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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, \and we'll never do long division in real life.\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.
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。
Translation
1
Word:inspire;vivid;scan;face up to;finally;what's more
苏珊(Susan)因车祸失去了双腿。有一段时间,她真不知如何面对自己再也不能行走的事实。
一天,苏珊在浏览书籍时,被一个真实故事吸引住了。那个故事生动地描写了一个残疾 (disabled) 姑娘是如何成为一位作家的。苏珊读后深受鼓舞,决心尽可能多读书,而且,她还想写关于自己童年的故事。苏珊开始相信,她会活下去,并最终成为一个有用的人。
Susan lost her legs because of / in a car accident. For a time, she didn't know how to face up to the fact that she would never (be able to) walk again.
One day, while scanning ( through ) books, a true story caught her eyes/she was attracted by a true story. It gave a vivid description of how a disabled girl became a writer. Greatly inspired, Susan made up her mind to read as much as she could, and what's more, she wanted to write stories about her own childhood. Susan began to feel
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that she, too, would finally be able to lead a useful life. 2
Word:a couple of;keep in touch with;come up;neighborhood;on one's mind;keep up;kind of;correspondence
和远方的朋友保持联系不是一件容易的事。对我来说,情形就是这样。
离开旧街区和那里的朋友们已有几年了。我一直打算给他们写信,可是总有这样那样的事儿,似乎就是抽不出空。现在可以说我与他们失去联系了。 但是我一直记挂着他们, 我想我今后也一定会努力与他们保持通信联系的。
It is not easy to keep in touch with friends when they are far away.
This is certainly true in my case.It has been a couple of years since I left my old neighborhood and all the friends I had there. I've been meaning to write to them but something or other comes up and I just don't seem to find the time. Now I have kind of lost touch with them. They are always on my mind, however, and I think I will certainly make an effort to keep up correspondence with them in future. 3
Word:do without;bring about;proportion;sufficient;educate;slow down;rate;put the clock back;inform
很难想象我们的先辈们 (forefathers) 在没有现代技术带来的这么多方便的情况下 (conveniences) ,日子是怎么过的。那个时候只有一小部分人享受一些舒适条件 (comforts) 。大部分人连饭都吃不饱,更不要说 (not to speak of) 接受教育的特权了。然而,许多人责怪现代技术,说它带来了很多问题。他们想减慢进步的速度。但是谁也不能阻止时代的前进。我们能做的是就技术向哪个方向发展做出明智的决定。
It is hard to imagine how our forefathers could do without so many conveniences that modern technology has brought about. Back then only a small proportion of the population enjoyed some comforts. The majority didn't even have sufficient food, not to speak of/let alone the privilege of being educated. However, many people blame modern technology for the problems it has created. They want to slow down the rate of progress. But no one can put the clock back. The best we can do is to make informed decisions as to the direction in which technology is to develop. 4
Word:graduate;turn down;call on;amaze;determination;create;loan
托尼大学毕业后决定自己开业。一开始好多家银行都拒绝了他的贷款要求。但他毫不泄气,继续一个个拜访银行家寻求帮助。有一位银行家被他的决心和乐观精神所打动,最终答应贷款给他。如今他成了一位富商。在谈到所取得的令人惊奇的成就时,托尼强调 (put emphasis on) 了创造机遇而不是等待机遇的重要性。
After graduating from college, Tony decided to start his own business. At the beginning, many a bank turned down his request for a loan. But he was not a bit discouraged, and continued to call on one banker after another seeking help. Impressed by his determination and optimism, one banker finally agreed to loan him the money. Now he has become a wealthy businessman. Talking about his amazing achievement, Tony puts great emphasis on the importance of creating, rather than waiting for opportunities. 5
Word:broaden;correspond;hesitate keen;locate;make one's way;overseas;previous to;sensible
李大伯自己虽然并不富裕,但在别人需要帮助时他从不犹豫。退休前他从希望工程(Project Hope)那里得到两个家境贫穷但渴望求学的农村孩子的地址。此后他定期给他们汇款。这两个孩子后来都考上了大学,还获得了海外留学的机会。他们常常思念李大伯,一直跟他通信。每次重读他们的来信,李大伯就会脸绽笑容。他觉得这是自己一生最理智的投资。
Not rich himself, Uncle Li never hesitates to help others. Previous to / Before his retirement, through Project
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Hope he located the addresses of two country kids who grew up in poor families but had a keen desire to study . From then on he sent them money regularly. Later the two made their way to college, and even got a chance to study overseas. They often thought of Uncle Li and kept corresponding with him. Whenever he read their letters, Uncle Li's face would broaden into a smile. He felt this to be the most sensible investment in his life. 6
Word:release;at first;relieve;extend;surround
我小的时候对动物产生了浓厚的兴趣,所以常去家乡的动物园参观。那里最吸引我的是一对老虎,特别是那只雄虎。它们起初被关在一只大的铁笼子(cage)里,后来放了出来,被安置在一个叫虎山的地方。山下有一道又阔又深的沟(ditch)将这山与参观者隔开,而且沿着沟还有一道高高的铁篱笆围着。
二十年后我再度访问了这个动物园,欣慰地发现虎山仍在,但已扩大了许多,在那里活动的共有大小六只老虎,而不是两只了。
When I was young I developed a keen interest in animals. So I often visited the zoo in my home town. There what attracted me most was a couple of tigers, especially the male. They were kept in a huge iron cage at first, but later was released from it and put in a place called Tiger Hill. The hill was separated from the visitors by a very wide and deep ditch. What's more, it was also surrounded by a high iron fence along the ditch.Twenty years later, I revisited the zoo and was relieved to find the Tiger Hill was still there but greatly extended. Moving around now were six tigers, old and young, instead of two! 7
Word:instant;cool down;draw sb.'s attention;injure;resume;calculate;nearby
教授一进教室,黑板上\欢迎您重返教室\几个字便引起了他的注意。前些日子教授在车祸中受伤,在附近的一个医院里接受了几次手术。医生估计他活下来的可能性最多只有10%。现在他不仅病愈,还能重新执教。每个学生见到教授都很激动,过了好几分钟课堂才平静下来。
The instant the professor entered the classroom, the words on the blackboard \Back Professor\drew his attention. He had been injured in a car accident, and had had several operations in a nearby hospital. The doctor calculated his chances of survival to be no more than 10%. Now, not only had he recovered from his injury, but he was also able to resume teaching. Every student felt excited at the sight of him, and minutes passed before the class cooled down. 8
Word:accumulate;idle;compete with;adequate;drive (sth.) home (to sb.);swear;acquire;portable
今天早晨我从我的便携式收音机中听到一则很有意思的新闻:一个三十六岁的男子和他十岁的儿子在同一个班级上课,为取得高分而互相竞争。事情是这样的:那个男子叫李伟,小时候太懒散,什么都不肯学。由于几乎没有受过教育,没有掌握有用的技术,所以他很难挣到足够维持生活的工资。他的生活经历使他充分认识到一个道理:他必须首先获得知识,然后才能积累财富。李伟发誓要跟儿子一起上学,下决心努力学习。
This morning I heard an interesting piece of news over my portable radio: A man of 36 and his son of 10 attend the same class competing with each other for high marks. The story goes/It's like this:The man, Li Wei by name, was too idle to learn anything when young. With little education, with no useful skills, he could hardly earn an adequate living wage. His life experiences drove home to him the point that he had to acquire knowledge before he was able to accumulate wealth. So Li Wei swore that he would go to school with his son, determined to learn.