[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