","status-publish","format-standard","hentry","category-children-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/posts\/9753","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/comments?post=9753"}],"version-history":[{"count":7,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/posts\/9753\/revisions"}],"predecessor-version":[{"id":9776,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/posts\/9753\/revisions\/9776"}],"wp:attachment":[{"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/media?parent=9753"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/categories?post=9753"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/tags?post=9753"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.coletree.com\/weblog\/wp-json\/wp\/v2\/series?post=9753"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}