毕业设计（论文）
外文文献翻译
译文题目：数学教学中的师生互动研究
学生姓名：吴薇
专业：数学与应用数学专业
指导教师：周红林
年月日
外文资料翻译译文
数学教学中的师生互动研究
[摘要] 基于心理学、教育学及数学学科特点的分析可知, 数学教学中的师生互动有着深厚的理论底蕴.师生互动的内涵体现在主体平等、认知协调、情感共鸣及教学互补四个方面.实施师生合作的教学模式是师生互动的必然要求, 为此, 在数学教学过程中, 教师应建立平等民主的师生关系;
加强师生间的交流与合作;创设探索性的问题情境;实施计划导控.
[ 关键词] 数学教学;师生互动;教学模式
长期以来, 数学教学中教师一言堂、满堂灌现象严重, 学生所领会的通常只是教师或课本编写者的观点 , 他们很少有表达自己思想观点的机会.这样 , 充当被动听讲角色的学生就不能发挥自己的主动性,知识掌握的效果会大打折扣, 并导致能力培养的速度减缓 , 严重阻碍学生创新精神和实践能力的培养.大学数学教育界近年来逐渐重视教学改革, 问题解决、启发式、研究式已渐入人心, 但这些改革方案往往停留在理论探讨上, 实际教学中仍旧是注入式盛行 .究其原因, 主要在于教师的教学观没有根本转变, 教学改革仅重视“教”的活动而忽视“学”的活动 , 因而不能准确地了解学生的真实思维活动 , 不能科学地把握教学的进程和节奏 , 极大地影响了教学效果 .为此, 就有必要对数学教学中的师生互动问题做出探讨.
一数学教学中师生互动的理论基础
从发展心理学的角度看, 实践活动是人的心理、认识、意识产生和发展的基础.人的心理是在活动中形成和发展的, 人的个性的丰富程度取决于他的活动内容 .如果剥夺人的活动自由, 他的心理发展就会受到阻碍 .在学生如何获得知识和经验的问题上, 美国教育学家杜威的观点值得我们借鉴 .他认为 , 知识和经验靠灌输是不行的, 要靠学生在各种实际活动中通过不断地发现和解决问题来丰富和改造自己的经验 , 获得真知 ;他主张发掘学生的智慧潜力 , 让学生在教学中扮演一种充分积极的角色 , 使学生的兴趣和才能得到自由的充分的发展 .现代教学论认为, 在教学过程中应当使学生系统地掌握学科的基础知识和技能, 以满足其认知的需要 , 而且还应促进学生的发展, 满足学生增长智力、培养能力和兴趣特长、形成良好的个性心理品质和发挥创造力的需要等等 .要做到既保证学生的认识任务又保证学生发展任务的全面完成, 需要以师生双方的积极性和主动性作为基础, 否则认识和发展双重任务的圆满完成是很难想象的.
按照教学过程中的矛盾分析, 教学过程中教师和学生共同构成了教学的主体, 师生双方扮演着不同的角色, 各自从事着具有相互联系、相互制约的活动.钟启泉先生认为 ,“教学的本质在于沟通和合作, 教与学的关系是沟通中的相互作用关系, 教育者与受教育者的关系是交互主体性的伙伴关系”[1] .在教学过程的某个时刻可以由教师对教学起支配作用, 教学活动的中心在教师, 然而在另一个时刻则由学生起支配作用 .这个时刻 , 教学活动的内容、组
织安排和速度可能主要由学生的学习活动来决定, 并要求教师的活动围绕着学生的学习活动
来进行.比如在学生独立探索、实验研究时, 学生需要的仅是教师的引导、点拨和鼓励, 知识
结论再也不是一味由教师告知.因此 , 只有把教师和学生都看成是教学活动中能动的角色和
要素, 把师生双方的关系看成互为主体、互相依存、互相配合的关系 , 才能真正反映教学活
动的本质, 使师生的生命活力在课堂上得到充分发挥 , 使教学过程本身具有生成新因素的
能力, 具有自身的、由师生共同创造的活力 .
从数学学习特点的角度看 , 数学的高度抽象性极易造成教学内容与学生的现实生活的分离, 相应的数学教学活动常常受到歪曲、变异、形式化、表面化 .在数学教学中, 由于数学教材是按照数学理论的逻辑体系编写的, 而这种逻辑体系中的知识呈现顺序与数学理论的真实发现过程往往是相反的(真实发现过程常用“分析法”, 而逻辑体系则采用“演绎法”), 从而 , 根据教材所进行的学习往往是“反思维过程”的活动 :把数学当成纯粹的数学推理 , 当成“逻辑推理”的一种形式来学习, 数学本来具有的丰富多彩性、变化性都被深深地掩盖起来 .显然, 在这样的活动中 , 学生对知识的理解、抽象概括、逻辑推理等能力的表现处于暂时滞后状态 , 主体性、创造性也是难以得到真正的发展 .因此, 教师应改变教材从概念到概念、从定理到推论, 处处强调逻辑演绎的严格性的局面 , 为学生提供数学活动和交流的情境和机会, 让学生的思维能够经历一个从模糊到清晰、从具体到抽象的过程 , 使学生在对概念形成过程的分析中, 在对公式、定理的发现过程的总结讨论中 , 掌握数学概念、原理的实质内涵, 领悟寻找真理和发现真理的方法和手段 , 体验数学思想和数学美学的魅力 .
二数学教学中师生互动的基本内涵
教学中的师生互动不是一种机械的信息传递的输出与输入关系 , 也不是一种简单的人际关系 , 师生互动有其特定的丰富内涵 , 师生互动需要从教师与学生之间的认知、心理、伦理等多方面重塑新型的师生关系.
1 .主体平等
教师与学生都是独立的人 , 都有着人格的尊严、物质与精神的需要 , 都有生存、学习、自我发展和自我实现的权利.师生互动要求建立具有伦理意义的师生关系 , 师生在人格面前、科学面前平等 , 在活动中民主 , 教师应注重学生的人格发展 , 尊重学生现实生活的需要, 发挥学生的主体性, 尊重学生参与教学过程的主体权力, 赋予课堂以生命的意义 .虽然教师可以在一定的程度上调节、控制和引导学生的发展方向, 能提供较为完善的环境和材料 , 把握教学进程 , 使学生在其原有基础上朝着社会要求的全面发展的方向发展 , 但是每个学生都是生动活泼的个体 , 他们会不断地对周围环境进行探索, 学生的信息来源和思考、判断、评价、解决问题的能力常常超越教师的预料.因此 , 教师应当以朋友的身份与学生交流情感和看法, 虚心征求和倾听学生的意见, 挖掘学生的潜能 , 赏识学生的优点和进步 , 学会站在学生的角度客观地评价和反省自己的教育策略、教育要求和教育方法 , 从学生的发展需要和利益出发去思考各个教育环节 .
2 .认知协调
知识的授受过程伴随着复杂的思维活动 , 教学过程中师生之间必然存在着认知结构、认
知方式上的差异和冲突.教学中的认识活动不是学生单向度的认知过程 , 而是师生双向信息沟通与加工的过程 , 学习任务与学生原有的认知水平之间的矛盾是教学过程发展的动力, 教学过程就是通过矛盾的不断冲突激化和解决而发展的 .但只有在学生认识到新的学习任务与自己原有的认知水平之间的矛盾的存在, 并且具有解决这一矛盾的必要性和可能性时, 学生才能成为真正的学习主体 .因此 , 教师和学生在知识的授受过程中应具有某种认知方式的“平行关系”或对应关系 , 教师应充分了解学生学习某一新课题的“初始能力”和“现有发展水平” , 确定学生某阶段的“终结能力”和“最近发展区” , 精心设计教学过程, 教师还应根据学生的认知发展情况, 及时灵活地加以调节 , 以求得教学同步 .
3 .情感共鸣
教学过程中师生关系不是一种简单的“教学相长”关系 , 而是渗透师生情感作用的教学关系, 教师与学生情感活动的互动 , 是贯穿整个教学过程的一种基本活动 .教师与学生在教学活动中的情感体验存在差异 , 教师的情绪情感及其表达方式影响着学生的情绪情感 , 也影响认知活动的效率.情感共鸣是指在教学过程中建立的师生之间的真诚、理解、民主、和谐的心理氛围 .和谐融洽的师生关系不仅可以引导学生积极主动地学习, 还有利于学生的健康人格的形成.因此 , 教学活动中, 教师要合理调控自己的情绪状态, 根据教学进程恰当地体现自己的情感 , 用真诚平等的态度关怀、理解学生 , 用积极乐观的情感去感化、激励学生。当教师在教学中，由职业需要上升为情感需要, 当学生也从认知需要上升为情感需要时双方就超脱了“有用”的功利观念, 转入“移情”和“无我”的超功利意境 , 教学就进入了美的境界 .
4 .教学互补
教学互补, 是指在教学中教师的教法和学生的学法的相互适应与配合 , 达到彼此受纳的境界 , 从而使教学过程中的师生关系从方法论的角度达到高度的和谐 .教学是一种有计划有目的可控制的过程, 要按教学计划达到预想的教学目的, 保证课堂教学的效率, 就必须实现教与学双方活动的适时调控 , 并让教与学在方法上彼此适应和配合.比如在“概念学习”时, 由于学生抽象思维能力的限制 , 就需要更多形象化的教学, 需要更多活动式的教学, 需要更多及时练习与反馈 .而在“巩固练习”时 , 学生分析和解决问题的需要强烈, 自主学习的可能性增大 , 就需要更多的讨论式、自学式和独立探究式的教学.教与学在方法上的互补的标志是教学信息的及时反馈以及由此产生的对教与学的调控.教学过程中师生之间应该时时有信息的交流, 我们应该追求这种信息流的稳定, 同时这种信息流应该是双向互动的 .师生双方按照这种反馈信息适时地调整自己教与学的活动的步骤、方式、速度、方向和进程, 在教的方面, 需要调整教学要求、进度 , 对相关的内容进行适当的补课与矫正教学 ;在学的方面, 则主要强调调整自己的精神状态和学习安排, 进行必要的总结和补缺补差等等.
三数学教学中实施师生互动的几点建议
数学教师要切实提高对师生互动重要性的认识 , 加强对数学教学中师生互动的研究, 转变教育观念、探索新的施教模式.若按师生在教学中的地位和作用, 众多的数学教学模式可分为三类:学生中心模式、教师中心模式和师生合作模式 .“学生中心模式”注重学生智能的发展 , 但否定了教师的主导作用,因而教学过程缺乏有效的控制 , 学生难以形成完善的智能结构.“教师中心模式”则较好地发挥了教师的主导作用, 在教学内容、教学时间上有严密的计
划安排, 可使学生在短时间内经济高效、循序渐进地掌握系统的知识.但最主要的问题是学生处于被动地位 , 主体作用难以发挥, 容易出现诸如“盲从”、“动手能力差”、“应用意识失落”等问题.因此 , 我国数学教育界的众多专家、学者在大声疾呼:教师和教科书不应该是至高无上的权威, 应把学习数学的主动权交给学生 .而“师生合作模式”作为一种新的教学模式,是实施师生互动的必然要求.它的核心思想是强调建立和谐新型的师生关系, 在教学中既重视强调学生的主体地位, 重视调动学生的积极性, 又重视教师的主导作用 , 重视系统知识的传授、能力的培养 , 这些特点正是“素质教育”所需要的 .
实施师生合作的教学模式 , 用互动的形式重塑教学过程, 就是要突出和重视“学”的主体活动 , 在教学过程的各个环节上都要注意学生实质上的学习自主 .因此 , 教师要创造条件 , 启发每个学生充分地与学习材料互动、与学习伙伴互动、与社会环境互动 , 调动学生的主动性、积极性、创造性 , 提高“教”的效果.怎样才能有效地实施师生互动呢? 笔者提出以下几点建议.
1 .建立平等民主、富有情感的师生关系
良好的师生关系是师生互动的基础 .“师生关系很有点像电路适配器 , 相同的教育条件、教育对象,通过一定的师生关系配置 , 或许能爆发出强劲的教育能量, 产生积极的教育效益 , 或许完全相反, 会产生短路 , 使学生厌学.可以说 , 师生关系对于教育质量、教学效益和学生成长的重要意义, 丝毫不亚于空气对人的价值”[2] .第一 , 教师要尊重学生.教师应该尊重学生的想法和建议 , 与学生平等地、协商地交流,这样 , 在传授数学知识时教师就不会是一种自上而下的“给予” , 而是与学生一道去探索、去体验, 学生在课堂中才可能变被动为主动, 将教学活动看作是自己主动参与、自我发展的活动 , 师生的相互交流、相互作用才有可能实现.第二 , 教师要给学生一份爱心 .爱和理解是教师和学生心灵沟通的基础, 是实施有效互动的心理前提 , 情感在互动中能起到润滑剂的作用, 它能弥合师生之间的分歧与隔阂 .教师要赋予学生一种真情实感 , 发自内心地去爱学生 , 关心、理解学生, 学生心灵的火花一旦被点燃, 就会收到意想不到的教学效果.教师还要善于以学生化的心态和行为参与到师生的交互中去 , 使自己能更好地理解学, 学生才能更好地理解教师 , 配合教师的教学活动.第三, 教师要信任学生 .要鼓励学生参与互动 , 给学生, 同时也给自己营造一种平等、合作的教学氛围 .要允许各类不同水平的学生大胆发表意见 , 学生发表创造性的意见, 教师要学会作创造性的评价, 鼓励创造性财富的萌芽 ;对学生在交互过程中表现出的不足, 不能奚落嘲笑, 要充分肯定学生想法中的合理成份 , 让其体验成功的喜悦 , 增强交流的热情和信心
.第四 ,教师要投入情感。教师要以饱满的热情投入教学之中 , 用自身的热情来感染学生, 最终使学生达到“亲其师, 信其道”的境界 .在教学中 , 教师要努力做到以充沛的感情、专注的精神、坚强的毅力、丰富的想象、生动的语言出现在学生面前, 从各个方面影响学生 , 使学生通过耳濡目染 , 激起学好数学的热情 , 这样才能形成适合进行情感教学的氛围.
2 .加强师生之间的交流与合作
在教学过程中, 交流与合作的主要形式有 :第一, 师生间的合作与交流 .这体现在多个方面, 如授课过程中的提问、课后辅导、作业批改 , 甚至一个眼神 , 一个手势, 都是一种合作与交流 .在合作与交流的内容上 , 教师除了就课本所学知识和学生进行探讨外 , 还应虚心听取学生意见 , 克服教学难点, 改进教学方法;同时在思想上、生活上关心学生 , 了解他们的真实想法和内心感受, 帮助他们树立正确的人生观 , 从而, 取得教书育人双丰收 .第二 , 学生之间的合作与交流 .由于合作双方都是学生 , 彼此有许多共同点, 所以可以保持一种无拘无束的学习气氛, 达到双方积极活动、积极思考的目的, 从而使学习过程中的信息交流更加便利和流畅 .第三, 教师间合作与交流.充分发挥教师的主导作用 , 成功地组织好每一堂课 , 教师间的合作与交流是必不可少的.这种合作与交流可以通过多方向实现, 如主讲、助讲间的合作与交流:集体备课商讨最优的授课教案 ;对教学中出现的问题, 集体讨论解决 , 开启思路 , 取长补短 .
3 .创设探索性问题情境
通过创设问题情境, 揭示学习任务与学生原有的认识水平的之间的矛盾, 使学生认识到解决这个矛盾的重要性, 从而激发学生的认知需求 , 使学生的注意力集中到新的学习任务中来.数学学习过程充满着观察、实验、模拟、推断等探索性与挑战性活动, 教师要“变封闭的、单一的教材内容为丰富的有利于学生观察与实践、猜想与验证、收集与处理、选择与判断、推理与交流等可探索的研究性学习材料”[3] , 引导学生投入到探索与交流的学习活动之中 .为了促使学生主动参与教学互动 , 创设问题情境应着眼于以下几点 :第一 , 问题要明确而且具体.当教师和学生都明确教学活动的要求和目的后, 教学活动才可能朝着有效互动的方向发展 .第二, 问题要有新意.学科前沿的、与学生自身素质密切相关的、生动精彩的问题会使学生有新鲜感, 能够吸引学生的注意力, 引导学生变“要我学”为“我要学” .第三 , 问题要有适当的难度 .教师可采用分步设置障碍的方法让学生面对适度的困难, 使问题呈阶梯式递进, 并保持每个问题适当的跨度, 由学生发挥思维去“填充” .第四 , 把握设问的时机.一般而言 , 问题主要设计在重点、难点、转折、联系、创新应用等关键处 , 但应随机应变 , 切勿拘泥程式 .比如, 有的学生在求导中偶然发现 , 所求的奇函数的导数都是偶函数, 这时, 教师可顺势提问 :对于一般的奇函数 f (x), 它的导函数 f′(x)是否一定为偶函数? 进一步去问:偶函数的导数又是什么性质的函数呢? 这样 , 通过一个又一个引发学生思维的问题 , 使学生的思维始终处于一个接一个的问题探索之中, 师生之间的互动显得水乳交融 .
4 .实施计划导控 , 增进师生互动的效果
成功的师生互动是以充分发挥学生学习的自主性为前提的 , 但是 , 这并不意味着把大量时间留给学生任意支配, 放任自流.其实,“教学中学生主体作用的发挥并不能成为学生自己的自觉行动, 而必须通过教师切实有效地诱导启发.”[4]因此 , 必须实施计划导控 , 在教师有计划的引导下为达到明确的教学目的进行有序的、分步骤的学习活动 , 激发、引导学生学习的主动性、自觉性和创新性, 从而在组织形式上保证师生互动的效果 .计划导控的基
本流程是“任务驱动、方向定位、自主研究、反馈审核” .“任务驱动”是根据学习内容提出明确的研究任务, 促使学生为圆满完成任务去自我学习 .比如, 为指导学生自学教材, 教师可给出自学思考题, 让学生自学后写出问题解决的方案、阶段内容总结等来引导学生自学.“方向定位”是为保障学生完成既定任务, 为学生提供一些学习资源的搜集、整理的方法和手段, 指导学生如何利用各种先进手段获取信息、加工信息、利用信息 , 以此来圈定学生的学习范围, 定位学生的学习方式, 防止学生偏离方向.“自主研究”指学生带着问题, 独立地查阅资料、搜集素材、分析问题症结、形成解决问题方案.“反馈审核”是指通过对学习任务的审核, 确认任务完成情况, 及时调控 .除了常规的课后练习和章节测验外 , 还有章节总结、专题的学习体会、阅读摘要等作业形式.上述各个流程间是顺序继承和相互作用的, 通过合理配置就为完满的师生互动提供了切实保证 .
外文原文
Research on the Teacher-Student Interaction in Mathematics Teaching Abstract:T he teache r-student interactio n was of primary impo rtance in mathema tics teaching .It consisted o f the follow ing four aspects :rela tions on an equal basis, cog nitio n coo rdina tion , sy mpathe tic feeling and mutua l aid of teaching and lear ning .T o car ry o ut the teacher-stude nt inte raction in ma thematics teaching , we offered sever al co nstr uctiv e sug gestio ns .
Key words:mathema tics teaching ;teacher-student inte ractio n;teaching pa tte rn
For a long time, math teaching teachers in a classroom, full house irrigation phenomenon is serious, the students usually understand only teachers or textbook writers point of view, they rarely have the opportunity to express their ideas and ideas, so as a passive role in listening to students can not play to their own The result of the knowledge control will be greatly reduced, and the speed of the ability cultivation will be slowed down, which will hinder the students' innovation spirit and practical ability training seriously.In recent years, the university mathematics education has paid more attention to the teaching reform, the problem solving, the heuristic, The teaching reform is only concerned with the activities of "teaching", while the neglect of the "teaching" is the main reason for the teaching reform. "Learning" activities, and thus can not accurately understand the students' real thinking activities, can not grasp the process of teaching and rhythm of teaching, greatly affected the teaching effect.Therefore, it is necessary to mathematics teaching interaction between teachers and students to do Out to explore.
The Theoretical Basis of Interaction between Teachers and Students in Mathematics Teaching
From the perspective of developmental psychology, practice is the basis of human psychology, cognition, consciousness generation and development.Human psychology is formed and developed in the activity, the richness of human personality depends on the content of his activities.If Depriving people of freedom of movement, his mental development will be hampered.In the students how to acquire knowledge and experience on the issue, the American educator Dewey's point of view is worth learning from him.He believes that knowledge and experience by indoctrination is not enough, Students in a variety of practical activities by constantly discover and solve problems to enrich and transform their experience to obtain true knowledge; he advocates the potential of students to explore the wisdom of the students in teaching play a fully active role in the student's Interest and ability to get free full development.The modern teaching theory, in the teaching process should enable students to systematically grasp the basic knowledge and skills to meet their cognitive needs, but also to promote the development of students to meet the students Growth of intelligence, ability to cultivate and interest expertise to form a good personality and the psychological quality of the needs of creativity, etc. To achieve both the task of ensuring the students' understanding and ensure the full completion of student development tasks, teachers and students need to both enthusiasm and Initiative as a basis, or awareness and development of the successful completion of the dual task is difficult to imagine.
According to the analysis of contradictions in the teaching process, teachers and students constitute the main body of teaching, teachers and students play different roles, each engaged in activities of mutual contact and mutual restraint.Zhong Qiquan believes that "the nature of teaching In the communication and cooperation, teaching and learning is the relationship between the interaction, the relationship between educators and educators are interactive subjective partnership. "At some point in the teaching process can be teachers to teaching But at another moment by the students dominate the role of this moment, the content of teaching activities, organizational arrangements and the speed may be mainly determined by the student's learning activities, and requires teachers to the activities of the activities of the teacher's activities, Such as students in the independent exploration, experimental research,
students need only the guidance of teachers, coaching and encouragement, knowledge is no longer blindly by the teachers to inform.Therefore, only the teachers and students are both teachers and students are learning, As the active role of teaching activities and elements of the relationship between teachers and students as the main body of each other, interdependence and cooperation with each other in order to truly reflect the nature of teaching activities, so that the vitality of teachers and students get in the classroom Give full play to make the teaching process itself has the ability to generate new factors, with their own, jointly created by the vitality of teachers and students.
From the perspective of the characteristics of mathematics learning, the highly abstract nature of mathematics can easily lead to the separation of teaching content from students' real life, and the corresponding teaching activities are often distorted, mutated, formalized and superficial.In mathematics teaching, Is based on the logical system of mathematical theory, and this logical system of knowledge in the order and the mathematical theory of the real discovery process is often the opposite (true discovery process commonly used "analysis", while the logical system is "deductive" ), Thus, according to the textbooks for learning is often the "anti-thinking process" activities: the mathematics as a purely mathematical reasoning, as "logical reasoning" to learn a form of mathematics originally has the richness and variety It is clear that in such activities, the students' understanding of knowledge, abstract generalization, logical reasoning ability in the performance of temporary lag, subjectivity, creativity is difficult to get real development.Therefore, the teacher We should change the teaching material from the concept to the concept, from the theorem to the inference, everywhere stressed the logical deduction of the strictness of the situation, to provide students with mathematical activities and exchange of situations and opportunities for students thinking to experience a from fuzzy to clear, The process of the concept of the formation of students in the analysis of the formation of the formula, the theorem of the summary process of discovery and discussion to master the concept of mathematics, the essence of the principle of comprehending the search for truth and discovery of the methods and means to experience mathematics The Charm of Thought and Mathematical Aesthetics.
The Basic Connotation of Interaction between Teachers and Students in Mathematics Teaching
Teacher-student interaction in teaching is not a kind of mechanical information transmission and input relationship, nor is it a simple interpersonal relationship, teacher-student interaction has its specific rich connotation, teacher-student interaction needs from teachers and students Knowledge, psychology, ethics and other aspects of remodeling a new type of teacher-student relationship.
Subject equality
Teachers and students are independent people, have the dignity of personality, material and spiritual needs, have the right to survival, learning, self-development and self-realization.The interaction between teachers and students requires the establishment of an ethical relationship between teachers and students, In front of personality, equality before science, in the activities of democracy, teachers should focus on the development of students 'personality, respect for the needs of students in real life, students' subjectivity, respect for students involved in the teaching process of the main power, giving life meaning. Although the teacher can adjust, control and guide students' development direction to a certain extent, can provide a more perfect environment and materials, grasp the teaching process, so that students in their original basis towards the overall development of social development direction, But each student is a lively individual, they will continue to explore the surrounding environment, the source of the student's information and thinking, judgment, evaluation, problem-solving ability often exceed teachers' expectations.Therefore, teachers should be friends And students to exchange feelings and views, humbly seek and listen to the views of students, tap the potential of students, students appreciate the advantages and progress, learn from the perspective of students objectively evaluate and reflect on their own educational strategies, educational requirements and educational methods, from The development needs of students and the interests of starting to think about various educational sectors.
Cognitive coordination
The process of teaching and learning is accompanied by complex thinking activities, and there are inevitable differences in cognition structure and cognition between teachers and students in the teaching process, and cognitive activities in teaching are not the one-dimensional cognitive process of students. Is the process of two-way communication and processing between teachers and students, the contradiction between learning tasks and students' original cognitive level is the driving force of the development of teaching process, and the teaching process is developed through contradictory conflict intensification and resolution. Students recognize that the new learning tasks and their existing level of awareness of the contradiction between the existence and the need to resolve this contradiction and the possibility of the students to become a real learning subject.Therefore, teachers and students in the Teachers should fully understand the students to learn a new topic of the "initial capacity" and "the level of existing development" to determine the stage of the students a "parallel relationship" or a corresponding relationship, The end of the ability "and" recent development zone ", carefully designed teaching process, teachers should be based on the cognitive development of students, timely and flexible to adjust to achieve teaching synchronization.
Emotional resonance
In the process of teaching, teacher-student relationship is not a simple "teaching and learning" relationship, but the interaction between teachers and students emotional activities, is a basic activity throughout the teaching process. Emotional feelings and their expression affect the emotions of students, but also affect the efficiency of cognitive activities.Emotional resonance refers to the teaching process in the establishment of teachers and students of sincerity, understanding of the relationship between teachers and students in the process of teaching, , Democratic and harmonious psychological atmosphere.Modern harmonious teacher-student relationship can not only guide students to actively learn, but also conducive to the formation of students' healthy personality.Therefore, teaching activities, teachers should be reasonable regulation of their emotional state, according to teaching Process properly reflect their emotions, with a sincere and equal attitude of care, understanding of students, with a positive and optimistic emotions to probation, motivate students. When the teacher in teaching, the need for professional needs increased to emotional needs, when the students need to rise from the cognitive needs of emotion when the two sides to transcend the "useful" utilitarian concept, into the "empathy" and "no" super Utilitarian mood, teaching to enter the realm of beauty.
Complementary teaching and learning
Teaching complementation refers to the mutual adaptation and cooperation of teachers 'teaching method and students' learning method in teaching, so as to achieve a high degree of harmony between teachers and students in the teaching process from the perspective of methodology. A planned purposeful control process, according to the teaching plan to achieve the desired teaching objectives to ensure the efficiency of classroom teaching, it is necessary to achieve both teaching and learning activities of the timely regulation and control, and teaching and learning in the method of adaptation and mutual For example, in the concept of learning, due to the ability of students to abstract thinking, you need more visualization of the teaching, the need for more active teaching, need more timely practice and feedback.In the "consolidation exercise" , Students need to analyze and solve the problem strongly, the possibility of increased self-learning, you need more discussion, self-learning and independent inquiry-style teaching.Teaching and learning in the method of complementary signs of teaching information in time Feedback and the resulting regulation and control of teaching and learning between teachers and students in the teaching process should always have information exchange, we should pursue the stability of this information flow, and this information flow should be two-way interaction. In accordance with this feedback, the two sides should adjust the pace, mode, speed, direction and progress of their teaching and learning activities in a timely manner. In terms of teaching, the two sides need to adjust teaching requirements and progress, and make appropriate remedial and correctional teaching on related contents. In school, the main emphasis on adjusting their mental state and
learning arrangements, the necessary summary and fill gaps and so on.
Several Suggestions on Teacher - Student Interaction in Mathematics Teaching
Mathematics teachers should enhance their understanding of the importance of interaction between teachers and students, strengthen the study of interaction between teachers and students in mathematics teaching, change the concept of education, explore new teaching mode, according to the status and role of teachers and students, The student-centered model emphasizes the development of student's intelligence, but denies the leading role of the teacher, so the teaching process lacks effective control, and the student-centered model, the student-centered model and the student-student cooperation model It is difficult to form a perfect intelligence structure.Teacher Center Model is a good teacher to play a leading role in the teaching content, teaching time, there are tight planning arrangements that enable students in a short time cost-effective, step by step to master the system The main problem is that the students are in a passive position, the main role is difficult to play, prone to such as \ Therefore, many of China's math education experts, The teacher and the textbook should not be the supreme authority, should take the initiative to study mathematics to the student.The teacher-student cooperation pattern as a kind of new teaching pattern, is carries on the teacher and student interaction the inevitable request. The core idea is to emphasize the establishment of a harmonious new teacher-student relationship, in teaching not only emphasizes the emphasis on the student's subjective position, attention to mobilize the enthusiasm of the students, but also pay attention to the leading role of teachers, emphasis on the transmission of knowledge of the system, the ability of these characteristics Is "quality education" needs.
It is necessary to reinforce the teaching process in the form of interaction, that is to highlight and attach importance to the main activities of "learning", and to pay attention to the students' learning autonomy in all aspects of the teaching process. Create conditions, inspire each student to fully interact with learning materials, interaction with learning partners, and social environment interaction, to mobilize the initiative, enthusiasm, creativity, and improve the effectiveness of teaching and learning how to effectively implement teacher-student interaction The author makes the following suggestions.
Establish a democratic and affectionate relationship between teachers and students
Good teacher-student relationship is the basis of interaction between teachers and students. "Teacher-student relationship is very similar to the circuit adapter, the same educational conditions, educational objects, through a certain teacher-student relationship configuration, may burst strong educational energy, Educational benefits, and perhaps the opposite, will produce short-circuit, so that students weariness .It can be said, the relationship between teachers and students for the quality of education, teaching effectiveness and student growth significance, no less than air on human value. Teachers should respect the students' ideas and suggestions, and students on an equal and consultative exchange, so that in the teaching of mathematics knowledge, teachers will not be a top-down "give", but And students to explore, experience, students in the classroom can become passive and active, the teaching activities as their own active participation, self-development activities, teachers and students of mutual exchange, interaction is possible to achieve. , Teachers should give students a love.Love and understanding is the basis of communication between teachers and students heart, is the effective prerequisite for the interaction, emotional interaction can play the role of lubricant, it can bridge the differences between teachers and students Teachers should give students a real feeling, from the heart to love the students, care, understanding students, the students once the spark of the soul is lit, you will receive unexpected teaching effect.Teachers should be good at the student-oriented The mentality and behavior to participate in the interaction between teachers and students, so that they can better understand the students, students can better understand the teacher, with teachers teaching activities.Third, teachers should trust students to encourage students to participate in interaction, To give students, but also to create a fair, cooperative teaching atmosphere.To allow all kinds of different levels of students boldly express their views, students published creative ideas, teachers should learn to make creative evaluation, to
encourage the seeds of creative wealth; Students in the interactive process to show the lack of ridicule can not ridicule, to fully affirm the rational thinking of students in the composition, let experience the joy of success and enhance the exchange of enthusiasm and confidence
Fourth, teachers should invest emotion. Teachers should be full of enthusiasm into teaching, with their own enthusiasm to infect students, and ultimately enable students to achieve In the teaching, teachers should strive to do with plenty of emotion, focus on The spirit, the strong perseverance, the rich imagination, the vivid language appears in front of the student, affects the student from each aspect, causes the student through the monasteries, stirs the enthusiasm which studies mathematics goodly, like this can form the suitable atmosphere for the emotion teaching.
Strengthen the communication and cooperation between teachers and students
In the teaching process, the main forms of communication and cooperation are: First, the cooperation and exchange between teachers and students, which is reflected in many aspects, such as teaching process questions, after-school tutoring, homework correction, and even a look, In the cooperation and exchange of content, teachers in addition to the textbook of knowledge and students to explore, but also humbly listen to the views of students to overcome the teaching difficulties, improve teaching methods; at the same time in the minds of , Students are concerned about life, to understand their real thoughts and inner feelings, to help them establish a correct outlook on life, thus, to obtain teaching and educating people to double harvest.Second, the cooperation and exchange between students.Because the cooperation of both students, So that the exchange of information in the learning process more convenient and smooth.Third, the cooperation between teachers and exchanges.Give full play to the full play of the teachers and students, The teacher's leading role in the successful organization of each class, the cooperation and exchanges between teachers is essential.This cooperation and communication can be achieved through multi-direction, such as the speaker, the cooperation and exchange between the group: collective lesson planning The best teaching lesson plans; teaching problems, collective discussion to solve, open ideas, learn from each other.
3. Create an exploratory problem context
Through the creation of problem situations, revealing the task of learning and students the original level of understanding of the contradiction between the students to recognize the importance of resolving this contradiction, so as to stimulate students' cognitive needs, so that students focus on new learning Task, mathematics learning process is full of observation, experiment, simulation, inference and other exploratory and challenging activities, teachers should be "closed, single textbook content is conducive to the observation and practice of students, conjecture and validation, collection And explore, explore, and communicate with others, such as processing, selection, judgment, reasoning, and communication. "3 In order to encourage students to actively participate in teaching interaction, the creation of problem situations should focus on The following points: First, the problem should be clear and specific.When teachers and students are clear requirements and objectives of teaching activities, teaching activities may be in the direction of effective interaction.Two, the problem should be innovative. , And students are closely related to their quality, lively and exciting issues will make students have freshness, to attract the attention of students, and guide students to change "to me" as "I want to learn." Third, the problem should be appropriate Teachers can use the method of step-by-step to set up obstacles so that students face moderate difficulties, so that the problem was ladder-type progressive, and maintain the appropriate span of each problem, the students play thinking to "fill." In general, the main design problems in the key, difficult, turning point, contact, innovative applications and other key office, but should be flexible, not rigidly stick to the program.For example, some students seek guidance in the accidental discovery, The derivative of the odd function is even function, this time, the teacher can take advantage of the opportunity to ask questions: for the general odd function f (x), its derivative function f '(x) is even as a function? Further asked: even derivative What is the nature of the function? In this way, through one after another to raise students thinking, so that students thinking is always one by one in the
exploration of the problem, the interaction between teachers and students seem to blend in harmony.
4.Improve teacher-student interaction by implementing planned control
However, this does not mean that a large amount of time is left to the students to control at will. In fact, "the role of students in the teaching of the main role can not become a student of the students' Their own conscious action, but must be effectively instructed by teachers to induce inspiration. "[4] Therefore, we must implement the program control, under the guidance of teachers in a planned order to achieve a clear purpose of teaching orderly and step-by-step learning activities , To stimulate and guide students to learn initiative, consciousness and innovation, so as to ensure the effect of teacher - student interaction in the form of organization.The basic process of planning and control is "task - driven, orientation, independent research, feedback audit". Task-driven "is based on learning content to make clear research tasks, to promote the students to complete the task to self-learning.For example, to guide students to self-study materials, teachers can give self-study questions, so that students write self-study solution to the problem, Stage orientation and so on to guide the students to learn by themselves.Under the guidance of "orientation orientation", students are provided with some methods and means of collecting and arranging learning resources to guide students how to use various advanced methods to obtain information, process information, The use of information, in order to delineate the scope of student learning, positioning students learning, to prevent students from the direction of "independent research" refers to the students with problems, independent access to information, data collection, analysis of the crux of the problem, the formation of solutions to problems. In addition to regular after-school exercises and chapter tests, there are chapter summary, learning experience of the topic, reading abstracts and other forms of operation. Each of the above-mentioned Process is the order of succession and interaction, through the rational allocation of teachers and students on the perfect interaction to provide a practical guarantee.