• 快速突破文化课瓶颈
  • 轻松跨过艺考高校门槛
  • 假期来学大辅导 开学即见分晓

400-888-4846

广州小学四年级数学一对一辅导:定制化教学如何破解学习难点

广州小学四年级数学一对一辅导:定制化教学如何破解学习难点

授课机构: 广州学大教育

上课地点: 校区地址

成交/评价:

联系电话: 400-888-4846

广州小学四年级数学一对一辅导:定制化教学如何破解学习难点课程详情

广州小学四年级数学一对一辅导:定制化教学如何破解学习难点

一、四年级数学学习的关键转折点

小学四年级是数学学习的重要过渡期,学生需要完成从基础运算到复杂应用、从直观图形认知到抽象几何概念的双重跨越。这一阶段,乘法分配律的灵活运用、质量单位的实际换算、三角形与平行四边形的特征辨析等内容,往往成为学生的主要卡点。数据显示,超60%的四年级学生在几何图形分类、多步骤应用题解答上存在明显薄弱环节,传统大班教学难以兼顾个体差异,此时针对性的一对一辅导显得尤为必要。

四年级数学辅导场景图

二、一对一课程的核心定位与服务模式

区别于标准化大班教学,本课程以"一人一案"为核心原则,通过课前学情诊断、课中动态调整、课后效果追踪的闭环体系,确保每个学生的学习路径与自身能力匹配。具体包含两大服务支撑:

1. 专属1对1教学:由具备5年以上小学数学教学经验的教师主导,围绕学生作业错题、单元测试失分点展开深度分析,例如针对"运算顺序混淆"问题,教师会通过实物演示(如砝码称重)+ 阶梯式习题(从两步运算到四步综合题)逐步强化逻辑;

2. 多维度6对1服务:除主讲教师外,配备学习规划师(制定周度/月度目标)、作业批改师(当日反馈错题解析)、心理辅导师(缓解畏难情绪)、家长沟通专员(定期同步学习进度)、教研支持组(提供最新考点资料)、阶段测评师(每月进行能力模型评估),形成全方位学习支持网络。

辅导团队协作示意图

三、覆盖课标的核心教学内容详解

课程内容严格对标人教版小学数学四年级上册大纲,重点突破以下六大板块,具体内容会根据学生实际掌握情况动态调整:

1. 数与代数模块

包含大数的认识(亿以内数的读写)、三位数乘两位数(竖式计算与简便运算)、除数是两位数的除法(试商技巧)。例如针对"乘法分配律应用",教师会设计"超市购物计价"等生活场景题,帮助学生理解(a+b)×c=a×c+b×c的实际意义。

2. 图形与几何模块

涉及平行与垂直的概念辨析、三角形/平行四边形/梯形的特征归纳(如三角形稳定性实验)、角的度量(量角器使用误区纠正)。通过七巧板拼搭、方格纸画图等实践活动,强化空间观念。

3. 量与计量模块

聚焦质量单位(克、千克、吨)的换算与应用,结合"家庭厨房称重""超市购物清单"等真实场景,让学生在实践中掌握1吨=1000千克、1千克=1000克的换算逻辑,避免死记硬背。

值得强调的是,所有教学内容均会通过"知识点讲解→例题示范→变式训练→错题复盘"四步流程推进,确保学生不仅"听懂"更能"会用"。例如在教授"平行四边形的高"时,教师会先通过推拉门的实物演示说明高的可变性,再通过不同底边对应的高的画法练习,最后结合"求平行四边形面积"的综合题检验掌握程度。

数学知识点讲解示意图

四、真实教学案例:从"畏难"到"自信"的转变

以去年辅导的陈同学为例,入学时存在两大问题:一是乘法竖式计算常因进位错误失分,二是对"梯形的高"概念理解模糊,画图时总将高画成腰。辅导教师首先通过"进位标记法"(在竖式旁用小字标注进位数字)纠正计算习惯,配合每天10道专项题训练,2周后计算准确率从65%提升至92%;针对几何部分,教师利用可活动的四边形模型,让陈同学亲自操作"拉成梯形→调整高度→测量长度",直观理解"高是两底之间的垂线段",并通过"在方格纸上画不同高度的梯形"练习强化认知。3个月后,陈同学单元测试成绩从72分提升至91分,更重要的是主动表示"数学题没那么难了"。

五、选择一对一辅导的常见疑问解答

Q:孩子基础较弱,一对一能跟上进度吗?
完全可以。课程会从学生当前水平出发,例如计算能力薄弱的学生会先补全表内乘除法口算,再逐步过渡到多位数运算,避免"一刀切"教学导致的挫败感。

Q:和大班课相比,一对一的优势在哪里?
大班课关注"平均进度",而一对一聚焦"个人痛点"。例如同样讲解"三角形分类",大班可能用20分钟讲完所有类型,而一对一可以用10分钟针对学生混淆的"锐角三角形与等边三角形关系"展开深度辨析。

Q:课程内容会和学校教学脱节吗?
不会。辅导教师会同步学校教学进度,例如学校讲到"平行四边形的面积"时,课程会增加"等底等高图形面积比较"的拓展练习,帮助学生实现"校内基础+课外提升"的双重巩固。

广州学大教育

广州学大教育
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 : 2026-04-18 03:29:48 HTTP/1.1 GET : http://www.aabrg.com/s/3165/c/46024.html
  2. 运行时间 : 0.071082s [ 吞吐率:14.07req/s ] 内存消耗:411.78kb 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:0.000409s ] mysql:host=127.0.0.1;port=3306;dbname=baijiao_branch_collect;charset=utf8
  2. SHOW FULL COLUMNS FROM `fqi_school` [ RunTime:0.001127s ]
  3. SELECT * FROM `fqi_school` WHERE `school_id` = '3165' AND `site_id` = 22 AND `school_status` = 1 LIMIT 1 [ RunTime:0.000318s ]
  4. SHOW FULL COLUMNS FROM `fqi_school_class` [ RunTime:0.000596s ]
  5. SELECT * FROM `fqi_school_class` WHERE `school_id` = 3165 [ RunTime:0.000263s ]
  6. SHOW FULL COLUMNS FROM `fqi_school_campus` [ RunTime:0.000615s ]
  7. SELECT * FROM `fqi_school_campus` WHERE `school_id` = 3165 [ RunTime:0.000264s ]
  8. SHOW FULL COLUMNS FROM `fqi_school_course` [ RunTime:0.000701s ]
  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` = 3165 AND `a`.`content_id` = '46024' AND `course_status` = 1 AND `school_status` = 1 LIMIT 1 [ RunTime:0.000939s ]
  10. (select content_id,course_name from fqi_school_course where school_id = '3165' and content_id < '46024' and site_id = '22' order by content_id desc limit 1) union all(select content_id,course_name from fqi_school_course where school_id = '3165' and content_id > '46024' and site_id <= '22' order by content_id asc limit 1) [ RunTime:0.001806s ]
  11. SELECT * FROM `fqi_school_course` WHERE `school_id` = 3165 AND `site_id` = 22 AND `course_status` = 1 AND `school_status` = 1 AND `school_class_id` = 11947 ORDER BY `course_id` DESC LIMIT 4 [ RunTime:0.000500s ]
  12. SELECT * FROM `fqi_school_course` WHERE `school_id` = 3165 AND `site_id` = 22 AND `course_status` = 1 AND `school_status` = 1 ORDER BY `course_id` DESC LIMIT 10 [ RunTime:0.000891s ]
  13. SELECT COUNT(*) AS think_count FROM `fqi_school_course` WHERE `school_id` = 3165 AND `course_status` = 1 [ RunTime:0.000336s ]
  14. SHOW FULL COLUMNS FROM `fqi_school_teacher` [ RunTime:0.000664s ]
  15. SELECT COUNT(*) AS think_count FROM `fqi_school_teacher` WHERE `school_id` = '3165' [ RunTime:0.000207s ]
  16. SHOW FULL COLUMNS FROM `fqi_school_comments` [ RunTime:0.000559s ]
  17. SELECT COUNT(*) AS think_count FROM `fqi_school_comments` WHERE `school_id` = '3165' [ RunTime:0.000211s ]
  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` = '22' AND `b`.`school_status` = '1' AND `course_status` = 1 AND `course_id` < '46024' ORDER BY `content_id` DESC LIMIT 20 [ RunTime:0.055428s ]
0.071625s