华琴的博客
    我已出发,向着梦的那方
频道栏目

查询

标题 作者


最新图库
暂未添加该信息。

博客统计
  • 今日数:0
  • 文章数:580
  • 收藏数:0
  • 图片数:0
  • 评论数:562
  • 开设时间:2009-10-29
  • 更新时间:2018-9-5

  • 最新链接
    暂未添加该信息。


    订阅本站的 RSS 2.0 新闻组


    华琴主页 >> 文章 >> 读书频道 >> 浏览信息《小学数学思想方法的梳理(一)》

    读书频道 | 评论(1) | 阅读(1774)
    查看详细访友列表 访友脚印

    星期四   晴天 
    主题 小学数学思想方法的梳理(一)

    小学数学思想方法的梳理(一)
    ----符号化思想

     

    1. 符号化思想的概念。

     

    数学符号是数学的语言,数学世界是一个符号化的世界,数学作为人们进行表示、计算、推理和解决问题的工具,符号起到了非常重要的作用;因为数学有了符号,才使得数学具有简明、抽象、清晰、准确等特点,同时也促进了数学的普及和发展;国际通用的数学符号的使用,使数学成为国际化的语言。符号化思想是一般化的思想方法,具有普遍的意义。

     

    2. 如何理解符号化思想。

     

    数学课程标准比较重视培养学生的符号意识,并提出了几点要求。那么,在小学阶段,如何理解这一重要思想呢?下面结合案例做简要解析。

     

    第一,能从具体情境中抽象出数量关系和变化规律,并用符号表示。这是一个从具体到抽象、从特殊到一般的探索和归纳的过程。如通过几组具体的两个数相加,交换加数的位置和不变,归纳出加法交换律,并用符号表示:a+b=b+a。再如在长方形上拼摆单位面积的小正方形,探索并归纳出长方形的面积公式,并用符号表示:Sab。这是一个符号化的过程,同时也是一个模型化的过程。

     

    第二,理解符号所代表的数量关系和变化规律。这是一个从一般到特殊、从理论到实践的过程。包括用关系式、表格和图象等表示情境中数量间的关系。如假设一个正方形的边长是a,那么4a就表示该正方形的周长,a2表示该正方形的面积。这同样是一个符号化的过程,同时也是一个解释和应用模型的过程。

     

    第三,会进行符号间的转换。数量间的关系一旦确定,便可以用数学符号表示出来,但数学符号不是唯一的,可以丰富多彩。如一辆汽车的行驶时速为定值80千米,那么该辆汽车行驶的路程和时间成正比,它们之间的数量关系既可以用表格的形式表示,也可以用公式s=80t表示,还可以用图象表示。即这些符号是可以相互转换的。

     

    第四,能选择适当的程序和方法解决用符号所表示的问题。这是指完成符号化后的下一步工作,就是进行数学的运算和推理。能够进行正确的运算和推理是非常重要的数学基本功,也是非常重要的数学能力。

     

    3. 符号化思想的具体应用。

     

    数学的发展虽然经历了几千年,但是数学符号的规范和统一却经历了比较慢长的过程。如我们现在通用的算术中的十进制计数符号数字0~9于公元8世纪在印度产生,经过了几百年才在全世界通用,从通用至今也不过几百年。代数在早期主要是以文字为主的演算,直到1617世纪韦达、笛卡尔和莱布尼兹等数学家逐步引进和完善了代数的符号体系。

     

    符号在小学数学中的应用如下表。

     

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
                

    知识领域            

     

                

                
                

    知识点            

     

                

                
                

    应用举例            

     

                

                
                

    应用拓展            

     

                

                
                

    数与代数            

     

                

                
                

    数的表示            

     

                

                
                

    阿拉伯数字:0~9            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    中文数字:一~            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    百分号:%            

     

                

                
                

    千分号:‰            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    用数轴表示数            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    数的运算            

     

                

                
                

    +、-、×、÷、( ) ﹝﹞﹛﹜2(平方)3(立方)            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    数的大小关系            

     

                

                
                

    =、≈、><            

     

                

                
                

    ≥、≤、≠            

     

                

                
                

                

     

                

                
                

    运算定律            

     

                

                
                

    加法交换律:a+b=b+a            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    加法结合律:a+b+c=a+(b+c)            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    乘法交换律:ab=ba            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    乘法结合律:(ab)c=a(bc)            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    乘法分配律a(b+c)=ab+ac            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    方程            

     

                

                
                

    ax+b=c            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    数量关系            

     

                

                
                

    时间、速度和路程:s=vt            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    数量、单价和总价:a=np            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    正比例关系:y/x=k            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    反比例关系:xy=k            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    用表格表示数量间的关系            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    用图象表示数量间的关系            

     

                

                
                

                

     

                

                
                

    空间与图形            

     

                

                
                

    用字母表示计量单位            

     

                

                
                

    长度单位:kmmdmcmmm            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    面积单位:km2m2dm2cm2mm2            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    质量单位:tkgg            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    用符号表示图形            

     

                

                
                

    用字母表示点:三角形ABC            

     

                

                

    用符号表示角:            

     

                

                

    1、∠2、∠3、∠4            

     

                

                
                

    ABC            

     

                

                

    线段AB            

     

                

                

    直线CD            

     

                

                

    直线 L            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    两线段平行:ABCD            

     

                

                

    两线段垂直:ABCD            

     

                

                
                

                                                                ABCD            

     

                

                
                

                

     

                

                
                

    用字母表示公式            

     

                

                
                

    三角形面积:S ab            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    平行四边形面积:Sah            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    梯形面积:S (a+b)h            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    圆周长:C2πr            

     

                

                

    圆面积:Sπr?            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    长方体体积:v=abc            

     

                

                

    正方体体积:v=a?            

     

                

                

    圆柱体积:v=sh            

     

                

                

    圆锥体积:v= sh            

     

                

                
                

                

     

                

                
                

    统计与概率            

     

                

                
                

    统计图和统计表            

     

                

                
                

    用统计图表描述和分析各种信息            

     

                

                
                

                

     

                

                
                

                

     

                

                
                

    可能性            

     

                

                
                

    用分数表示可能性的大小            

     

                

                
                

                

     

                

                

    4.符号化思想的教学。

     

    符号化思想作为数学最基本的思想之一,数学课程标准把培养学生的符号意识作为必学的内容,并提出了具体要求,足以证明它的重要性。教师在日常教学中要给予足够的重视,并落实到课堂教学目标中。要创设合适的情境,引导学生在探索中归纳和理解数学模型,并进行解释和应用。学生只有理解和掌握了数学符号的内涵和思想,才有可能利用它们进行正确的运算、推理和解决问题。

     

    数学符号是人们在研究现实世界的数量关系和空间形式的过程中产生的,它来源于生活,但并不是生活中真实的物质存在,而是一种抽象概括。如数字1,它可以表示现实生活中任何数量是一个的物体的个数,是一种高度的抽象概括,具有一定的抽象性。一个数学符号一旦产生并被广泛应用,它就具有明确的含义,就能够进行精确的数学运算和推理证明,因而它具有精确性。数学能够帮助人们完成大量的运算和推理证明,但如果没有简捷的思想和符号的参与,它的工作量及难度也是很大的,让人望而生畏。一旦简捷的符号参与了运算和推理证明,数学的简捷性就体现出来了。如欧洲人12世纪以前基本上用罗马数字进行计数和运算,由于这种计数法不是十进制的,大数的四则运算非常复杂,严重阻碍了数学的发展和普及。直到12世纪印度数字及十进制计数法传入欧洲,才使得算术有了较快发展和普及。数学符号的发展也经历了从各自独立到逐步规范、统一和国际化的过程,最明显的就是早期的数字符号从各自独立的埃及数字、巴比伦数字、中国数字、印度数字和罗马数字到统一的阿拉伯数字。数学符号经历了从发明到应用再到统一的逐步完善的过程,并促进了数学的发展;反之,数学的发展也促进了符号的发展。因而,数学和符号是相互促进发展的,而且这种发展可能是一个慢长的过程。因而,符号意识的培养也应贯穿于数学学习的整个过程中,并需要一定的训练才能达到比较熟练的程度。

     

    华琴 发表于:2012-6-21 5:43:12

    评论 

    One of the largest decisions that wig wearers ought to build is whether or not they need to possess an individual's or artificial ones. Obviously, there’s nothing wrong with having each, however Gatlin says it’s vital to understand the benefits and drawbacks of every.While a high quality human hair wig won’t be low-cost, and can need an equivalent daily maintenance of your real hair and may react to weather (frizz, loss of curls), it’s additionally additional versatile and tangle-free. On the contrary, an artificial wig is typically more cost-effective and needs very little to no maintenance. At an equivalent time, you’re sacrificing skillfulness and can most likely got to replace additional typically than an individual's one.Both designs are often created into a lacefront, that is best delineate as a wig with a mesh hairline. Gatlin says, “The mesh or ‘lace’ ought to have neutral tone that may mix with the skin tone and appears invisible once applied to your hairline.Again, your selection is basically a matter of preference and modus vivendi, 2 stuff you ought to contemplate before shopping for. As somebody World Health Organization is consistently on-the-go and customarily lazy together with her hair routine, I fell taken with with my micro-twist wig as a result of I may throw it on and run out the door in no time.The Greek deity Air Georgia home boy 90/1 could be a new hybrid vogue that 1st born within the OG University Red colorway. The sneaker simply created its debut overseas in another OG theme of optical device Blue this August. The sneaker’s Air Georgia home boy one higher is roofed in white mesh and contrastive animal skin overlays in black and light-weight gray for the Swooshes, whereas the pop of optical device blue is value-added on the tongue disapproval, higher eyelets, and exterior of the visible Air Georgia home boy padding. Finally, a white rubber sole crack it all off.Retailing for $140, explore for the Greek deity Air Georgia home boy 90/1 optical device Blue at Greek deity stores overseas these days, however a stateside drop is returning presently. continuously keep it bolted to KicksOnFire for the most recent in sneaker news, unharness dates and wherever to get your favorite kicks.human hair wigscheap lace front wigsfull lace wigslace front wigshuman hair lace front wigssynthetic wigswigs for womencheap human hair wigscheap synthetic wigscheap wigs for womencheap bob wigsafrican american wigs cheapafro wigs cheapcheap full lace wigscheap curly wigscheap cosplay wigscheap wigs for mencheap costume wigscheap hair extensionscheap nike shoes nike air maxnike air max 90 roshe run women roshe run mennike force 1nike air max 90 womens white white roshes mens roshes women cheap air max 90 air max 270 mens nike air max 1 mens cheap nikes online nike sb janoski nike skateboarding shoes nike air force one men nike air force 1 low black huaraches nike huarache womenair max 270  air max sale nike air max saleair jordan 4
    码确 发表于:2018-9-5 14:58:02