• 北京学诚国际教育是国际课程辅导的专业机构
  • 学诚国际教育由深耕国际课程教学、教研领域多年的优师组成
  • 学诚国际教育从创立开始就致力于研究和开发国际课程辅导专业模式

400-882-1633

北京学诚国际教育HiMCM竞赛课程全解析:中学生数学建模能力进阶指南

北京学诚国际教育HiMCM竞赛课程全解析:中学生数学建模能力进阶指南

授课机构: 北京学诚国际教育

上课地点: 校区地址

成交/评价:

联系电话: 400-882-1633

北京学诚国际教育HiMCM竞赛课程全解析:中学生数学建模能力进阶指南课程详情

HiMCM竞赛:国际认可的中学生数学建模舞台

美国高中数学建模竞赛(HiMCM)作为国际数学教育领域的重要赛事,自1999年由美国数学及其应用联合会(COMAP)发起以来,持续得到美国国家科学基金会(NSF)、运筹和管理科学研究所(INFORMS)等权威机构的支持。这项竞赛打破传统数学考试模式,将现实问题转化为数学模型,要求学生通过团队协作完成分析、求解与论证,是检验综合学术能力的关键平台。

北京学诚国际教育基于对HiMCM竞赛的深度研究,推出针对性竞赛课程,帮助学生适应“从知识记忆到问题解决”的思维转变。课程不仅涵盖竞赛规则解析,更注重数学工具应用、英文论文写作及团队协作技巧的系统训练,为学生参与国际赛事提供全方位支持。

HiMCM竞赛课程核心设计逻辑

区别于常规数学课程,HiMCM竞赛课程以“解决现实问题”为导向,参考大学生数学建模竞赛框架并结合中学生认知特点优化。课程设置三大模块:

  • **数学建模基础**:教授数据收集、模型构建、结果验证等核心方法,重点掌握Excel、MATLAB等工具的实际应用;
  • **团队协作训练**:模拟4人团队分工场景,培养问题拆解、观点整合及冲突解决能力;
  • **英文论文写作**:从摘要提炼到参考文献规范,系统训练学术写作逻辑,确保成果清晰传达。

通过阶梯式教学,学生不仅能掌握竞赛所需技能,更能形成“用数学视角观察世界”的思维习惯,为未来理工科学习打下坚实基础。

HiMCM竞赛规则深度解读

参与HiMCM竞赛需清晰掌握以下核心规则,北京学诚国际教育课程将通过模拟赛帮助学生提前适应:

1. 参赛基本要求

参赛主体为9-12年级高中生,每队由4名学生与1名指导教师组成。学生需具备以下特质之一:数学基础扎实、计算机编程能力突出、英语写作流畅,或具备较强的团队组织能力。课程将根据学生特长进行针对性分组,化发挥团队优势。

2. 竞赛流程与时间

竞赛每年6月开放注册,11月进入正式阶段。以近年安排为例,赛事通常从11月周的星期五启动,持续17天,其中需选择连续36小时集中完成解题。题目为2道现实问题(如城市交通优化、环境资源分配等),学生可自主选择其一,通过数学建模提出解决方案。

3. 参赛形式与限制

竞赛允许使用书本、软件及网络资源,但禁止与队外人员(包括指导教师)讨论。最终需提交英文论文,内容需包含问题分析、模型建立、结果验证及参考文献。特别提醒:未标注引用来源可能被判定为抄袭,直接取消成绩。

选择HiMCM竞赛的四大核心优势

作为国际认可度极高的中学生数学竞赛,HiMCM的价值远超竞赛本身:

1. 升学竞争力提升

国内外高校在本科生选拔中,普遍关注学生的学术实践能力。HiMCM竞赛成绩不仅是数学能力的证明,更能体现逻辑思维、跨学科应用及团队协作等综合素养,为升学简历增添关键亮点。

2. 专业方向预探索

竞赛涉及数学、计算机、自然科学及社会经济等多领域知识,学生在备赛过程中能深入了解不同学科的应用场景,为大学专业选择提供实践参考,尤其对意向报考应用数学、工程、商科的学生具有重要指导意义。

3. 综合能力全面锻炼

从数据收集到模型构建,从团队讨论到论文撰写,HiMCM竞赛全程考验学生的信息整合、批判性思维及跨语言表达能力。这些能力不仅是竞赛成功的关键,更是未来学术研究与职业发展的核心竞争力。

4. 国际视野拓展

作为国际性赛事,HiMCM吸引全球优秀中学生参与。通过与国际选手的“无形较量”,学生能接触多元解题思路,拓宽学术视野,为未来参与国际交流或留学奠定基础。

北京学诚国际教育课程的独特价值

针对HiMCM竞赛的复杂性,北京学诚国际教育课程设计注重“实战导向”与“个性化培养”:

一方面,课程团队由具备多年竞赛指导经验的教师组成,熟悉COMAP评分标准,能精准把握“模型创新性”“结果合理性”“论文逻辑性”等关键得分点;另一方面,通过阶段性模拟赛与一对一论文批改,帮助学生快速定位薄弱环节,实现能力短板的针对性提升。

无论是数学基础扎实的“学术型”学生,还是擅长编程或写作的“特长型”学生,都能在课程中找到适合自己的成长路径,最终以状态应对HiMCM竞赛挑战。

北京学诚国际教育

北京学诚国际教育
认证 7 年

成立: 2006年

认证 地址认证 教学保障 在线预约 到店体验 售后支持
基本 文件 流程 错误 SQL 调试
  1. 请求信息 : 2026-04-06 09:55:45 HTTP/1.1 GET : http://www.edujk.com/s/6118/c/85477.html
  2. 运行时间 : 0.031722s [ 吞吐率:31.52req/s ] 内存消耗:395.32kb 文件加载:136
  3. 缓存信息 : 0 reads,0 writes
  1. /data/web/baijiao_branch_collect/public/index.php ( 0.79 KB )
  2. /data/web/baijiao_branch_collect/vendor/autoload.php ( 0.75 KB )
  3. /data/web/baijiao_branch_collect/vendor/composer/autoload_real.php ( 1.63 KB )
  4. /data/web/baijiao_branch_collect/vendor/composer/platform_check.php ( 0.90 KB )
  5. /data/web/baijiao_branch_collect/vendor/composer/ClassLoader.php ( 15.99 KB )
  6. /data/web/baijiao_branch_collect/vendor/composer/autoload_static.php ( 4.26 KB )
  7. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/helper.php ( 8.34 KB )
  8. /data/web/baijiao_branch_collect/vendor/topthink/think-validate/src/helper.php ( 2.19 KB )
  9. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/helper.php ( 1.47 KB )
  10. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/stubs/load_stubs.php ( 0.16 KB )
  11. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Exception.php ( 1.69 KB )
  12. /data/web/baijiao_branch_collect/vendor/topthink/think-container/src/Facade.php ( 2.71 KB )
  13. /data/web/baijiao_branch_collect/vendor/symfony/deprecation-contracts/function.php ( 0.99 KB )
  14. /data/web/baijiao_branch_collect/vendor/symfony/polyfill-mbstring/bootstrap.php ( 8.26 KB )
  15. /data/web/baijiao_branch_collect/vendor/symfony/polyfill-mbstring/bootstrap80.php ( 9.78 KB )
  16. /data/web/baijiao_branch_collect/vendor/symfony/var-dumper/Resources/functions/dump.php ( 1.49 KB )
  17. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/App.php ( 15.30 KB )
  18. /data/web/baijiao_branch_collect/vendor/topthink/think-container/src/Container.php ( 15.76 KB )
  19. /data/web/baijiao_branch_collect/vendor/psr/container/src/ContainerInterface.php ( 1.02 KB )
  20. /data/web/baijiao_branch_collect/app/provider.php ( 0.19 KB )
  21. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Http.php ( 6.04 KB )
  22. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/helper/Str.php ( 7.29 KB )
  23. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Env.php ( 4.68 KB )
  24. /data/web/baijiao_branch_collect/app/common.php ( 10.83 KB )
  25. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/helper.php ( 18.78 KB )
  26. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Config.php ( 5.54 KB )
  27. /data/web/baijiao_branch_collect/config/app.php ( 1.29 KB )
  28. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Env.php ( 1.67 KB )
  29. /data/web/baijiao_branch_collect/config/cache.php ( 1.22 KB )
  30. /data/web/baijiao_branch_collect/config/config.php ( 0.26 KB )
  31. /data/web/baijiao_branch_collect/config/console.php ( 0.29 KB )
  32. /data/web/baijiao_branch_collect/config/cookie.php ( 0.56 KB )
  33. /data/web/baijiao_branch_collect/config/database.php ( 2.29 KB )
  34. /data/web/baijiao_branch_collect/config/filesystem.php ( 0.63 KB )
  35. /data/web/baijiao_branch_collect/config/lang.php ( 0.81 KB )
  36. /data/web/baijiao_branch_collect/config/log.php ( 1.37 KB )
  37. /data/web/baijiao_branch_collect/config/middleware.php ( 0.19 KB )
  38. /data/web/baijiao_branch_collect/config/route.php ( 1.54 KB )
  39. /data/web/baijiao_branch_collect/config/session.php ( 0.57 KB )
  40. /data/web/baijiao_branch_collect/config/trace.php ( 0.34 KB )
  41. /data/web/baijiao_branch_collect/config/view.php ( 0.81 KB )
  42. /data/web/baijiao_branch_collect/app/event.php ( 0.25 KB )
  43. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Event.php ( 7.67 KB )
  44. /data/web/baijiao_branch_collect/app/service.php ( 0.13 KB )
  45. /data/web/baijiao_branch_collect/app/AppService.php ( 0.26 KB )
  46. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Service.php ( 1.64 KB )
  47. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Lang.php ( 7.35 KB )
  48. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/lang/zh-cn.php ( 13.70 KB )
  49. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/initializer/Error.php ( 3.31 KB )
  50. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/initializer/RegisterService.php ( 1.33 KB )
  51. /data/web/baijiao_branch_collect/vendor/services.php ( 0.14 KB )
  52. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/service/PaginatorService.php ( 1.52 KB )
  53. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/service/ValidateService.php ( 0.99 KB )
  54. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/service/ModelService.php ( 2.04 KB )
  55. /data/web/baijiao_branch_collect/vendor/topthink/think-trace/src/Service.php ( 0.77 KB )
  56. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Middleware.php ( 6.72 KB )
  57. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/initializer/BootService.php ( 0.77 KB )
  58. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/Paginator.php ( 11.86 KB )
  59. /data/web/baijiao_branch_collect/vendor/topthink/think-validate/src/Validate.php ( 63.20 KB )
  60. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/Model.php ( 23.55 KB )
  61. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/Attribute.php ( 21.05 KB )
  62. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/AutoWriteData.php ( 4.20 KB )
  63. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/Conversion.php ( 6.75 KB )
  64. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/DbConnect.php ( 5.16 KB )
  65. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/ModelEvent.php ( 2.33 KB )
  66. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/concern/RelationShip.php ( 28.30 KB )
  67. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/contract/Arrayable.php ( 0.09 KB )
  68. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/contract/Jsonable.php ( 0.13 KB )
  69. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/model/contract/Modelable.php ( 0.09 KB )
  70. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Db.php ( 2.88 KB )
  71. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/DbManager.php ( 8.52 KB )
  72. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Log.php ( 6.28 KB )
  73. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Manager.php ( 3.92 KB )
  74. /data/web/baijiao_branch_collect/vendor/psr/log/src/LoggerTrait.php ( 2.69 KB )
  75. /data/web/baijiao_branch_collect/vendor/psr/log/src/LoggerInterface.php ( 2.71 KB )
  76. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Cache.php ( 4.92 KB )
  77. /data/web/baijiao_branch_collect/vendor/psr/simple-cache/src/CacheInterface.php ( 4.71 KB )
  78. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/helper/Arr.php ( 17.45 KB )
  79. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/cache/driver/Redis.php ( 6.94 KB )
  80. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/cache/Driver.php ( 9.03 KB )
  81. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/contract/CacheHandlerInterface.php ( 1.99 KB )
  82. /data/web/baijiao_branch_collect/app/Request.php ( 0.09 KB )
  83. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Request.php ( 55.78 KB )
  84. /data/web/baijiao_branch_collect/app/middleware.php ( 0.26 KB )
  85. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Pipeline.php ( 2.61 KB )
  86. /data/web/baijiao_branch_collect/vendor/topthink/think-trace/src/TraceDebug.php ( 3.40 KB )
  87. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Route.php ( 23.73 KB )
  88. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/RuleName.php ( 5.75 KB )
  89. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Domain.php ( 2.53 KB )
  90. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/RuleGroup.php ( 22.43 KB )
  91. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Rule.php ( 26.95 KB )
  92. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/RuleItem.php ( 9.78 KB )
  93. /data/web/baijiao_branch_collect/route/app.php ( 3.05 KB )
  94. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Route.php ( 4.70 KB )
  95. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/dispatch/Controller.php ( 4.74 KB )
  96. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Dispatch.php ( 10.44 KB )
  97. /data/web/baijiao_branch_collect/app/controller/Index.php ( 33.26 KB )
  98. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Request.php ( 9.20 KB )
  99. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/route/Url.php ( 14.07 KB )
  100. /data/web/baijiao_branch_collect/app/model/IndexModel.php ( 19.95 KB )
  101. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Config.php ( 1.37 KB )
  102. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/facade/Cache.php ( 2.06 KB )
  103. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/facade/Db.php ( 0.93 KB )
  104. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/connector/Mysql.php ( 5.73 KB )
  105. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/PDOConnection.php ( 53.74 KB )
  106. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/Connection.php ( 8.39 KB )
  107. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/ConnectionInterface.php ( 4.57 KB )
  108. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/builder/Mysql.php ( 16.58 KB )
  109. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/Builder.php ( 24.07 KB )
  110. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/BaseBuilder.php ( 27.50 KB )
  111. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/Query.php ( 15.97 KB )
  112. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/BaseQuery.php ( 45.13 KB )
  113. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/TimeFieldQuery.php ( 7.43 KB )
  114. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/AggregateQuery.php ( 3.26 KB )
  115. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/ModelRelationQuery.php ( 20.07 KB )
  116. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/ParamsBind.php ( 3.66 KB )
  117. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/ResultOperation.php ( 7.01 KB )
  118. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/WhereQuery.php ( 19.37 KB )
  119. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/JoinAndViewQuery.php ( 7.11 KB )
  120. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/TableFieldInfo.php ( 2.63 KB )
  121. /data/web/baijiao_branch_collect/vendor/topthink/think-orm/src/db/concern/Transaction.php ( 2.77 KB )
  122. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/log/driver/File.php ( 5.96 KB )
  123. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/contract/LogHandlerInterface.php ( 0.86 KB )
  124. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/log/Channel.php ( 3.89 KB )
  125. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/event/LogRecord.php ( 1.02 KB )
  126. /data/web/baijiao_branch_collect/vendor/topthink/think-helper/src/Collection.php ( 16.47 KB )
  127. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Response.php ( 8.81 KB )
  128. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/response/View.php ( 3.29 KB )
  129. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/Cookie.php ( 6.06 KB )
  130. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/View.php ( 4.39 KB )
  131. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/view/driver/Php.php ( 6.44 KB )
  132. /data/web/baijiao_branch_collect/vendor/topthink/framework/src/think/contract/TemplateHandlerInterface.php ( 1.60 KB )
  133. /data/web/baijiao_branch_collect/view/index/pc/school_course_details.php ( 6.12 KB )
  134. /data/web/baijiao_branch_collect/view/index/pc/school_top.php ( 5.76 KB )
  135. /data/web/baijiao_branch_collect/view/index/pc/school_bottom.php ( 1.16 KB )
  136. /data/web/baijiao_branch_collect/vendor/topthink/think-trace/src/Html.php ( 4.42 KB )
  1. CONNECT:[ UseTime:0.000351s ] mysql:host=127.0.0.1;port=3306;dbname=baijiao_branch_collect;charset=utf8
  2. SHOW FULL COLUMNS FROM `fqi_school` [ RunTime:0.000998s ]
  3. SELECT * FROM `fqi_school` WHERE `school_id` = '6118' AND `site_id` = 4 AND `school_status` = 1 LIMIT 1 [ RunTime:0.000256s ]
  4. SHOW FULL COLUMNS FROM `fqi_school_class` [ RunTime:0.000570s ]
  5. SELECT * FROM `fqi_school_class` WHERE `school_id` = 6118 [ RunTime:0.000223s ]
  6. SHOW FULL COLUMNS FROM `fqi_school_campus` [ RunTime:0.000592s ]
  7. SELECT * FROM `fqi_school_campus` WHERE `school_id` = 6118 [ RunTime:0.000221s ]
  8. SHOW FULL COLUMNS FROM `fqi_school_course` [ RunTime:0.000630s ]
  9. SELECT `a`.*,`content` FROM `fqi_school_course` `a` LEFT JOIN `fqi_school_course_content` `b` ON `b`.`content_id`=`a`.`content_id` WHERE `school_id` = 6118 AND `a`.`content_id` = '85477' AND `course_status` = 1 AND `school_status` = 1 LIMIT 1 [ RunTime:0.000726s ]
  10. (select content_id,course_name from fqi_school_course where school_id = '6118' and content_id < '85477' and site_id = '4' order by content_id desc limit 1) union all(select content_id,course_name from fqi_school_course where school_id = '6118' and content_id > '85477' and site_id <= '4' order by content_id asc limit 1) [ RunTime:0.001160s ]
  11. SELECT * FROM `fqi_school_course` WHERE `school_id` = 6118 AND `site_id` = 4 AND `course_status` = 1 AND `school_status` = 1 AND `school_class_id` = 21007 ORDER BY `course_id` DESC LIMIT 4 [ RunTime:0.000290s ]
  12. SELECT * FROM `fqi_school_course` WHERE `school_id` = 6118 AND `site_id` = 4 AND `course_status` = 1 AND `school_status` = 1 ORDER BY `course_id` DESC LIMIT 10 [ RunTime:0.000223s ]
  13. SELECT COUNT(*) AS think_count FROM `fqi_school_course` WHERE `school_id` = 6118 AND `course_status` = 1 [ RunTime:0.000148s ]
  14. SHOW FULL COLUMNS FROM `fqi_school_teacher` [ RunTime:0.000623s ]
  15. SELECT COUNT(*) AS think_count FROM `fqi_school_teacher` WHERE `school_id` = '6118' [ RunTime:0.000187s ]
  16. SHOW FULL COLUMNS FROM `fqi_school_comments` [ RunTime:0.000599s ]
  17. SELECT COUNT(*) AS think_count FROM `fqi_school_comments` WHERE `school_id` = '6118' [ RunTime:0.000191s ]
  18. SELECT `content_id`,`course_name`,`a`.`school_id`,`b`.`school_name` FROM `fqi_school_course` `a` LEFT JOIN `fqi_school` `b` ON `b`.`school_id`=`a`.`school_id` WHERE `a`.`site_id` = '4' AND `b`.`school_status` = '1' AND `course_status` = 1 AND `course_id` < '85477' ORDER BY `content_id` DESC LIMIT 20 [ RunTime:0.020196s ]
0.032034s