大学英语综合教程 第一册 unit 8b

[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