推荐回答(1个)
转化思想是把一个实际问题通过某种转化、归结为一个数学问题,把一个较复杂的问题转化、归结为一个较简单的问题。也就是说,转化方法的基本思想是在解决数学问题时,将待解决的问题,通过某种转化过程,归结到一类已经解决或者比较容易解决的问题,然后通过容易问题还原解决复杂的问题。将有待解决或未解决的问题,转化为在已有知识的范围内可解决的问题,是解决数学问题的基本思路和途径之一,是一种重要的数学思想方法。
小学是学生学习数学的启蒙阶段,这一阶段让学生真正理解并掌握一些基本的数学思想便显得尤为重要。转化思想是数学思想的重要组成部分。它是从未知领域发展,通过数学元素之间的因果联系向已知领域转化,从中找出它们之间的本质联系,解决问题的一种思想方法。在小学数学中,主要表现为数学知识的某一形式向另一形式转变,即化新为旧、化繁为简、化曲为直、化数为形等。21世纪的数学教师,应该结合相应的数学情景,培养学生善于和习惯利用转化思想解决问题的意识。使复杂的问题简单化、抽象的问题具体化,特殊的问题一般化,未知的问题已知化,提高学生解决数学问题的能力,从而使学生爱上学数学。
1.计算的纵向转化
加减计算: 20以内数的加减←―100以内数的加减←―多位数的加减←―小数加减 ← 分数加减 。其中 20以内数的加减计算是基础。如23+15可以转化成2+1和3+5两道十以内数的计算,64-38 可以转化成14-8和5-3两道计算。多位数计算也同样。
分数加减计算如 7/8+3/8 就是 7个1/8 加3个1/8 ,就是(7+3)个1/8 ,最后也可以看作是20以内数的计算。乘除计算:一位数乘法← 多位数乘法← 小数乘法。一位数乘法口诀是基础,多位数乘法都可以把它归结到一位数乘法。除数是一位数的除法←―多位数除法←-小数除法。除法中除数是一位数除法的计算方法是基础,多位数除法都可以把它归结到一位数除法。 2.计算的横向转化
加法与减法之间可以转化,乘法与除法之间可以转化。几个相同加数连加的和,可以转化成乘法来计算。被减数连续减去几个相同的减数,差为零,可以转化成除法来表示。分数的除法,可以将除数颠倒位置变成乘法进行计算。
3.图形中的转化
面积计算公式的推导可以把长方形面积公式作为基础,其它图形面积公式都可以通过转化变成长方形或平行四边形后得出公式。体积计算公式以长方体的体积计算公式为基础,圆柱体的体积公式的推导也是通过转化为长方体来得出。转化思想是解决数学问题的一种最基本的数学思想,在研究数学问题时,我们通常是将未知问题转化为已知的问题,将复杂的问题转化为简单的问题,将抽象的问题转化为具体的问题,将实际问题转化为数学问题,我们也常常在不同的数学问题之间互相转化,可以说在解决数学问题时转化思想几乎是无处不在的。
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