《对分课堂在《微积分》课程教学中的探索》论文范文

<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>摘要<span style=“font-family:
宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>：对分课堂是复旦大学心理系张学新教授提出一种新的教学模式，我们将该教学模式应该于应用型本科专业基础课《微积分》的教学，有效激发学生学习的积极性，提高学生自主学习能力，增加师生和生生互动，较好地培养学生的逻辑思维能力和创新意识，促进学生个性化发展，更好地提升学生学习能力、教学质量和教师教学水平。<o:p> </o:p>
<img src=“/image/image?path=group8/M01/22/94/wKgIO2Gd45WAcoMeAAB8qm0l5Sg230.jpg”>《微积分》是我国高等院校理工、经管各专业的一门重要公共基础课，课程具有概念繁多、内容抽象、逻辑性强等特点，这些特点给学生的学习带来了一定的难度。传统的微积分教学重理论轻应用、重演绎轻归纳，追求数学的系统性与严密性，忽略考虑学生的理解能力，导致学生渐渐丧失了学习兴趣、产生畏难情绪，出现课堂出勤率低、课程通过率低等现象。为了提高教学质量，作者在会计学、市场营销专业基础课《微积分》教学中尝试引入对分课堂的教学模式，努力改变以教师为中心的知识传授教学模式，有效激发和增强学生的学习积极性和自主性，提高学习效率和教学效果。 <span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>一、对分课堂简介<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂是张学新教授针对当前高校课堂存在的一些主要问题， <span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>结合讲授式课堂与讨论式课堂的优点，提出了一种课堂教学改革新模式[1]<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>。它的核心理念是将课堂时间分配一半给教师讲授，另一半时间给学生讨论，并把讲授和讨论时间错开，让学生课后有充足时间自主安排学习，进行个性化的内化吸收。对分课堂把教学时间清晰地分成三部分，即课堂讲授、课下内化吸收和课堂讨论。对分课堂自2014<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>年9<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>月推广以来，在国内受到广泛关注，迅速得到很多一线教师的实践，并且都取得了较好的效果，不少教师认为对分课堂有可能给传统课堂带来深刻变革[2][3][4][5]<span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>。<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>二、对分课堂在《微积分》教学中的实践及效果(<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>一) <span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>教学组织<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>由于微积分注重体系的教学且逻辑性强、方法性强，对分课堂主要采取“隔堂讨论”的模式，即PAD<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>课堂。为了让学生对新的教学模式有充分了解，教师先把教学大纲通过互联网发送给学生，并在第一节课详细解释该教学模式的关键点及要求。教学设计主要分为以下几点: <span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>①由于讲授时间缩短，所以上课时只讲授章节的重难点内容，学生课后自主阅读教材，写出读书笔记和课后作业。依据教学大纲对书上的重要概念和问题进行复习，完成“亮考帮”任务，为课堂讨论做准备。下次课的前一天要求学生将作业拍照上传指定文件夹进行评分，下次课的前半时间进行交流讨论，后面的时间教师讲授下一节内容，并且不定期检查作业。作业的目的是督促学生复习，掌握和理解基本的概念和理论，为能够进入深入和有意义的交流讨论做准备。②讨论内容和意义。主要回顾重要概念和理论，围绕作业表达自己的理解和——————————————————————<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>作者简介：覃荣存，（1983<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>—），女，侗，广西三江县人，理学硕士，讲师。主要从事高等数学教育研究。南宁市，收刊详细地址：广西大学行健文理学院数学系，邮编：530005<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>，电话：18776039843<span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>，E-mail<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
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mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>课题项目：广西高等教育本科教学改革工程项目（2018JGA326<span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>）；广西壮族自治区中青年教师基础能力提升项目（2017KY1301<span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>）；广西自然科学基金项目（2018GXNSFBA138038<span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>）。疑问，通过相互交流、挑战和启发，突破难点，分享智慧，锻炼合作。③分组方式。教师通过随机进行分组，每组成员 4 <span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>分；期末考试成绩占50%<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>。⑤学生反馈。从学生的读书笔记以及和部分学生交流中，我们可以看出大部分学生喜欢这种授课方式。大部分学生认为讨论交流对他们学习微积分有显著的促进作用，甚至有同学认为讨论环节是最令人兴奋的环节。.(<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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Calibri;mso-hansi-theme-font:minor-latin”>采用对分模式授课后，学生的课堂表现与传统课堂相比有显著变化，具体表现在以下几个方面:1<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>．课堂气氛活跃，讨论积极，主动参与课堂的意识增强。由于学生上课前已经完成讨论的准备内容，带着作业到课堂上进行讨论，所以在讨论中不仅积极参与小组讨论，而且还积极总结小组讨论之后的收获和尚未解决的问题，会针对一些问题积极发言。例如，“<!–[if gte msEquation 12]><m:oMath><m:f><m:fPr><m:ctrlPr></m:ctrlPr></m:fPr><m:num><m:r><m:rPr><m:nor/></m:rPr>0</m:r></m:num><m:den><m:r><m:rPr><m:nor/></m:rPr>0</m:r></m:den></m:f></m:oMath><![endif]–><!–[if !msEquation]–><span lang=“EN-US” style=“font-size:10.5pt;mso-bidi-font-size:12.0pt;font-family:"Calibri","sans-serif";
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宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>”不定式极限的运算，有同学会结合课堂上介绍的解题方法进一步的细分和归纳，用更接近地气的方式分享给其他同学。2<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>．激发学生对知识的探索精神，学习积极性提高。学生认真完成作业，在笔记中可以看到学生对当次课的总结和反思，其中深层次、延伸性问题逐渐增多，甚至还会收到学生对教师授课的建议。
<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:
minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>如有学生建议在讲解例题之前可以多预留2<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>—3<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>分钟的时间让学生独立思考。授课一个学期后，本人收集到部分学生对对分课堂的感受，总结如下: <span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
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mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>②课后作业形式比传统课堂更优，可以让学生认真的阅读教材，通过自主翻阅教材完成作业更有成就感，同时还能培养良好的学习习惯。③问题与建议。讨论过程存在一些问题过大、过难的情况，无法通过讨论得出明确结果。教师讲授环节中，例题讲解前可以预留一些时间给学生思考。这些反馈既肯定了对分课堂教学模式在《微积分》课程教学中的优点，又指出了改进的方向。从满足学生的角度出发，给老师的教学带来了思路和启发。<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>三、对分课堂在《微积分》课程教学中的优势和对教师的挑战 <span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂以学生的分组讨论为开端，增强学生对微积分课程学习的主动性，学生温习上次课内容，自然进入后续内容，无需导入技巧就能让学生进入良好的学习状态，提升学习效果。通过讨论交流理解数学概念和定理，改变了传统教师单一“教授者”的角色定位，使教师角色从覆盖内容、灌输知识，变为引导学生学习，把课堂的主动权交给学生，使学生真正成为学习的主体和知识的主人，并能让学生感受到数学的乐趣。对分课堂鼓励平时学习，把有效学习应该付出的努力分散到整个学期，符合数学学习的规律，并能避免考前死记硬背过关，提升考评准确度[1]<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>。<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>然而，《微积分》课程是一门理论课，知识结构严谨，逻辑性强，学生普遍觉得难，如何利用对分课堂教学模式组织好教学将是对教师的一次挑战。对分课堂在《微积分》课程教学中的应用对教师的挑战如下: <span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>①由于授课时间缩短，课程内容结构必须简化明了，因此要求教师必须重新制定教学大纲，简化教学内容，突出基础、重点、难点，不仅要帮学生熟悉课程内容，还要让学生有效地理解课程的重点和难点。②一堂好课必须有教师精心准备，如何组织课堂，如何安排好课后作业，如何分配好每一堂课的讨论时间，如何营造和谐安全的课堂氛围，如何指导学生讨论等都会影响教学效果。③紧跟科研前沿，深化专业素养。教师既要教学生教材上的知识，还要能有效地引导学生了解学科前沿，就一定要求自己提升专业知识和实时掌握国内外研究的最新进展。<o:p> </o:p><a name=“_GoBack”></a><span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>四、
<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:
minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>结束语<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂教学模式虽然在高等数学中的应用案例较少，但该教学模式比传统讲授式更有优势，更能激发学生课堂参与性，并能及时反馈课堂学习情况，提高学习效率。因此对分课堂教学模式在《微积分》课程教学中是可以应用的。然而，教学模式的转变必将带来一场课堂教学的革命，因此更需要广大高校数学教师的大胆创新与尝试。相信经过广大高校数学教师的努力，会逐渐解决对分课堂上出现的问题，使其成为改变当前高校数学教育困境的一种教学模式，让更多学生爱上数学，感受学习数学的乐趣！<o:p> </o:p><span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>参考文献<o:p></o:p><!–[if !supportLists]–>[1] <!–[endif]–><span style=“font-family:
宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>张学新. <span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂：大学课堂教学改革的新探索[J].<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>复旦教育论坛, 2014, 05.<!–[if !supportLists]–>[2] <!–[endif]–><span style=“font-family:
宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>罗德仁. <span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>苏利娟.<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂在高校公共数学课堂教学中的应用[J].<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>科技经济导刊, 2019, 27<span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>（02<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>）.<!–[if !supportLists]–>[3] <!–[endif]–><span style=“font-family:
宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>杜艳飞，张学新．“对分课堂”: <span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>高校课堂教学模式改革实践与思考［J<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>］．
<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:
minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;
mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>继续教育研究，2016( 3) : 116 <span style=“font-family:宋体;mso-ascii-font-family:
Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>－ 118<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>．<!–[if !supportLists]–>[4] <!–[endif]–><span style=“font-family:
宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>罗德仁,<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>苏利娟.<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂在高校公共数学课堂教学中的应用[J].<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>科技经济导刊，2019<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>，27<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>（02<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>）.<!–[if !supportLists]–>[5] <!–[endif]–><span style=“font-family:
宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:
宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;
mso-hansi-theme-font:minor-latin”>李宾.<span style=“font-family:宋体;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;
mso-fareast-font-family:宋体;mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:
Calibri;mso-hansi-theme-font:minor-latin”>对分课堂在“线性代数”课堂教学中的实践[J].<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>长春师范大学学报，2018<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>，37<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋体;mso-fareast-theme-font:
minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>（8<span style=“font-family:宋体;mso-ascii-font-family:Calibri;
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minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin”>）.
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<w:LsdException Locked=“false” Priority=“39” Name=“toc 8”/>
<w:LsdException Locked=“false” Priority=“39” Name=“toc 9”/>
<w:LsdException Locked=“false” Priority=“35” QFormat=“true” Name=“caption”/>
<w:LsdException Locked=“false” Priority=“10” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Title”/>
<w:LsdException Locked=“false” Priority=“1” Name=“Default Paragraph Font”/>
<w:LsdException Locked=“false” Priority=“11” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Subtitle”/>
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UnhideWhenUsed=“false” QFormat=“true” Name=“Strong”/>
<w:LsdException Locked=“false” Priority=“20” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Emphasis”/>
<w:LsdException Locked=“false” Priority=“0” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Table Grid”/>
<w:LsdException Locked=“false” UnhideWhenUsed=“false” Name=“Placeholder Text”/>
<w:LsdException Locked=“false” Priority=“1” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“No Spacing”/>
<w:LsdException Locked=“false” Priority=“60” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Shading”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1”/>
<w:LsdException Locked=“false” Priority=“66” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 2”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading”/>
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UnhideWhenUsed=“false” Name=“Colorful List”/>
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UnhideWhenUsed=“false” Name=“Colorful Grid”/>
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UnhideWhenUsed=“false” Name=“Light Shading Accent 1”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List Accent 1”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid Accent 1”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1 Accent 1”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2 Accent 1”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1 Accent 1”/>
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UnhideWhenUsed=“false” QFormat=“true” Name=“Quote”/>
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UnhideWhenUsed=“false” QFormat=“true” Name=“Intense Quote”/>
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UnhideWhenUsed=“false” Name=“Medium List 2 Accent 1”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1 Accent 1”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2 Accent 1”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3 Accent 1”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List Accent 1”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading Accent 1”/>
<w:LsdException Locked=“false” Priority=“72” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful List Accent 1”/>
<w:LsdException Locked=“false” Priority=“73” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Grid Accent 1”/>
<w:LsdException Locked=“false” Priority=“60” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Shading Accent 2”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List Accent 2”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid Accent 2”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1 Accent 2”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2 Accent 2”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1 Accent 2”/>
<w:LsdException Locked=“false” Priority=“66” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 2 Accent 2”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1 Accent 2”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2 Accent 2”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3 Accent 2”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List Accent 2”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading Accent 2”/>
<w:LsdException Locked=“false” Priority=“72” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful List Accent 2”/>
<w:LsdException Locked=“false” Priority=“73” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Grid Accent 2”/>
<w:LsdException Locked=“false” Priority=“60” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Shading Accent 3”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List Accent 3”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid Accent 3”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1 Accent 3”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2 Accent 3”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1 Accent 3”/>
<w:LsdException Locked=“false” Priority=“66” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 2 Accent 3”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1 Accent 3”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2 Accent 3”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3 Accent 3”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List Accent 3”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading Accent 3”/>
<w:LsdException Locked=“false” Priority=“72” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful List Accent 3”/>
<w:LsdException Locked=“false” Priority=“73” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Grid Accent 3”/>
<w:LsdException Locked=“false” Priority=“60” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Shading Accent 4”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List Accent 4”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid Accent 4”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1 Accent 4”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2 Accent 4”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1 Accent 4”/>
<w:LsdException Locked=“false” Priority=“66” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 2 Accent 4”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1 Accent 4”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2 Accent 4”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3 Accent 4”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List Accent 4”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading Accent 4”/>
<w:LsdException Locked=“false” Priority=“72” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful List Accent 4”/>
<w:LsdException Locked=“false” Priority=“73” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Grid Accent 4”/>
<w:LsdException Locked=“false” Priority=“60” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Shading Accent 5”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List Accent 5”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid Accent 5”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1 Accent 5”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2 Accent 5”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1 Accent 5”/>
<w:LsdException Locked=“false” Priority=“66” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 2 Accent 5”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1 Accent 5”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2 Accent 5”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3 Accent 5”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List Accent 5”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading Accent 5”/>
<w:LsdException Locked=“false” Priority=“72” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful List Accent 5”/>
<w:LsdException Locked=“false” Priority=“73” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Grid Accent 5”/>
<w:LsdException Locked=“false” Priority=“60” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Shading Accent 6”/>
<w:LsdException Locked=“false” Priority=“61” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light List Accent 6”/>
<w:LsdException Locked=“false” Priority=“62” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Light Grid Accent 6”/>
<w:LsdException Locked=“false” Priority=“63” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 1 Accent 6”/>
<w:LsdException Locked=“false” Priority=“64” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Shading 2 Accent 6”/>
<w:LsdException Locked=“false” Priority=“65” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 1 Accent 6”/>
<w:LsdException Locked=“false” Priority=“66” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium List 2 Accent 6”/>
<w:LsdException Locked=“false” Priority=“67” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 1 Accent 6”/>
<w:LsdException Locked=“false” Priority=“68” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 2 Accent 6”/>
<w:LsdException Locked=“false” Priority=“69” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Medium Grid 3 Accent 6”/>
<w:LsdException Locked=“false” Priority=“70” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Dark List Accent 6”/>
<w:LsdException Locked=“false” Priority=“71” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Shading Accent 6”/>
<w:LsdException Locked=“false” Priority=“72” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful List Accent 6”/>
<w:LsdException Locked=“false” Priority=“73” SemiHidden=“false”
UnhideWhenUsed=“false” Name=“Colorful Grid Accent 6”/>
<w:LsdException Locked=“false” Priority=“19” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Subtle Emphasis”/>
<w:LsdException Locked=“false” Priority=“21” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Intense Emphasis”/>
<w:LsdException Locked=“false” Priority=“31” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Subtle Reference”/>
<w:LsdException Locked=“false” Priority=“32” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Intense Reference”/>
<w:LsdException Locked=“false” Priority=“33” SemiHidden=“false”
UnhideWhenUsed=“false” QFormat=“true” Name=“Book Title”/>
<w:LsdException Locked=“false” Priority=“37” Name=“Bibliography”/>
<w:LsdException Locked=“false” Priority=“39” QFormat=“true” Name=“TOC Heading”/>
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<o:p> </o:p>

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