全新版大学英语综合教程第一册学习笔记（原文及全文翻译）——8B - Ditch the Calculator（扔了计算器）
Unit 8B - Ditch the Calculator
Do you think the use of calculators in learning math is a good idea If you do, perhaps this article will change your mind.
Ditch the Calculator
Diane Hunsaker
I sigh inwardly as I watch yet another student, this one a ninth grader, struggle with an advanced math problem that requires simple multiplication. He mentally battles with 5×6, looks longingly at the off-limits calculator on the corner of my desk and finally guesses the answer: "35."
The growth in the use of calculators in the classroom amazes me. The students I tutor tell me regularly that their teachers allow unlimited access to this tool. The National Council of Teachers of Mathematics actively encourages its use. Recently I attended a math seminar where the instructor casually stated that teachers were no longer reluctant to permit calculators in the classroom. Now "everyone" agrees on their importance, she said. The more I hear from the education establishment about the benefits of these devices in schools, the less surprised I am when middle- and high-school students who have difficulty with arithmetic call for tutoring in algebra and geometry. Having worked six years as an electrical engineer before switching to teaching, I often suggest to my students that they consider technical and scientific careers, but I'm discouraged when I see an increasing number of kids who lack simple math skills.
Educators have many arguments in defense of calculators, but each one ignores the reason that we teach math in the first place. Math trains the mind. By this I mean that students learn to think logically and rationally, to proceed from known information to desired information and to become competent with both numbers and ideas. These skills are something that math and science teach and are essential for adolescents to become thinking, intelligent members of society.
Some teachers argue that calculators let students concentrate on how to solve problems instead of getting tied up with tedious computations. Having a calculator doesn't make it any easier for a student to decide how to attack a math problem. Rather, it only encourages him to try every combination of addition, subtraction, multiplication or division without any thought about which would be more appropriate. Some of my elementary-school children look at a word problem and instantly guess that adding is the correct approach. When I suggest that they solve the problem this way without a calculator, they usually pause and think before continuing. A student is much more likely to 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.
A middle-school teacher once said to me, "So what if a student can't do long division? Give him a calculator, and he'll be fine." I doubt it. I don't know when 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?
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.
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 "number sense," or the relationship between numbers.
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. 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 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?
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.
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.
Many teachers as well as students insist, "Why shouldn't we use calculators They will always be around, and we'll never do long division in real life." This may 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. 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.
参考译文——扔了计算器
你认为学数学时使用计算器好吗如果你认为好，也许这篇文章会改变你的看法。
扔了计算器
黛安·亨萨克
看着又一个学生，这次是个九年级学生，费劲地解一道需要运用简单的乘法运算的高级数学题，我暗自叹气。他苦苦地心算着5×6，眼巴巴地望着我桌头那个可望不可及的计算器，最后凭空猜测了一个答案：35。
课堂上使用计算器越来越多，这令我惊讶。我辅导的学生常常告诉我，他们的老师允许无限制地使用这一工具。全国数学教师协会积极鼓励使用计算器。最近我参加了一个数学研讨会，会上一位教师随口说，教师已不再不愿意让学生在课堂上使用计算器了。目前“人人”都认识到了计算器的重要性，她说。我听到教育机构谈论学校里使用这些工具的好处，听到越多，对于算术有困难的初、高中生需要家庭教师辅导几何、代数一事，我就越觉得不足为怪了。由于改行教书前我曾当过六年电气工程师，因此常常建议学生将来从事技术或科学工作，但看到越来越多的孩子缺乏基本的数学运算技能，我不由深感失望。
教育工作者有诸多理由为使用计算器辩解，但每每都忽略了我们教数学的首要理由。数学能培养智力。我是说，学生能学会逻辑地、理性地思维，学会根据已知信息找到所需信息，进而变得既会运算又善于思维。这类技能是通过数学和科学课程传授的，对青少年成长为善于思考的、有才智的社会成员有着重要意义。
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。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。
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。
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。
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。
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？
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。
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。
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。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。
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