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[12-20]
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In everyday life, and especially in the workplace, almost everyone encounters the need to make calculations. Until recently, paper and pencil were the most common means of solving problems that people could not do by mental arithmetic. For most students, school mathematics has meant doing calculations on paper. This usually takes the form of learning how to do long division, find percentages, or compute ratios, but not of learning why those algorithms work, when to use them, or how to make sense out of the answers.
“úí�ｿｽ�ｿｽŠˆ‚Ì’†‚ÅA‚»‚µ‚Ä“Á‚ÉŽdŽ–ê‚Å‚ÍA‚Ù‚Æ‚ñ‚Ç‚Ìl‚ªŒvŽZ‚ðs‚¤•K—v«‚É’¼–Ê‚·‚éB‚‚�ｿｽ�ｿｽÅ‹ß‚Ü‚Å‚ÍAŽ†‚Ɖ”•M‚ªˆÃŽZ‚Å‚«‚È‚�ｿｽ�ｿｽ–â‘è‚ð‰ðŒˆ‚·‚éÅ‚àˆê”Ê“I‚ÈŽè’i‚¾‚Á‚½B‚Ù‚Æ‚ñ‚Ç‚Ì�ｿｽ�ｿｽ“k‚É‚Æ‚Á‚ÄAŠwZ‚ÅK‚¤”Šw‚ÍŽ†ã‚ÅŒvŽZ‚·‚é‚�ｿｽ}‚Æ‚ðˆÓ–¡‚µ‚Ä‚�ｿｽ�ｿｽ‚½B‚�ｿｽ}‚ê‚Í’ÊíA‚ǂ̂悤‚ÉŠ„‚èŽZ‚ðs‚¤‚©‚âAŠ„‡‚Ì‹‚ß•ûA”ä—¦‚ÌŒvŽZ•û–@‚ðK‚¤‚Æ‚�ｿｽ�ｿｽ‚¤Œ`‚ð‚Ƃ邪A‚È‚º‚�ｿｽ}‚̂悤‚ȉð–@‚ª—LŒø‚È‚Ì‚©A‚�ｿｽ�ｿｽ‚‚»‚ê‚ç‚ðŽg‚¦‚΂æ‚�ｿｽ�ｿｽ‚Ì‚©A‚»‚µ‚Ä“š‚¦‚ð‚Ç‚¤—‰ð‚·‚ê‚΂æ‚�ｿｽ�ｿｽ‚Ì‚©‚ÌŠwK‚Æ‚�ｿｽ�ｿｽ‚¤Œ`‚ðŽæ‚é‚�ｿｽ}‚Æ‚Í‚È‚�ｿｽ�ｿｽB
[12-21]
The advent of the small, inexpensive electronic calculator has made it possible to change that situation radically. Because calculators are so fast, they can make available instructional time in school for doing and learning real mathematics. Students can readily learn how to figure out steps for solving ordinary numerical problems, which operations to use, and how to check the reasonableness of their answers. Universal numeracy becomes a real possibility.
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[12-22]
The advantage of the calculator is not only pedagogical. Paper-and-pencil calculations are slow, prone to error, and as conceptually mysterious to most users as electronic tools are. When precision is desired, when the numbers being dealt with have multiple digits, or when the computation has several steps, the calculator offers many practical advantages over paper and pencil. But those advantages cannot be realized unless people learn how to use calculators intelligently. Calculator use does require skill, does not compensate for human errors of reasoning, often delivers answers with more precision than the data merit, and can be undermined by operator error. The key is for students to start using calculators early and to use them throughout the school years in as many different subjects as possible.
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[12-23]
Everyone should be able to use a calculator to do the following:
EAdd, subtract, multiply, and divide any two whole or decimal numbers (but not powers, roots, or trigonometric functions).
EFind the decimal equivalent of any fraction.
ECalculate what percentage one number is of another and take a percentage of any number (for example, 10 percent off, 60 percent gain).
EFind the reciprocal of any number.
EDetermine rates from magnitudes (for example, speed from time and distance) and magnitudes from rates (for example, the amount of simple interest to be paid on the basis of knowing the interest rate and the principal, but not calculations using compound interest).
ECalculate circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids.
EFind the mean of a set of data.
EDetermine by numerical substitution the value of simple algebraic expressions—for example, the expressions aX+bY, a(A+B), and (A-B)/(C+D).
EConvert compound units (such as yen per dollar into dollars per yen, miles per hour into feet per second).
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[12-24]
To make full and effective use of calculators, everyone should also be able to do the following:
ERead and follow step-by-step instructions given in calculator manuals when learning new procedures.
EMake up and write out simple algorithms for solving problems that take several steps.
EFigure out what the unit (such as seconds, square inches, or dollars per tankful) of the answer will be from the inputs to the calculation. Most real-world calculations have to do with magnitudes (numbers associated with units), but ordinary calculators only respond with numbers. The user must be able to translate the calculator's "57," for example, into "57 miles per hour."
ERound off the number appearing in the calculator answer to a number of significant figures that is reasonably justified by those of the inputs. For example, for the speed of a car that goes 200 kilometers (give or take a kilometer or two) in 3 hours (give or take a minute or two), 67 kilometers per hour is probably accurate enough, 66.67 kilometers per hour is clearly going too far, and 66.666667 kilometers per hour is ridiculous.
EJudge whether an answer is reasonable by comparing it to an estimated answer. A result of 6.7 kilometers per hour or 667 kilometers per hour for the highway speed of an automobile, for example, should be rejected on sight.
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