好玩是数学学科特点的需要

好玩是数学学科特点的需要 博兴县第一小学宋春京2011年11月2日 19:17浏览:26评论:4 指导教师 韩国栋于11-11-2 20:56推荐尊重学生的认知，将解决认知冲突的过程与学生数学学习活动巧妙结合，有效激发学生的思维的浪花，让整堂课的教学充满思考情趣。 让数学好玩，也是我多年对自己数学的课堂的要求和追求，这是数学这一学科特点的需要。每位数学老师都知道，思维是数学的核心。只有学生学会“数学地思维”，才能走进数学这一神圣且神秘的智慧殿堂。 思 维主要是靠启迪，而不是靠传授，越是传授的一清二楚，学生就越不需要思维。只能增加了知识性的储存。要使教学过程成为思维活动的教学，就要为这种活动创造良好的条件，我们要通过知识建构，充分展开知识发生发展的过程;通过问题解决，充分展开发现解法的过程;让数学思维在这种展开了的过程中附着在典型的知识和问题上;同时我们的教学过程必须也应该具有开放性和自主性，只有这样，才能诱发学生思维的独立性、深刻性、批判性和创造性。 而上述教学目标的达成，必须借助于“情感”这一催化剂。„数学思维“和“情感”是一个互动的过程。良好的数学情感对数学思维具有启动、维护、加速的作用;而数学思维的结果又对学生喜欢数学、乐意接受数学思维的挑战具有强化的作用。而数学好玩正是学生积极情感的体现，只有在好玩情感的催化下，学生才会开启数学这一智慧殿堂的大门。 关于“数学活动经验”模块的网络材料精品剪辑 博兴县第一小学宋春京2011年11月10日 22:49浏览:36评论:1 省专家 徐大有于11-11-11 18:31推荐感谢宋老师提供的理论学习材料。认真学习这些材料，有助于弄清概念，提高理论水平，以便更有效地指导教学实践。不解决理论问题，只能在实践中盲目探索，人云亦云，在迷茫中原地踏步或原地打转转。 指导教师 商艳霞于11-11-11 22:36推荐每次看宋老师的作品不仅收获很大，而且是一种享受，我为有这样的同事而感到骄傲～ Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 关于“数学活动经验”模块的网络材料精品剪辑 积累学生的数学活动经验是一个陌生而又似曾相识的话题。说它陌生，是因为在研修以前我们很少提及这个话题。说它似曾相识，是因为在新课标中看到过，但是没引起太多的注意，更没有引起思考，因为我们那时正在努力打造新型课堂，需探讨的问题很多。今天关注情境的创设，后天关注学生的问题意识的培养;然后是学生的自主探索与合作交流„„随着关注点的变化，我们一线教师的教学理念和教学方式也有了很大的改观。最大的改变是自己所有的教学活动都围绕着“孩子”着想了。想了很多，也做了很多，但是当这个话题来到眼前时还是一脸的茫然。没有理论、没有经验、没有案例积累。于是反复观看视频、案例，再从网络和书籍中收集这方面的信息资料细细评味。虽然是临时“抱佛脚”，庆幸的 是收获还颇丰，下面是个人收集资料中的精华，愿与各位同仁分享: 摘抄一:关于不同数学活动经验的定义与分类介绍 一、基本数学活动经验 (一)含义 在数学教学中，数学活动的一个主要目的是让学生经历探究的过程、思考的过程、抽象的过程、预测的过程、推理的过程以及反思的过程等，获取丰富的过程性知识，最终形成应用数学的意识。数学活动经验可以这样理解:数学活动经验是指学习者在参与数学活动的过程中所形成的感性知识、情绪体验和应用意识(感性知识是指具有学生个人意义的过程性知识，也包括学生大脑中那些未经训练的、不那么严格的数学知识;情绪体验是指对数学的好奇心和求知欲、在数学学习活动中获得的成功体验、对数学严谨性与数学结果确定性的感受以及对数学美的感受与欣赏等;应用意识包括“数学有用”的信念、应用数学知识的信心、从数学的角度提出问题与思考问题的意识以及拓展数学知识应用领域的创新意识。 数学基本活动经验是建立在人们的感觉基础上的，又是在活动过程中具体体现的，与形式化的数学知识相比，它没有明确的逻辑起点，也没有明显的逻辑结构，是动态的、隐性的和个人化的(它可以是米三国藏眼中的使人受益终生的深深铭刻在头脑中的数学的精神、数学的思维方法、研究方法、推理方法，甚至经 历的挫折等;也可以是克莱因笔下的从整体意义上对数学活动的领悟。在数学Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 学习中，要使学生真正理解数学知识，感悟数学的理性精神，形成创新能力，就应该让学生积累丰富而有效的数学活动经验。 (二)分类 张奠宙与赵小平给我们大致把数学基本经验分为: 日常生活中的数学经验， 社会科学文化情境中的数学经验， 以及纯粹数学活动累积的数学经验。 二、日常生活中的数学经验 (一)含义 经验，是指由过去的实践得来的知识或技能。它是个体立足于客观世界，建立在感官知觉上的对事物的认识和反映，是人类和个体认识成果的积累。儿童的生活经验是指学生在生活中通过亲身经历、体验而获得的对事物的认识和反映，具有自然性、生成性、发展性等特点。 自然性是指学生生活在瞬息万变的社会中，各种各样的生活现象都会毫无阻拦地进入他们的认知领域，从而形成他们“自己的经验”。当然这种经验很大程度上是原始的、粗浅的、局部的、零散的，甚至是不准确的、不科学的，但却是十分难得和可贵的。 生成性是指学生在生活和学习的过程中，存在着对自己已有的经验进行调用、调整、提升或者重新确立的过程，也存在着对活动中新的认识不断接受、理解和内化的过程。这些过程实质上就是新的经验建立和生成的过程。 发展性是指经验的建立和运用是一个动态的、不断积累、丰富发展的过程，这也是人的内在素质和能力提高的过程。任何学习都是在先前经验基础上的主动建构，这种建构的结果又会导致经验系统的变化，在这种螺旋上升的发展过程中，学生的经验得以进一步丰富和发展，学习的质量进一步提高。 生活中的数学经验，就是生活中的与数、形、位置、大小有关的经验。 (二)分类 第一类:可以直接拿来促进学生数学学习的生活经验。这样的生活经验有许许多多。例如在学习长方体和正方体、认识人民币等内容时，学生便有不少生活经验可以直接促进他们的数学学习。我们应当充分地加以挖掘和利用，很好地把握Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 住学生认知的起点。 第二类;可以通过类比来促进学生数学学习的生活经验。这样的生活经验，从表面上看，似乎不能与数学知识的学习构成什么直接联系，但却可以通过类比来促进学生的数学学习。比如，在学习线段、角的加法运算时，我随后拿起一只粉笔，折成两段，“得到整体,部分之和”这个生活经验，用它去理解图形的加减就很容易了。很多时候应用这种方式可以使抽象的知识变得更形象、更易于理解。 第三类:可能对学生的数学学习产生负面影响的生活经验。比如，生活中对角的概念经验，就会对平角、周角的概念学习产生负面影响。生活经验的丰富性也必然导致有些生活经验会对学生的数学学习产生负面影响，甚至有些经验本身便是错误的。对于这一类的生活经验我们也必须正视，因为经验无论是正确的、错误的，它往往都是根深蒂固的，想强制性地加以取代必然会影响学生主体性和创造性的发挥，应当允许学生在学习过程中逐步加深认识。 第四类:包含着一搬规律的生活经验。我们能从中提取出一般性的学习方法，问题解决的方法，提高学习效率的方法。 (三)关注学生生活经验 《标准》说，数学教学应该是从学生的生活经验出发，向他们提供充分从事数学活动与交流的机会，帮助他们在自主探索的过程中，真正理解和掌握基本的数学知识与技能、数学思想与方法，同时获得广泛的数学活动经验，成为学习数学的主人。小学数学具有现实的性质，所以教学要基于学生的生活现实，基于学生的生活经验。学生学习的是与他们生活实践、活动经验有着密切联系的数学。对小学生来说，数学是现实的、有趣的、有用的，小学数学是学生在生活与活动中产生的数学。学生并不是入学后才接触数学，也不仅仅在学校中才接触数学。 他们在上小学之前，已经遇到许多数学，积累了一些初步的经验。他们玩过各种形状的积木，比过物体长短、大小、轻重、厚薄、宽窄，他们知道几点起床几点睡觉，他们随着父母一起外出购物等等。所有的活动都使他们获得了数量和几何形体的最初步的观念，尽管这些往往是非正规的、不系统的，甚至是模糊的，或许还有错误隐藏其中，我们有必要对他们的生活经验即日常数学进行数学化，Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 进行经验提升，以生成新的经验，促进学生的经验从一个水平上升到更高水平，实现经验改造或重新改组。 摘抄2、什么是数学活动经验, 数学活动经验是一种过程性知识，主要由感性知识、情绪体验和应用意识三种成分构成。感性知识是指具有学生个人意义的过程性知识，也包括学生大脑中那些未经训练的、不那么严格的数学知识;情绪体验是指对数学的好奇心和求知欲、在数学学习活动中获得的成功体验、对数学严谨性与数学结果确定性的感受以及对数学美的感受与欣赏等;应用意识包括“数学有用”的信念、应用数学知识的信心、从数学的角度提出问题与思考问题的意识以及拓展数学知识应用领域的创新意识，而且应用意识是数学基本活动经验的核心成分。 摘抄3、数学活动经验包括哪些, 在数学学习中，要使学生真正理解数学知识，形成能力，就应该让学生积累丰富而有效的数学活动经验，这些经验包括检索、抽取数学信息的经验，操作的经验、探究的经验、思考的经验、选择和运用已有知识的经验、建立数学模型的经验，预测结论的经验，对有关结论进行证明的经验，对所得结果进行解释和说明的经验，巩固、记忆、应用所得知识的经验等等( 摘抄4:数学活动经验的特征 1、主体性。数学活动经验是由学生这个主体通过自我意识靠自主活动获得的，它带有明显的主体性特征，也具有学生的个性特征。它对于每个人来说获取了什么、获取了多少都是不同的。 2、实践性。数学活动经验是学生在学习的活动过程中所获得的，离开了活动过程，这个实践过程是不会形成有意义的数学活动经验的。 3、发展性。数学活动经验反映的是学生在特定的学习环境中或某一学习阶段对所学知识的一种经验性认识，这种经验性认识更多的时候是一种“渔”的本领，而非“鱼”本身。在活动认知中，学生原来的生活经验或直接感受的、非严格理性的一些知识经验，可以充实、完善、转化为更科学的内在经验。 4、多样性。即使外部条件相同、参与相同的活动、学习相同的知识内容，每一个学生仍然可能具有不同 的经验。 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 摘抄五:什么样的活动是一个好的数学活动呢, 对数学课堂教学来说，应满足以下条件:所设计的数学活动应该是每一个学生都能进行的，能为层次上进行指导和引领。 摘抄六、积累数学活动经验的方法一: 1、在操作活动中侧重于丰富来自感官、知觉的经验。 “基本活动经验是个体在经历了具体的学科活动之后留下的、具有个体特色的内容，既可以是感觉知觉的，也可以是经过反省之后形成的经验。”在数学活动中，学生通过外显的行为操作，对学习材料的第一手直观感受、体验和经验一般是直接经验。这类操作的直接价值并不是问题的解决，而是对学习材料的感性认识。 2、在探究活动中侧重于融合行为操作经验与思维操作经验。 在数学课堂中，我们经常会向学生抛出特定情境下的某些问题，让学生进行动手操作、自主探究、合作交流，这其中，既有外显的行为操作活动，也有思维层面的操作活动。学生能获得融直接经验与间接经验为一体的数学活动经验。这类探究活动直接指向 问题的解决而非获取第一手直观体验。学生不仅在活动中有体验，在活动前、活动中、活动后都经历着数学思考。 3、在思维活动中侧重于积累和提升策略性、方法性经验。 在思维操作活动中获得的经验即思维操作的经验，比如归纳的经验、类比的经验、证明的经验，等等。就一个人的理性而言，思维过程也能积淀出一种经验，这种经验就属于思考的经验。一个数学活动经验相对丰富并且善于反思的学生，他的数学直觉必 然会随着经验的积累而增强。 4、在综合活动中侧重于发展复合、应用的经验。 现实中，许多数学活动都会要求学生有多种经验参与其中，不仅有操作的经验、探究的经验，也有思考的经验，更需要有应用的意识。 摘抄7:积累数学活动经验的方法(二) 1、放手积累收集信息、提出问题的经验 2、放手积累合作交流、分析问题的经验 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 3、放手积累动手操作、理解问题的经验 4、放手积累自主探索、解决问题的经验 摘抄8:积累数学活动经验的方法(三) 1(“做游戏”——让学生在“玩”中积累数学基本活动经验 2(“文本阅读”——让学生在“读”中积累数学基本活动经验 3(“实践操作”——让学生在“动”中积累数学基本活动经验 4(“自主探究”——让学生在“悟”中积累数学基本活动经验 5(“解决问题”——让学生在“用”中积累数学基本活动经验 摘抄9:积累数学活动经验的方法(四) 1、为学生精心设计一个好的数学活动 数学活动经验是在数学学习活动中产生的，因此使学生获得数学活动经验的核心是要提供一个精心设计的数学活动。对数学课堂教学来说，好的数学活动是每一个学生都能进行的，能为学生提供良好的学习环境和问题情境，为学生获得更多的活动经验提供广阔的探索空，能使学生积极参与，充分交流。 2、课堂教学中重视过程性目标的落实 《标准》明确了“过程”本身就是课程的目标，即必须结合具体内容让学生在数学学习活动中去“经历过程” 3、充分发掘“做数学”的课堂教育价值 “做数学”(do mathematics)并不能单纯地理解为 “动手操作”，这样比较狭隘、片面的理解，往往在数学教学过程中造成表面热闹、实质无效或低效等状况。在后课程改革的背景下，“做数学”的内涵应该是更加丰富的，如动手做(hands-on)，做中学(1earning from Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. doing)、数学试验等，通过这些形式，使学生动脑、动手、动口，充分利用多种感官协同活动，从多渠道有效地获得数学活动经验 4、数学活动经验重点在积累与必要的提升 数学学习具有累积性，后一阶段的学习是建立在学生已有的知识和经验的基础之上的，是对前一阶段知识与经验的深化与发展。因此，数学活动经验重点在积累，教师切不可“包办代替”，同时也不能仅仅停留在感性层面，需要通过一定的教学手段予以提升。 关于“构建小学数学模型”的理论资料剪辑 博兴县第一小学宋春京2011年11月17日 20:42浏览:21评论:1 省专家 徐大有于11-11-20 21:43推荐无推荐理由～ 关于“构建小学数学模型”的理论资料剪辑 1、什么是数学模型 所谓数学模型指的是对数学知识进行简化和提炼、再通过数学语言、符号或图形等形式对其进行概括与归纳、描述、反映特定的问题或具体事物之间关系的数学结构。 2、小学数学中的数学模型主要指什么, 小学数学中的数学模型，主要指数学概念、法则、公式、性质、数量间的关系等，大多可以在现实生活中找到它们的足迹。 3、对建构数学模型的认识 数学模型是建立在数学一般的基础知识与应用数学知识之间的一座重要的桥梁，建立数学模型的过程，就是指从数学的角度发现问题、展开思考，通过新旧知识间的转化过程，归结为一类已经解决或较易解决的问题中去，再综合运用已有的数学知识与技能解决这一类问题。这是在平时的数学教学中教师应该着重Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 培养学生所具备的一种数学思想和方法。就是将数学理论知识应用于实际问题的思想和方法。 建立模型更为重要的是强调用真实的情景展示问题，营造解决问题的环境，以帮助学生在解决问题的过程中活化知识，变事实性知识为解决问题的工具。学生在探索、获得数学模型的过程中，也同时获得了建构数学模型、解决实际问题的思想与方法，而这对学生的发展来说，其意义远大于仅仅获得某些数学知识。 4、 建构数学模型的方法 (1)、 建立数学模型应该上学生大胆的去猜想，再在直观的事例中进行具体地分析。 猜想是一种带有一定直觉性的比较高级的思维方式，对于探索或发现性学习来说，猜想是一种非常重要的思维方法。 (2)、建构数学模型应该让学生在许多直观或贴近生活的实例中进行有效地综合比较。 综合是指学生在学习的过程中将数学现象、数学实例的分析情况进行整理组合，从而形成对这一类数学知识的总体认识。比较是对有关的数学现象、数学实例，区别它们的相同之处和不同之处。数学中的比较是多方面的，包括多少与大小的比较，相同与不同的比较，结构与关系的比较，定律与性质的比较等。比较的目的是认识事物的联系与区别，明确彼此之间存在的同一性与相似性，一边解释其背后的共同模型。 (3)、建构数学模型应该让学生从具体的实例中抽象出它们所具有的共性，再用数学的语言或符号等进行概括。 抽象是从许多数学实例或数学现象中，发现其共同的本质特点。而概括则是把抽象出来的共同点用数学的语言或符号等形式进行归纳和总结。 (4)、建构数学模型一定要让学生进行充分地验证，得出结论之后再进行有效的应用。 学生在初步得出结论时要给于足够的空间让学生进行充分地验证，在验证的过程中可能会发现新的现象，并在解决新问题的过程中，进一步完善自己的猜想，最终发现规律得出结论。并运用这个规律解决更多的实际问题。这不仅是一个主动学习的过程，更是发现学习、创新学习的过程。 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. (5)、建构数学模型应当以数学活动为主要形式。 由于数学思想方法不同于数学知识点，不是一个定义、概念就能代替的。有其活动形式和丰富的内涵。因此，应当在多种形式的数学活动中教授数学思想方法。 a 问题的生活实景——选择恰当的环境背景与相关材料引起讨论(以兴趣或认知不协调为选择标准)。 b 问题的合理诠释——选择适当的数学形式，重新进行表述(以引起关于主体的讨论)。 c 问题的充分解决——展示数学思想方法形成的心理活动过程，主要通过认知对象或问题解决来进行。 d 问题的数学模式——形成认知与思维的模式，使数学概念或模式游离于具体材料之外，进而促进学生数学观念(意识)的形成。 (6)、建构数学模型应当溶多种思维方式于一体。 概括—演示的方法，同类比较—抽象的方法，直观思维、形象思维、抽象思维、逻辑思维等都应当在数学教学中不断地出现，使得教学过程经历:直观化—准模型化—模型化的过程。 、构建数学模型的环节 5 它应是:具体的生活实景——分析——抽象——数学描述——模型的建立——思想方法的形成——问题解决(或认识形成)——观念(意识)形成——解决更多的实际问题。 6、构建数学模型的思维方法 学模型构造过程的本质是数学思维的活动，因此，讨论建立数学模型的方法，不能离开思维的方法。我们认为，分析与综合、比较与分类、抽象与概括、猜想与验证等既是思维的重要方法，同样是构建数学模型的重要方法。 (1)(分析与综合。 分析与综合是重要的思维方式，同样是重要的数学方法，是学习数学过程中建立数学模型的重要途径之一。应用题教学中用“分析法”与“综合法”来分析数量关系，寻求解答方法的过程，就是用这种思维方式来建立一个具有典型意义的数学模型的过程。分析是对所获得的数学材料或数学问题的构成要素进行研究，把握各要素在整体中的作用，找出其内在的联系与规律，从而得出有关要素的一般化的结论的思维方式。事实上，Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 不少学生在掌握某些数学知识或方法的时候，常常表现为一种点式的、孤立的记忆，或者只感知了某些知识之间的浅层的联系，而缺乏对他们之间的内在本质联系的把握，即缺乏一种建构意义上的链式结构，因而，其头脑中的认知结构是很不合理的，很不完善的，这样的认知结构不具有模型的价值，即不能有效地促成一些较复杂的问题的解决。如果运用分析法深人研究，以上的认知结构就可以真正建立为有价值的模型。 综合是将对数学材料、数学问题的分析结果和各要素的属性进行整合;以形成对该对象的本质同性的总体认识的思维方法。因而,分析与综合相结合，在建立起具有本质特征和方法论意义的数学模型上具有重要的意义。 (2)(比较与分类。 比较是对有关的数学知识或数学材料，辨别它们的共同点与不同点。数学中的比较是多方面的，包括多少与大小的比较，相同与不同的比较，结构与关系的比较，定律与性质的比较等。比较的目的是认识事物的联系与区别，明确彼此之间存在的同一性与相似性，以便揭示其背后的共同模型。分类是在比较的基础上，按照事物间性质的异同，将具有相同性质的对象归入一类;不同性质的对象归入另一类的思维方法。因此，比较与分类常常是联系在一起的，在建立数学模型的诸多思维方法中，比较与分类有着重要的作用，它往往是抽象概括、合情推理的前提，而正确地进行比较与分类的基础是仔细、深入地观察。 3(抽象与概括。 在数学学习过程中，抽象与概括是数学能力的核心要素之一，是形成概念、得出规律的关键性手段，因而，也是建立数学模型最为重要的思维方法。抽象是从许多数学事实或数学现象中，舍去个别的、非本质的属性，而抽出共同的本质的属性。在数学中表现为抽取数量之间、空间形体之间的关系和形式。而概括则是把抽象出来的事物间的共同特征，归结出来，它以抽象为基础，是抽象过程的进一步发展。 4(猜想与验证。 猜想是对研究的数学对象或数学问题进行观察。实验、比较、归纳等一系列的思维活动，依据已有的材料或知识经验，做出符合一定规律或事实的推测性想象。猜想是一种带有一定直觉性的比较高级的思维方式，对于探索或发现性学习来说，猜想是一种重要的思维方法。“在你证明一个数学定理之前，你必须猜想到这个定理，在你搞清楚证明细节之前，你必须猜出证明的主导思想。” Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 关于“构建小学数学模型”的理论资料剪辑 博兴县第一小学宋春京2011年11月17日 20:42浏览:21评论:1 省专家 徐大有于11-11-20 21:43推荐无推荐理由～ 关于“构建小学数学模型”的理论资料剪辑 1、什么是数学模型 所谓数学模型指的是对数学知识进行简化和提炼、再通过数学语言、符号或图形等形式对其进行概括与归纳、描述、反映特定的问题或具体事物之间关系的数学结构。 2、小学数学中的数学模型主要指什么, 小学数学中的数学模型，主要指数学概念、法则、公式、性质、数量间的关系等，大多可以在现实生活中找到它们的足迹。 3、对建构数学模型的认识 数学模型是建立在数学一般的基础知识与应用数学知识之间的一座重要的桥梁，建立数学模型的过程，就是指从数学的角度发现问题、展开思考，通过新旧知识间的转化过程，归结为一类已经解决或较易解决的问题中去，再综合运用已有的数学知识与技能解决这一类问题。这是在平时的数学教学中教师应该着重培养学生所具备的一种数学思想和方法。就是将数学理论知识应用于实际问题的思想和方法。 建立模型更为重要的是强调用真实的情景展示问题，营造解决问题的环境，以帮助学生在解决问题的过程中活化知识，变事实性知识为解决问题的工具。学生在探索、获得数学模型的过程中，也同时获得了建构数学模型、解决实际问题的思想与方法，而这对学生的发展来说，其意义远大于仅仅获得某些数学知识。 4、 建构数学模型的方法 (1)、 建立数学模型应该上学生大胆的去猜想，再在直观的事例中进行具体地分析。 猜想是一种带有一定直觉性的比较高级的思维方式，对于探索或发现性学习来说，猜想是一种非常重要的思维方法。 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. (2)、建构数学模型应该让学生在许多直观或贴近生活的实例中进行有效地综合比较。 综合是指学生在学习的过程中将数学现象、数学实例的分析情况进行整理组合，从而形成对这一类数学知识的总体认识。比较是对有关的数学现象、数学实例，区别它们的相同之处和不同之处。数学中的比较是多方面的，包括多少与大小的比较，相同与不同的比较，结构与关系的比较，定律与性质的比较等。比较的目的是认识事物的联系与区别，明确彼此之间存在的同一性与相似性，一边解释其背后的共同模型。 (3)、建构数学模型应该让学生从具体的实例中抽象出它们所具有的共性，再用数学的语言或符号等进行概括。 抽象是从许多数学实例或数学现象中，发现其共同的本质特点。而概括则是把抽象出来的共同点用数学的语言或符号等形式进行归纳和总结。 (4)、建构数学模型一定要让学生进行充分地验证，得出结论之后再进行有效的应用。 学生在初步得出结论时要给于足够的空间让学生进行充分地验证，在验证的过程中可能会发现新的现象，并在解决新问题的过程中，进一步完善自己的猜想，最终发现规律得出结论。并运用这个规律解决更多的实际问题。这不仅是一个主动学习的过程，更是发现学习、创新学习的过程。 (5)、建构数学模型应当以数学活动为主要形式。 由于数学思想方法不同于数学知识点，不是一个定义、概念就能代替的。有其活动形式和丰富的内涵。因此，应当在多种形式的数学活动中教授数学思想方法。 a 问题的生活实景——选择恰当的环境背景与相关材料引起讨论(以兴趣或认知不协调为选择标准)。 b 问题的合理诠释——选择适当的数学形式，重新进行表述(以引起关于主体的讨论)。 c 问题的充分解决——展示数学思想方法形成的心理活动过程，主要通过认知对象或问题解决来进行。 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. d 问题的数学模式——形成认知与思维的模式，使数学概念或模式游离于具体材料之外，进而促进学生数学观念(意识)的形成。 (6)、建构数学模型应当溶多种思维方式于一体。 概括—演示的方法，同类比较—抽象的方法，直观思维、形象思维、抽象思维、逻辑思维等都应当在数学教学中不断地出现，使得教学过程经历:直观化—准模型化—模型化的过程。 5、构建数学模型的环节 它应是:具体的生活实景——分析——抽象——数学描述——模型的建立——思想方法的形成——问题解决(或认识形成)——观念(意识)形成——解决更多的实际问题。 6、构建数学模型的思维方法 学模型构造过程的本质是数学思维的活动，因此，讨论建立数学模型的方法，不能离开思维的方法。我们认为，分析与综合、比较与分类、抽象与概括、猜想与验证等既是思维的重要方法，同样是构建数学模型的重要方法。 (1)(分析与综合。 分析与综合是重要的思维方式，同样是重要的数学方法，是学习数学过程中建立数学模型的重要途径之一。应用题教学中用“分析法”与“综合法”来分析数量关系，寻求解答方法的过程，就是用这种思维方式来建立一个具有典型意义的数学模型的过程。分析是对所获得的数学材料或数学问题的构成要素进行研究，把握各要素在整体中的作用，找出其内在的联系与规律，从而得出有关要素的一般化的结论的思维方式。事实上，不少学生在掌握某些数学知识或方法的时候，常常表现为一种点式的、孤立的记忆，或者只感知了某些知识之间的浅层的联系，而缺乏对他们之间的内在本质联系的把握，即缺乏一种建构意义上的链式结构，因而，其头脑中的认知结构是很不合理的，很不完善的，这样的认知结构不具有模型的价值，即不能有效地促成一些较复杂的问题的解决。如果运用分析法深人研究，以上的认知结构就可以真正建立为有价值的模型。 综合是将对数学材料、数学问题的分析结果和各要素的属性进行整合;以形成对该对象的本质同性的总体认识的思维方法。因而,分析与综合相结合，在建立起具有本质特征和方法论意义的数学模型上具有重要的意义。 (2)(比较与分类。 Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation. 比较是对有关的数学知识或数学材料，辨别它们的共同点与不同点。数学中的比较是多方面的，包括多少与大小的比较，相同与不同的比较，结构与关系的比较，定律与性质的比较等。比较的目的是认识事物的联系与区别，明确彼此之间存在的同一性与相似性，以便揭示其背后的共同模型。分类是在比较的基础上，按照事物间性质的异同，将具有相同性质的对象归入一类;不同性质的对象归入另一类的思维方法。因此，比较与分类常常是联系在一起的，在建立数学模型的诸多思维方法中，比较与分类有着重要的作用，它往往是抽象概括、合情推理的前提，而正确地进行比较与分类的基础是仔细、深入地观察。 3(抽象与概括。 在数学学习过程中，抽象与概括是数学能力的核心要素之一，是形成概念、得出规律的关键性手段，因而，也是建立数学模型最为重要的思维方法。抽象是从许多数学事实或数学现象中，舍去个别的、非本质的属性，而抽出共同的本质的属性。在数学中表现为抽取数量之间、空间形体之间的关系和形式。而概括则是把抽象出来的事物间的共同特征，归结出来，它以抽象为基础，是抽象过程的进一步发展。 4(猜想与验证。 猜想是对研究的数学对象或数学问题进行观察。实验、比较、归纳等一系列的思维活动，依据已有的材料或知识经验，做出符合一定规律或事实的推测性想象。猜想是一种带有一定直觉性的比较高级的思维方式，对于探索或发现性学习来说，猜想是一种重要的思维方法。“在你证明一个数学定理之前，你必须猜想到这个定理，在你搞清楚证明细节之前，你必须猜出证明的主导思想。” Shang, and action Shang with to XI comrade for General Secretary of Central keep height consistent; any when are put discipline rules is in front, enhanced organization concept, and obey Organization decided; to set right of worldview, and Outlook on life And to lead a clean slim family, always adhere to the Communists ' spiritual home; to consciously practice the party's purpose, keeping qualities. CPC requirements in section-level cadres above to be a benchmark, play an exemplary role, "adhere to the loyal clean play, Jiao Yulu-a good cadre of" activities carried out in the ordinary party members "practicing pioneer standard post set up" activities. We all party members to further enhance political par core, situation awareness, awareness, awareness, belief and faith, according to positions, downtown River regulation, diversion of hydraulic Process, protection of the mother River, rural safety water drinking project, construction of flood control and drought relief, water in ecological civilization construction and other key, think, often, more active, hands-on, disciplined and strict rules, play, courage, give full play to the exemplary role, the successful completion of tasks. Three "reform" as the core of real change, completely change, and change image. This fundamental aim of education in order to solve the problem, for this reason, we insist on problem-oriented, enhance the awareness of problems, problems of reform in place, continuous improvement in style, to better serve the people, to better promote the water conservancy work. First of all, to find the problem. I'm learning education programme, in view of the current construction of the party, proposed to focus on solution of fuzzy ideals and beliefs waver, consciousness, purpose of the party weak sense, honesty and self-discipline awareness is not strong, depressed, six issues of ethical misconduct. Vast numbers of party members and cadres should closely real life personal and ideological work, reflections on the standard control, check the pendulum problem, pinpoint problems, get real, deep, identification, find the main "target", laying the Foundation for further corrective action implementation.