浅谈小学生数感培养几点思考

来源:软件水平 发布时间:2020-08-20 点击:

  浅谈小学生数感培养的几点思考

  浅谈小学生数感培养的几点思考

  浅谈小学生数感培养的几点思考

 【内容提要】:数感是一种主动地、自觉地理解和运用数的态度和意识,是人的一种基本数学素养。如何培养小学生具有良好的数感?本文从生活实践、自主探索、动手操作、不断估算和实际运用等五个方面来进行阐述,力求让学生的数学能力、数学素养得以发展和提高,让学生终生受益。

 【关键词】:数感;培养方法;实践运用

 数学课堂教学中,常常会看到学生出现这样的作业:小明的身高125(米),一个苹果140(千克),绕操场跑一圈要1(小时),一瓶矿泉水500(升)等等。看到这样的作业,很多教师会有点哭笑不得。但作为数学老师,我们就应该去思考:为什么学生对于数量单位,也就是数的大小感觉会这么差?是学生本身的问题,还是教学问题呢?笔者认为,主要原因是学生在平时的学习和生活中缺少了“数感”的培养,故而导致数量单位使用的混淆,出现令人啼笑皆非的答案。

 那什么是“数感”呢?在《数学课程标准》中介绍:“数感主要表现在理解数的意义;能用多种方法来表示数;能在具体的情境中把握数的相对大小关系;能用数来表达和交流信息;能为解决问题而选择适当的算法;能估计运算结果,并对结果的合理性做出解释。”简单来说就是人对数学的感觉,感知它的“大小”“多少”等。学会“数学地”思考,一个人有了“数感”,才能将数与实际生活联系起来,用数学的方式思考问题。

 如何培养学生良好的数感,是一个值得我们每一个数学老师必须思考的问题。下面就结合笔者教学过程中的一些体会,谈一谈对小学生数感培养的几点思考。

 一、从日常生活出发,体会数感

 儿童学习数学往往是从数数开始的,学生的生活经历中到处充满着与数相关的活动,培养学生的数感就是让学生感知周围的世界有着数量化的意味。因此,在“数”概念的教学中,应该注意引导学生数一数、说一说自己身边的“数”。因此,教师要创设有助于学生理解数学的教学情境,让学生切身体会数感、积累数感。

 在平时的教学过程中,教师可以引导学生联系自己身边具体的、有趣的事物,通过主动地观察分析生活现象,用数来表示身边的事物。比如,在低年级中可以让学生数一数:铅笔盒里有几样文具?每样文具各有几个?请学生想一想:家中的门牌号,妈妈和爸爸的电话号码、手机号、生日、车牌号等;说一说学生身边看得见的数。

 例如,在教学“0”时,先启发学生说一说在日常生活中哪些地方见过“0”。这时学生的积极性一下子就高涨起来“在门牌号上见过”、“爸爸妈妈手机上”、“尺子上”、“温度计上”……在大家的交流中,学生直观体会到“0”除了表示没有外,还可以在尺子上表示开始,也可以在日历、车牌上与其它数字组成号码。这些都是学生身边的事,很容易理解和接受。学生在丰富多彩的活动中感受数的意义,在现实生活中建立数感。

 二、从自主探索出发,体验数感

 《标准》明确提出要使学生“经历用数学符号和图形描述现实世界的过程,建立数感和符号感,发展抽象思维”。著名数学家波利亚说过:“学习任何知识的最佳途径是自己去发现,因为这种发现理解最深,也最容易掌握其中内在的规律、性质和联系。”

 如教学《长方形、正方形面积计算》时,我先让学生猜一猜,长方形的面积会跟什么有关,数学猜想实际上是一种数学想象,是人的思维在探索数学规律、本质时的一种策略,数学猜想能锻炼数学思维,也能培养学生的数感。再让学生小组合作拿出准备好的12个面积是1平方厘米的小正方形摆出不同的长方形,并且共同讨论所摆长方形的长跟每排所摆的小正方形的个数有什么关系?长方形的宽跟摆的排数有什么关系?长方形的长、宽跟它的面积有什么关系?这样学生经过了猜想、探索、验证,经历了知识的发现、发生过程,经历了数学思维逐渐形成的过程。学生在生动活泼、动手动脑的学习过程中,解决问题的策略和数感正在逐渐生成。

 又如,在教学算除数是两位数除法时,老师可以让学生先探索试商,学生在自主研究的过程中,经历了估算、猜想、试商、调商,再试商、调商,最后得到正确答案的过程。让学生在自我探索的过程中经历了知识发现的过程,有助于学生良好数感的形成。

 三、从实践活动出发,增强数感

 富兰克林说过:“告诉我,我会忘记;教给我,我可能记住;让我参与,我才能学会”。苏霍姆林斯基也曾说过:“智慧之花开在指尖上。”实践证明,学生在动手操作时,眼、耳、口、手相结合,多种感官参与学习,有助于学生正确、全面、深刻地感知数、认识数。通过实践操作,使学生动手做数学、用数学,而不是听数学、记数学。

 (一)动手操作,巧解难题

 在教学《分数的初步认识》时,教师在引导学生理解了一个月饼的二分之一后,让学生挑选自己喜欢的图形(长方形、正方形、圆形、正三角形)表示出二分之一。学生通过折一折、涂一涂、说一说,从而认识到虽然形状不同、折法不同,但只要把这个图形平均分成了两份,取其中的一份,都可以用二分之一来表示。学生在自己动手的基础上真正理解了二分之一的意义。接着,让学生在一个图形上表示出自己喜欢的几分之一,然后进行比较,学生在折、涂、比、说的实际操作过程中正确把握了分数的大小,建立了数感。

 (二)动手实验,破解新知

 小学的数学教学中有很多单位的教学,如果单纯讲解名词术语、抽象方法,而脱离事物,具体形象和感知,就很难让学生理解,更谈不上知识的掌握。所以教师可以让学生亲自动手实验。

 例如:到操场上去走走、跑跑、测测、量量,让学生感受50米、100米、400米的距离,在春游、秋游过程中感受1千米、20千米的路程;到食堂去看看、称称、掂掂各种蔬菜、水果的重量,感受100克、1千克、10千克的实际重量等等。在教学体积单位时让学生动手做一做1立方厘米和1立方分米和1立方米的框架模型,并试验1立方米的空间大概可以容纳多少个同学,1立方厘米大概可以装多少滴水等。最后让他们选定一个合适的参照物作为参考标准,如:1立方厘米大概是手指头占的空间、1立方分米大概是粉笔盒所占的空间、1立方米大概是水池占的空间。这些活动深受学生的喜爱,不仅可以获得数感的启蒙,还能培养学生的“亲数学”行为,对数学学习充满乐趣。

 四、从估算体验出发,发展数感

 《数学课程标准》在“课程实施意见”中指出:“估算在日常生活与数学学习中有着十分广泛的应用,培养学生的估算意识,发展学生的估算能力,让学生拥有良好的数感,具有重要的价值。”可见,估算在对学生数感的培养起着重要的作用。

 生活中很多时候都要用到估算,而不需要精确计算。新课标也指出估算相对于精确计算在日常生活中有着更广泛的实际应用,更是发展学生数感的有效途径之一。因此,我们在教学中要善于抓住各种有利时机,改变学生对估算的认识,创造性地活用教材,让学生常估算,多交流,从而感受估算魅力,增强估算意识,形成较强的量化能力,逐渐养成良好的估算习惯,从而发展学生的数感。

 如:“小皮球每个9元,幼儿园一个班有32人,每人买一个大约需要多少钱?”在估算过程中,有的学生认为:“10×30=300,估计在300元左右。”有的学生认为:“10×32=320,不到320元。”有的学生可能说:“9×30=270,肯定比270元多。”对于这些方法,教师都应该加以鼓励,并为他们提供合作交流的机会,让他们在相互交流中,比较各种算法的特点,不断完善自己的估算方法,教师要经常训练学生正确地运用估计、大约、略小于、远大于、接近于等术语,来促进学生对数的感觉,逐渐使学生养成良好的估算习惯,并能将这种习惯内化为一种自觉、自主的意识,使学生在不断的估算中发展自己的数感。

 五、从实际运用出发,升华数感

 数学的教学目的是让学生掌握数学知识,理解数学知识,以及懂得运用数学知识。而数感就是学生在掌握数学知识和理解数学知识基础上最好的产物。所以为了培养学生的数感,有必要给学生搭造一个运用知识的平台,让数感的培养得到进一步的巩固。

 (一)设计综合练习

 结合学生生活实际设计出以下练习题:

  这些综合题目的设计有利于学生达到训练和培养数学感觉的目的。

 (二)设计猜数游戏

 在小学生的数学学习中,教师可以设计一些学生喜欢的游戏进行教学,例如“猜数”游戏就深受学生喜爱,而且对数感的形成有着不可低估的作用。在教学比较100以内数的大小后,教师设计了这样一个环节:老师心里想好了一个数,它在0--100之间,请你来猜?学生的兴趣一下子就来了,争先恐后地说起来。这时一个学生起来回答:“10”。老师提示:“比10大得多。”又一个学生起来回答:“98”老师再一次提示学生再猜。就在这样的反复提示猜想中,学生准确猜中了老师心目中想好的那个数。如此猜数游戏,既锻炼了学生在结合具体的情境中把握数的大小的比较的本领,还能学到一种解决问题的有效策略。这类游戏也可以在学生之间进行,这样的游戏不仅让学生觉得数学学习是充满乐趣的,又对培养学生良好的数感具有十分重要的作用。

 (三)设计实践性题目

 江苏特级教师魏洁说过:设计一些具有综合性、趣味性和挑战性的活动,不仅可以体现数学的本质,更有助于提高学生的数学素养。那么在学生数感培养方面,我们也可以设计一些可操作性的活动,例如:

 1.估计高度

 让学生估计学校教学楼的高度是多少?自己住的楼房有多高?它们的高度分别相当于几个自己的身高?或相当于多少个学生手拉手的长度?还可以用哪些你熟悉的事例来描述这些高度?

 2.请你调查

 同学们,你们天天在上学,但你是否知道:从你家到学校的路程大约有多远?你步行(或骑车、乘车)上学通常要多少时间?请估算你步行(或骑车)的速度。

 总之,数感的形成不是通过一个单元或一个学期的教学就能完成的,它是一个潜移默化、循序渐进的过程,需要用较长时间逐步培养。作为教师必须在实际教学中根据不同的教学内容,利用不同的教学手段,创设不同的教学情景,探索不同教学方法,让学生在每一节课中,每一个内容中都可以形成良好的数感,达到提升数学素养的目的。

 

 Plenary Session of the 15th CPC Central Committee, two session of the five plenary meeting spirit, fully implement the Scientific Outlook on Development based XX youth career development planning in accordance with the" 11th Five-Year "," building a first-class team, with first-class team. First-class performance, the overall requirements of first-class image of the tree ", focusing on" human services, standardized management, work fine, first-class achievements ", give full play to staff assistant, supervision and inspection, comprehensive coordination, service guarantee, focus on the global and group work of the Communist Youth League in the city Municipal Party Central work, and strive to improve the decision-making ability, comprehensive coordination ability, writing ability, supervision ability, logistics ability, innovation ability, continuously consolidate and maintain the education on Party members'advancement activities and enhance awareness of the Communist Youth League education achievements, and vigorously promote the construction of civilization advanced units, units and staff home building activities, balanced, focused, pragmatic, innovation, high standard, high quality, high level, high efficiency to complete various tasks throughout the year.First, pay close attention to research information, efforts to improve decision-making servicesIn accordance with the "information reflect the information, promote the work of information leading work" requirements, adhere to grasp the team construction, mechanism construction and quantitative assessment, give full play to the assistant role of leadership, actively promote the innovation of research information development, and vigorously promote the research work of information to mention upgrading, efforts to improve the ability and level of decision-making.(a) adhere to the decision in the first place. To make the decision service as the focus of the work, participate in the point, and in the key place, in order to promote the democratization of decision-making, scientific advice. Based on the city's youth career "11th Five-Year" good bureau and the Communist Youth League work across the development, focus on the implementation of Scientific Outlook on Development theory and practice subject adolescents and youth work process of building a socialist harmonious society, pay close attention to the global, strategic, forward-looking major problems, grasp the overall situation, pay attention to plan and implement the specific tasks assigned by the leadership from the overall situation, think ahead on major issues concerning the overall situation, in-depth Study, grasp the dynamic, put forward suggestions, reflect in time.(two) adhere to the investigation. As an important way to firmly grasp the important link of scientific and democratic decision-making, focus on key leadership concern, concern and hot points of youth practice work, adhere to the practice to investigate and research, fully and accurately grasp the actual situation, for the leadership decision-making comes from practice, practical to provide first-hand information. To enhance the initiative, according to municipal Party committee leadership activities, week activities, in the "research" make great efforts to provide more targeted for leadership, predictability and effectiveness of comments and suggestions.(three) adhere to the information planning as an important means of expanding. The sources of information, through the network, the media and other channels, increase integration efforts the work of the Communist Youth League and youth information dynamic information resources, increase the information planning efforts to refine the Communist Youth League, and give full play to the role of information reference, to improve the quality of information as a fundamental, outstanding information work sensitivity and timeliness, timely, accurately, comprehensively reflect the municipal Party committee, municipal government, the Central Committee of the implementation of a major deployment, leadership attention, hot and difficult issues of concern to the masses and some important emergencies, timely provide all kinds of deep and valuable component of the following information. Continue to deepen the information research and information feedback system, information report system, information reporting system, information delivery system and information notification system, and constantly improve the information work of the assessment, incentive mechanism, improve the long-term mechanism to improve the information work of sustainable development.Two, pay close attention to contact and communication, efforts to improve the ability of comprehensive coordinationGive full play to a contact, pivotal role, coordination of the parties in accordance with the standard, efficient, high quality principles, firmly establish the principle of service, and effectively improve the level of policy theory, grasp the method of coordinating work, conscientiously do service leadership, service and Service Corps cadres.(a) do to actively carry out coordination. 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Further increase communication efforts, strengthen the organizations at various levels to guide the work of the office and communication, to ensure the situation, reported lower levels of strength, and strive to the grassroots, inspired by the basic spirit of innovation, the formation of good ability of the league office work.Three, pay close attention to the quality of official documents, efforts to improve the ability to deal with textAdhere to high standards, strict requirements, careful attention to the drafting of the draft work, strict document drafting, audit clearance, proof reading and quality control, and strive to improve the ability to deal with the text, and the overall work of the service center.(a) earnestly. 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Further the implementation of electronic document processing mode, the full implementation of OA office system, efforts to improve the work efficiency.Four, pay close attention to the work of supervision, efforts to improve the executive abilityThe city's major issues and focus on the overall work of the Communist Youth League to carry out supervision and inspection, insist on the idea, the handling of the key, efforts to promote the implementation of decisions, to ensure that government decrees.(a) on the center of focus on supervision. In accordance with the "grasp the overall situation, focused, practical, quantitative refinement" principle, conscientiously fulfill the supervision function, focusing on the important deployment, major decisions of the party will, secretary's office, department heads meeting agreed matters assigned by the leadership group, the book down and do the important matters and the regiment the key work to focus on supervision, to ensure that the inspection item piece is an echo, everything in the bag, to promote the work carried out smoothly.(two) grasp the key special supervision. According to different periods of work needs, focus on leadership, social concern, hot and difficult problem of youth reflects the implementation of regular and dynamic supervision of special work assigned by the leadership of the special work of tracking supervision, regularly held the Department responsible for the regular inspection work carried out inspection stage. 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Adhere to the financial reporting system, improve the efficiency in the use of assets, and the Communist Youth League work continued to develop.(four) to further strengthen security work earnestly. Confidentiality of confidential confidential documents, strict implementation of the management system, security system, focus on the secret of the computer and network security management, strict management measures. Actively carry out regular security education, provided security awareness high cadres of workers, to prevent the loss occurred leak phenomenon. To strengthen the archives management work, conscientiously implement the archives, seal management system, actively carry out the relevant documents, materials, letters and pictures materials collection, registration and filing. The strict safety responsibility system, strictly holidays and night security duty system, strengthen the major work Moving safety work, to ensure safe and orderly.(five) to further strengthen the daily service work. To firmly establish the "rules as standard" point of view, whether do the text, do, act, or on duty, reception, security in strict accordance with the rules, according to the procedures, to ensure standardized operation. Take care of cadres of workers life, seriously deal with the party to do things for the project for the masses and actively improve the cadres of workers welfare. Strict management of vehicles, official vehicles. To ensure the implementation of office smile service system and first asked the first joint service system, the implementation of service complaints system, ensure the quality of service continues to increase.Six, pay close attention to team building, focus on improving the ability to open up innovationIn accordance with the "build a first-class team, with first-class team, a first-class performance, tree class image," the overall requirements, and vigorously strengthen the construction of cadres and workers, and promote the healthy growth of cadres and workers and all-round development.(a) establish the right work ethic. Firmly establish the concept of office work, have a brilliant future, strengthen the sense of innovation, enhance innovation and courage, to free from old ideas, actively respond to the development requirements of the new situation, actively adapt to the new leadership strictly from the high requirements, innovation and breakthrough, promote office work the steps in innovation.(two) to strengthen the ideological and political construction. Continue to consolidate communist education on Party members'advancement activities and enhance awareness of the Communist Youth League education achievements, serious ideological and political work of office staff, carry out the "dedication in the post work, first-class theme contest activities, and guide the cadres and workers to firmly establish a correct outlook on life. And values, the firm high political consciousness, firm political position, strict political discipline, strengthen the cadres and workers of political awareness, overall awareness, sense of service, efforts to form a diligent, efficient, innovative,Rigorous working atmosphere.(three) to carry out the policy theory of learning. To improve the office of cadres and workers pay close attention to the quality of training and learning, strengthen business knowledge and comprehensive

 Plenary Session of the 15th CPC Central Committee, two session of the five plenary meeting spirit, fully implement the Scientific Outlook on Development based XX youth career development planning in accordance with the" 11th Five-Year "," building a first-class team, with first-class team. First-class performance, the overall requirements of first-class image of the tree ", focusing on" human services, standardized management, work fine, first-class achievements ", give full play to staff assistant, supervision and inspection, comprehensive coordination, service guarantee, focus on the global and group work of the Communist Youth League in the city Municipal Party Central work, and strive to improve the decision-making ability, comprehensive coordination ability, writing ability, supervision ability, logistics ability, innovation ability, continuously consolidate and maintain the education on Party members'advancement activities and enhance awareness of the Communist Youth League education achievements, and vigorously promote the construction of civilization advanced units, units and staff home building activities, balanced, focused, pragmatic, innovation, high standard, high quality, high level, high efficiency to complete various tasks throughout the year.First, pay close attention to research information, efforts to improve decision-making servicesIn accordance with the "information reflect the information, promote the work of information leading work" requirements, adhere to grasp the team construction, mechanism construction and quantitative assessment, give full play to the assistant role of leadership, actively promote the innovation of research information development, and vigorously promote the research work of information to mention upgrading, efforts to improve the ability and level of decision-making.(a) adhere to the decision in the first place. To make the decision service as the focus of the work, participate in the point, and in the key place, in order to promote the democratization of decision-making, scientific advice. Based on the city's youth career "11th Five-Year" good bureau and the Communist Youth League work across the development, focus on the implementation of Scientific Outlook on Development theory and practice subject adolescents and youth work process of building a socialist harmonious society, pay close attention to the global, strategic, forward-looking major problems, grasp the overall situation, pay attention to plan and implement the specific tasks assigned by the leadership from the overall situation, think ahead on major issues concerning the overall situation, in-depth Study, grasp the dynamic, put forward suggestions, reflect in time.(two) adhere to the investigation. As an important way to firmly grasp the important link of scientific and democratic decision-making, focus on key leadership concern, concern and hot points of youth practice work, adhere to the practice to investigate and research, fully and accurately grasp the actual situation, for the leadership decision-making comes from practice, practical to provide first-hand information. To enhance the initiative, according to municipal Party committee leadership activities, week activities, in the "research" make great efforts to provide more targeted for leadership, predictability and effectiveness of comments and suggestions.(three) adhere to the information planning as an important means of expanding. The sources of information, through the network, the media and other channels, increase integration efforts the work of the Communist Youth League and youth information dynamic information resources, increase the information planning efforts to refine the Communist Youth League, and give full play to the role of information reference, to improve the quality of information as a fundamental, outstanding information work sensitivity and timeliness, timely, accurately, comprehensively reflect the municipal Party committee, municipal government, the Central Committee of the implementation of a major deployment, leadership attention, hot and difficult issues of concern to the masses and some important emergencies, timely provide all kinds of deep and valuable component of the following information. Continue to deepen the information research and information feedback system, information report system, information reporting system, information delivery system and information notification system, and constantly improve the information work of the assessment, incentive mechanism, improve the long-term mechanism to improve the information work of sustainable development.Two, pay close attention to contact and communication, efforts to improve the ability of comprehensive coordinationGive full play to a contact, pivotal role, coordination of the parties in accordance with the standard, efficient, high quality principles, firmly establish the principle of service, and effectively improve the level of policy theory, grasp the method of coordinating work, conscientiously do service leadership, service and Service Corps cadres.(a) do to actively carry out coordination. Upstream municipal Party committee, municipal government work report, and the central mission to understand, grasp the key ideas and working organs, targeted focus on reporting the work of mission, to focus on the city's superior league, major activities, attention, support and help.(two) do parallel coordination. To strengthen the contact and communication with the municipal departments, actively seek for the work of care, support, optimize the external environment. To strengthen the group work of the Communist Youth League and other provinces and cities, to grasp the work around the dynamic, active learning around the work experience, the effective integration of resources within the group, and the Communist Youth League career development.(three) earnestly grassroots coordination. Further increase communication efforts, strengthen the organizations at various levels to guide the work of the office and communication, to ensure the situation, reported lower levels of strength, and strive to the grassroots, inspired by the basic spirit of innovation, the formation of good ability of the league office work.Three, pay close attention to the quality of official documents, efforts to improve the ability to deal with textAdhere to high standards, strict requirements, careful attention to the drafting of the draft work, strict document drafting, audit clearance, proof reading and quality control, and strive to improve the ability to deal with the text, and the overall work of the service center.(a) earnestly. To further establish the draft document presentation system research, adhere to the practice, especially the drafting of important days and months multiplying, concentrating on the presentation of the research, understand the situation the situation, fully understand the intention of the leadership, to ensure the output, quality, and constantly improve the quality of manuscript. A manuscript quality appraisal system, the implementation of quantitative assessment, each quarter the comparison of office draft manuscript quality. Establish a reward system to reward the outstanding manuscript selection out, the wrong investigated persons responsible for the major errors.(two) strict master document quality. Strengthening document quality awareness, efforts in the drafting of documents, audit checks, printed all aspects of efforts, strict policy documents audit, content, format and procedures, adhere to the upper and lower check, and check before and after the check, ensure the document style format in the understanding of leadership intentions in place, ideas in the language in place, and strive to improve the quality of various documents.(three) a comprehensive specification document operation. To further standardize the document transfer procedures, emphasizing the precision in document processing, in strict accordance with the operating procedures document sign, registration, approval, distribution, handling, repaying, filing, ensure the document processing standard, accurate, and efficient. Especially to strict dispatch, strict audit document content. Strictly implement the document procedures step by step Shenqian, strict and unified file format, to ensure the normative document. Further the implementation of electronic document processing mode, the full implementation of OA office system, efforts to improve the work efficiency.Four, pay close attention to the work of supervision, efforts to improve the executive abilityThe city's major issues and focus on the overall work of the Communist Youth League to carry out supervision and inspection, insist on the idea, the handling of the key, efforts to promote the implementation of decisions, to ensure that government decrees.(a) on the center of focus on supervision. In accordance with the "grasp the overall situation, focused, practical, quantitative refinement" principle, conscientiously fulfill the supervision function, focusing on the important deployment, major decisions of the party will, secretary's office, department heads meeting agreed matters assigned by the leadership group, the book down and do the important matters and the regiment the key work to focus on supervision, to ensure that the inspection item piece is an echo, everything in the bag, to promote the work carried out smoothly.(two) grasp the key special supervision. According to different periods of work needs, focus on leadership, social concern, hot and difficult problem of youth reflects the implementation of regular and dynamic supervision of special work assigned by the leade

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