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    魏光明主页 >> 文章 >> 我的论文 >> 浏览信息《“缓坡”为引领,“陡坡”促跨越》

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    星期日   晴天 
    主题 “缓坡”为引领,“陡坡”促跨越

    教学经验告诉我们,在教学中,教师不仅需要采用小步前行的教学方式,引领全体学生积极参与进数学学习活动之中,不断增加数学知识学习的感受、体验,积蓄快速前行的“能量”;还需要采用大步跨越,甚至去攀登高峰的教学方式,最大限度地挖掘教学内容的思维含量,发展学生的问题意识、创新精神和创造能力。再来看五年级上册用计算器计算》一课中关于一道数学问题的教学方法:

     [数学问题]

     先用计算器计算第(3)、(4)题,找出规律后直接写出后面几题的商,并求出它们的近似数。(得数保留两位小数)

     11÷11=0.0909……    22÷11=0.1818……   33÷11=           

     44÷11=                         55÷11=                    

     66÷11=                       77÷11=                    

     88÷11=                       99÷11=                    

      [教学环节]

     出示前四道算式,让学生用计算器计算并核对第(3)题的结果,组织讨论、互动:

     师:观察一至三题的结果,看一看有什么规律?

     生:商是一个循环小数,循环节依次是091827

     生:循环节是9的倍数。

     生:循环节的和是9

     ……

     接着,让学生猜一猜第(4)题的结果,并用计算器计算进行验证。

     师:你猜对了吗?照这样的规律,猜一猜5÷11的结果是多少?

     生:0.4545……。

     师:你是怎么想的?

     生:根据小数部分的变化规律,下面5÷11的商应该是“45循环”。

     生:还可以这么想。1÷11=0.0909……,5÷11的商应该是它的5倍,用0.0909……乘以5,等于0.4545……。

     师:这也是一种好方法!前一种方法是根据规律得出结果,后一种方法是根据1÷11的结果计算出结果,两种方法都可以。这题保留两位小数是多少?

     生:约等于0.45

     师(显示7÷11=                     ):这题的结果是多少?你是怎么想的?

     生:7÷11等于0.6363……,约等于0.64。我根据商的变化规律直接得出结果。

     师:同学们还知道哪些数除以11的结果?并说出你的想法。

     生:8÷11= 0.7272……,用0.0909……乘以8

     生:9÷11=0.8181……,用0.0909……乘以9

     师:根据结果的变化规律能得出这个结果吗?

     生:能!

     师:你们还知道哪些数除以11的结果?

     生:10÷11=0.9090……,用0.0909……乘以10或者根据规律进行判断。

     师:真不错!我们已经掌握了两种解决问题的方法!根据1÷11的结果你能算出11÷11的结果吗?

     生:能!11÷11=0.9999……

     生:不对。11÷11应该等于1,不等于0.9999……。

     师:是呀!直接计算结果等于1,用今天探索的规律却得出了0.9999……,这是怎么回事呢?

     生:可能哪里出错了!

     生:可能用1÷11的结果计算其他数除以11的结果有局限性!

     师:同学们,如果两种方法都是正确的!咱们可以得出怎样的结论?

     生:0.9999……和1相等。

     生:不对!0.9999……后面全是9,不可能等于1

     学生沉默。

     师:今天老师就告诉同学们一个将来要学到的知识。在数学里,0.9999……和1其实是相等的!刚才同学们计算的过程就是验证0.9999……与1相等的过程。至于这个结论更严密的证明,同学们课后可以查资料或请教老师!这道题就研究到这。

     品味这个教学片断,前面部分如行云流水般自然流畅,使学生初步感知除数是11算式的商的规律,后面部分则不断增大思维的跨度和难度,适时地促使学生“跳一跳”,深究此题中蕴含的“理”,让学生既掌握了规律,发展了思维能力,又为后续学习埋下了必要的伏笔。我们知道,课堂时间是有限的,完全搭建便于“行走”、近乎平坡的学习支架是不可能的,也不利于学生探究和思维能力的发展。因而,为学生搭建学习的支架需要掌握好“坡度”。我们既需要面向全体,唤醒他们的参与意识,提高全体学生的学习水平,又要学会调整支架的倾斜角度,甚至“隐去”支架的几个部分,促使学生积极思考,深入思考。在这里,教师要善于根据学生差异,实施分层指导,使每一个学生都在原有基础上获得提高。随着学生知识量的增加和探究能力的提高,教师要逐渐减少指导直至完全放手,使学生逐步减小对支架的依赖,逐步增长独立获取新知识和综合运用所学知识解决实际问题的能力,防止出现把“指导”沦为“灌输”的现象,使学生主动探究、自我建构成为一句空洞的口号。
    (本文节选自《支架,究竟该如何搭建?》第三部分,发表于《湖北教育》2008年第9期)

    魏光明 发表于:2011-2-13 16:53:29

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