[00:00.00] benefit\  in the first place\  proceed\  competent
[00:04.00]利益\首先\继续进行\有能力
[00:07.99]essential\  concentrate on\ solve\   efective
[00:12.21]必要的\集中\解决\有效的
[00:16.43]confuse\ what if\  focus\  at hand
[00:20.75]使困惑\如果…怎么样\集中注意力\在手边
[00:25.08]claim\  contribute\ ultimate
[00:31.11]Do you think the use of calculators inleapning math is a good idea?
[00:37.15]If you do,perhaps this artic will change your mind.
[00:41.98]DITCH THE CALCULATOR    by Diane Hunsaker
[00:47.83]I sigh inwardly as I watch yet anotber student,this one a ninth grader
[00:49.45]struggle with an advanced math problem that requires simple multiplication.
[00:57.39]He mentally battles with5×6×6
[01:02.25]looks longly at the off-limits calcu-lator on the corner of my desk and fina1y guesses the answer:35
[01:13.09]The rowth in the use of calculators in the classroom amazes me.
[01:18.45]The students I tutor tell me regularly 
[01:22.60]that their teachers allow unlimited access to this tool
[01:28.22]The National Coulcil of Teachers 0f Mathematics actiVely encourages its use．
[01:35.37]Recently I attended a math seminar
[01:38.93]where the instructor casually stated that teachers were no longer reluctant 
[01:45.82]to permit calculators in the classroom
[01:49.30]Now "everyone" agrees on their importance,she said
[01:55.23](1) The more I hear from the education esablishment 
[01:59.77]about the benefits of these devices in schools,the 1ess surprised I am
[02:05.70]when  midle and  high-school students 
[02:09.46]who have difficulty with arithmetic call for toring in algebra and geometry
[02:15.50]Having worked six years as an electrical engineer before switching to teaching
[02:22.50]I often suggest to my students that they consider technical and scientific careers
[02:29.63]but I'm d1iscouraged when I see an increasing number of kids
[02:35.56]who lack simple math skills．
[02:38.80]Educators have many arguments in defense of calculators,
[02:44.68]but each one ignores the reason that we teach math in the first place
[02:50.55]Math trains the mind.
[02:53.87]By this I mean that students learn to think logically and rationally
[02:59.23]to proceed from known information to desired information 
[03:04.82]and to become competent with both numbers and ideas
[03:09.57]These skills are something that math and science teach 
[03:15.11]and are essential for adolescents to become thinking 
[03:19.68]intelligent members of society.
[03:23.34]Some teachers argue that calculators let students concentrate on
[03:30.08]how to solve problems instead of getting tied up with tedious computations
[03:37.23](2) Having a calculator doesn't make it any easier 
[03:42.07]for a student tn decide how to attack a math nrohlem
[03:46.74]Rather,it only encourage him to try every combination of addition, subtraction
[03:54.48]Multiplication or division 
[03:58.29]without any thought about which would be more appropriate 
[04:02.65]Some of my elementary-school children look at a word problem 
[04:08.84]and instantly guess that adding is the correct approach
[04:13.60]When I suggest that they solve the problem this way without a calculator,
[04:20.81]they usually pause and think before continuing
[04:24.65]A student is much more likely to cut down his work by reflecting on the problem first
[04:33.87]if he doesn't have a calculator in his hand.
[04:39.59]Learning effective methods for approaching confusing problems 
[04:45.91]is essential,not just for math but for life.
[04:50.06]A middle-school teacher once said to me, 
[04:55.63]"So what if a student can't do long division? 
[04:59.39]Give him a calculator,and he'll be fine."
[05:03.05]I doubt it.I don't know when learning by heart and repetitious problem 
[05:10.99]solving fell to Such a low priority in education circles
[05:15.85]How could we possibly communicate with each other,much less create new ideas
[05:24.39]without the immense store of information in our brains?
[05:30.89]Math is as much about knowing why the rules work as knowing what the roles are
[05:40.25]A student who cannot do long division obviously does not comprehend the principles on which it is based
[05:49.81]A true understanding of why often makes learning by rote unnecessary,
[05:58.35]because the student can figure out the rules himselt
[06:02.61]My students who view the multiplication tables as a list of unrelated numbers
[06:10.55]have much more difficulty in math than those
[06:14.62]who know that multiplication is simply repeated addition
[06:21.28]Calculators prevent students from seeing this kind of natural structure and beauty in math
[06:31.00]A student who learns to handle numbers mentally can focus 
[06:38.08]on how to attack a problem and then complete the actual calculations easily
[06:45.24]He will also have a much better idea of what the answer should be
[06:51.77]since experience has taught him"number sense,"or the relationship between numbers.
[07:00.39]A student who has grown up with a calculator 
[07:05.95]will struggle with both strategies and computations.
[07:10.81]When youngsters used a calculator to solve 9×4 in third grade,
[07:19.07]they are still using one to solve the same problem in high school.
[07:27.01]By then they are also battling with algebra
[07:30.95](3) Because they never felt comfortable working with numbers as children,
[07:38.40]they are seriously disadvantaged when they attempt the generalized math of algebra
[07:46.26]Permitting extensive use of calculators invites a child's mind to stand still.
[07:55.61]If we don't require students to do the simple problems that calculators can do
[08:04.86]how can we expect them to solve the more complex problem 
[08:11.68]that calculators cannot do?
[08:14.55]Students learn far more when they do the math themselves. 
[08:21.71]I've tutored youngsters on practice SAT exams
[08:27.56]where they immediately reach for their calculators.
[08:33.83]If they'd take a few  seconds to understand the problem at hand
[08:39.39]they most likely would find a simpler solution without needing a stick to lean on
[08:48.01]I have also watched students incorrectly
[08:52.66]enter a problem like 12 + 32 into their calculators as 112 + (32×32)
[09:04.29]and not bat an eye at the obviously incorrect answer.
[09:12.05]After all,they useo al calculator,so it must be right.
[09:17.09]Educators also claim that calculators are so inexpensive and commonplace
[09:24.79]that students must become competent in using them.
[09:31.25]New math texts contain whole sections on solving problems with a calculator.
[09:39.61]Most people,including young children,can learn its basic functions in about five minutes
[09:46.74]Calculators do have their place in the world outside school and,
[09:54.29]to a limited extent, in higher-level math classes
[09:58.36]but they are hardly education tools.
[10:03.51]Many teachers as well as students insist,
[10:09.88]"Why shouldn't we use calculators?They will always be around
[10:14.84]and we'll never do long division in real life.
[10:20.30]"This may be true.It's true of most math
[10:24.27]Not many of us need to figure the circumference of a circle 
[10:30.94]or factor a quadratic equation for any practical reason
[10:35.98]But that's not the sole purpose of teaching math.
[10:41.72](4)We teach it for thinkin and discipline,both of which expand the mind
[10:48.18]and increase the student's ability to function 
[10:52.93]as a contributing individual in society:the ultimate goals of education