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cut down his work by reflecting on the problem first if he doesn't have a calculator in his hand.
Learning effective methods for approaching confusing problems is essential, not just for math but for life.
有教师争辩道，计算器使学生集中精力解题，而不为繁琐的运算拖累。(2) 计算器并不能方便学生确定解数学
题的方法。相反，计算器只会鼓励他乱试加减乘除的各种组合，而不去考虑哪种组合更加适当。我的一些小学生一
看某道应用题立刻就猜测加法是正确的运算方法。当我建议他们不依赖计算器用加法解题时，他们往往在继续运算
前先思考一番。如果手里没有计算器，学生更有可能停下来先对问题思考一番，以减少运算工作。学会用有效的方
法解决复杂的问题是必要的，不仅学数学如此，在生活中也一样。
5 A middle-school teacher once said to me, \what if a student can't do long division? Give him
a calculator, and he'll be fine.\learning by heart and repetitious problem
solving fell to such a low priority in education circles. How could we possibly communicate with each
other, much less create new ideas, without the immense store of information in our brains?
一位中学教师曾对我说：“学生不会运算长除法又怎么样？给他个计算器，他就有办法了。”我不敢苟同。我不
知道，从什么时候起，背诵和反复解题在教育界变得如此不受重视。没有大脑中储存的大量信息，我们如何相互交 流？更不用说创新出主意了。
6 Math is as much about knowing why the rules work as knowing what the rules are. A student who
cannot do long division obviously does not comprehend the principles on which it is based. A true
understanding of why often makes learning by rote unnecessary, because the student can figure out
the rules himself. My students who view the multiplication tables as a list of unrelated numbers
have much more difficulty in math than those who know that multiplication is simply repeated addition.
Calculators prevent students from seeing this kind of natural structure and beauty in math.
数学要讲有哪些规则，更要讲这些规则为什么成立。不会做长除法的学生显然不理解长除法所依据的原理。真
正理解了所以然常常使得死记硬背毫无必要，因为学生自己就能算出这些规则。我的那些把乘法表看作一串不相关
数字的学生在数学上的困难远比那些懂得乘法只是连加的学生多得多。计算器
妨碍学生认识数学中这类自然结构和 美。
7 A student who learns to handle numbers mentally can focus on how to attack a problem and then
complete the actual calculations easily. He will also have a much better idea of what the answer should
be, since experience has taught him \relationship between numbers.
学会心算的学生能把注意力集中到如何解题上，然后轻而易举地完成实际运算。他对答案该是个什么样儿心里
也更有数，因为经验使他把握了“数字感”，或者说数字间的关系。
8 A student who has grown up with a calculator will struggle with both strategies and computations.
When youngsters used a calculator to solve 9×4 in third grade, they are still using one to solve the
same problem in high school. By then they are also battling with algebra. (3)Because they never felt
comfortable working with numbers as children, they are seriously disadvantaged when they attempt
the generalized math of algebra. Permitting extensive use of calculators invites a child's mind to stand 全新版大学英语综合教程1课文对照翻译 BY12020212 - 54 -
still. If we don't require students to do the simple problems that calculators can do, how can we expect
them to solve the more complex problems that calculators cannot do?
一个伴着计算器长大的学生既要对付解题策略又要对付实际运算。三年级时借助计算器算出9×4的孩子到了高
中仍在借助计算器做同样的运算。届时他们还得应付代数。(3) 因为他们在孩提时代对数字计算从未感到过轻松，
当他们试图攻读代数这一广义数学时就会处于极其不利的地位。允许广泛使用计算器会使孩子的智力发展停滞不前。
如果我们不让学生做那些计算器能代劳的简单的运算，又怎么能期待他们去解决计算器解决不了的更为复杂的问题 呢？
9 Students learn far more when they do the math themselves. I've tutored youngsters on
practice SAT exams where they immediately reach for their calculators. If they'd take a few seconds
to understand the problem at hand, they most likely would find a simpler solution without needing a
stick to lean on. I have also watched students incorrectly enter a problem like 12 + 32 into their
calculators as 112 + 32 and not bat an eye at the obviously incorrect answer. After all, they used a calculator, so it must be right.
学生自己进行数学运算所获得的收益远比依赖计算器多。我辅导过孩子做学业能力倾向测试的模拟试题，他们
一坐下就拿计算器算。如果他们对手头的题目略加思考，就很可能不需要倚靠拐杖就能找到一种更简单的解题方法。
我还观察到学生错把12＋32 当作112＋32输入计算器，对算出的明显错误的答案连眼都不眨一下。毕竟，他们 用的是计算器，所以，一定没错。
10 Educators also claim that calculators are so inexpensive and commonplace that students must
become competent in using them. New math texts contain whole sections on solving problems with a
calculator. Most people, including young children, can learn its basic functions in about five minutes.
Calculators do have their place in the world outside school and, to a limited extent, in higher-level
math classes, but they are hardly education tools.
教育家们还声称，计算器如此便宜而又普遍，学生必须学会熟练使用。新的数学教材有整节整节关于用计算器
解题的内容。大多数人，包括年幼的孩子们，用大约五分钟就能掌握计算器的基本功能。计算器在学校之外的社会
中的确有其地位，在高等数学课堂上也有一定的作用，但它们很难算得上是教育工具。
11 Many teachers as well as students insist, \we use calculators? They will always be
around, and we'll never do long division in real life.\be true. It's true of most math. Not
many of us need to figure the circumference of a circle or factor a quadratic equation for any practical
reason. But that's not the sole purpose of teaching math. (4) We teach it for thinking and discipline,
both of which expand the mind and increase the student's ability to function as a contributing
individual in society: the ultimate goals of education.
不少老师以及学生坚持认为，“我们为什么不能用计算器？计算器永远就在身边，我们在实际生活中根本不会做
长除法运算。”这或许是事实。大多数数学运算也都如此。我们当中没有多少人会出于实际需要而计算圆的周长或求
解一项二次方程的因子。但那并非数学教学的惟一目的。(4) 我们为培养思维和训练而教数学，这两者都能扩展思
维，增强学生为社会作贡献的能力：这是教育的终极目的。__