Should a Pocket Calculator Be in Your Pocket?

THE couple had been thinking of buying a new set of dishes. They narrowed it down to one of two choices. But it would take some figuring to compare the prices of the two sets the wife had located. See which you think would be the better buy:

One was on sale in a nearby store for $55, not including the 8 percent sales tax. She saw the other set in a German catalog, and her mother could bring it from Germany when she visited. They preferred the design of these dishes, and the set included a coffeepot. The catalog price was 178 German marks, though it likely could be picked up when there was a 15-percent discount. The exchange rate was 39 cents for each mark.

Would it take you long to work out the two prices? In this case the husband got out a pocket calculator and in a few seconds had both prices. It was no work at all, but it clearly was going to mean some work for his mother-in-law!

In figuring it out on a miniature electronic calculator, the husband was joining the millions of persons in various lands who are using such devices in handling their everyday mathematics.

Many women are using calculators to balance checkbooks, to make pattern and recipe adjustments and to figure foreign-currency conversions when traveling. Men use them when filling out tax forms, when determining gasoline mileage on the automobile or when calculating the amount of wallpaper, lumber or paint they will need for redecorating. Students use calculators to speed up their homework or to cut down on laborious figuring by hand in mathematics class.

Pocket calculators are increasingly popular because of their low price. In the early 1970’s it might have cost you $400 to buy one. But in many places now you can buy a simple mini-calculator for about the cost of a blouse or a dress shirt. It is said that they may soon sell for as little as $5. So more and more persons are considering buying one. But can you use a pocket calculator? Are they practical? Are there disadvantages to consider?

Are You in Need?

Whether you have a pocket calculator or not, you already are the sole owner and user of a calculator or computer of far greater capacity. Which one? Why, your brain! It is better than any man-made computer. In The Brain Revolution (1973), M. Ferguson wrote: “A computer sophisticated enough to handle the functions of a single brain’s ten billion cells would more than cover the face of the earth.”

Then how would a mini-calculator compare to your brain? Well, there are many types of pocket calculators on the market. Some have circuitry for doing complicated scientific and engineering problems. But a simple one basically does four things. It adds, subtracts, multiplies and divides. And your brain? With it you are already equipped to do those four, aren’t you? Some low-priced calculators have a percent key. Yet, figuring a percentage, such as 14 percent of $15, merely means multiplying $15 by 0.14, which you can do without a calculator. Also, some mini-calculators have a memory function so you can store a figure, such as a subtotal, while you perform another calculation. However, your brain has a memory capability that is much vaster and more flexible.

So, since you already have a marvelous brain, does that mean that a pocket calculator is of no real use, that it would be just a toy or a waste of money? For some persons, Yes. They simply don’t need one. Still, an electronic calculator is able to do rather involved figuring with amazing speed and accuracy. Recall the example of the two sets of dishes. Thus, if you have quite a bit of such mathematics to do, a calculator might save you a lot of time. And, depending on how prone you are to make mistakes in mathematics, the results may be much more accurate.

For example, what if you faced this problem, which, complex as it looks, involves just multiplying and dividing:

13.08 x .09 x 18⁴ x 7.96 =

8.386

To work that out by hand you would have to write about 230 numerals, and it could take five to ten minutes of tiring writing. (Want to try to do it in ten minutes? But make just one mistake, and who knows how long it will take!) If you worked it out using logarithm tables, you might do it in less than three minutes. But with a pocket calculator you could do it in under thirty seconds! So an electronic calculator could save a lot of time.a

Everyday Uses

The type of mathematics that you use may be less like that problem and more like the one with the dishes. So let’s see how pocket calculators are being used to simplify everyday problems.

Some owners find them valuable in doing their grocery shopping. (Many a husband might find shopping to be less of a chore if, with calculator in hand, he were “Assistant Shopper in Charge of Figures.”) As you select each item you enter it on your calculator. In that way you will have a progressive total of how much you are spending. (Can you really afford that large-size can of coffee?) And since all humans make mistakes, including checkout-counter clerks, with your calculator you could double-check the bill. In fact, if you happened on a cashier who was tempted to “pad” your bill, his just seeing the calculator in your hand might nudge him toward the path of honesty!

Another common use is in unit pricing or price comparison to see which is your best buy. For instance, you want to get some crackers. They come in boxes of two sizes. The 16-ounce (454-gram) size costs 77 cents. But the 7-ounce (198-gram) box is on sale, two boxes for 65 cents. No problem with a pocket calculator. Dividing 77 cents by 16, you see that crackers in the large box cost 4.8 cents an ounce, while those in two small boxes cost 4.6 cents an ounce. But what if, up until the cracker problem, you had been keeping a running count of your purchases? If your calculator has an independent memory key, you can put in the memory storage the bill up to that point, next figure out which crackers to buy, and then add the cracker cost to the figure you stored in the memory.

A money problem of a different sort presents itself when you travel in foreign countries. Have you ever looked at a price tag that said, “63 francs,” “128 pesos,” “19 shillings” or something of the sort? You may have thought, “I wonder how much that is in my money?” An electronic calculator could come to your rescue. How?

Many calculators allow you to enter a figure as a constant. (Some even have a special key for it marked “K”) That lets you use the same figure repeatedly to multiply, divide, add or subtract. So once you’ve determined the exchange rate, you can enter it as a constant. Next, put in the price as given in pesos, dollars, marks, francs, pounds or whatever the foreign currency is. Then you use the constant to convert that to a price you can easily understand, in the currency you use back home.

Do you cook? Then you may face a different conversion problem. Your neighbor gave you an excellent recipe for beef stroganoff. You want to make it when your relatives visit. But the recipe is for six persons, and you are expecting fourteen. Easy. All you need to find out is by how much to increase the quantity for each ingredient. On your calculator you divide the number of guests (14) by the recipe servings (6). So your multiplier is 2.3. Now the recipe. It calls for 2 pounds (.906 kilo) of beef. Applying your multiplier, you find you will need 4.6 pounds (2.08 kilos) of meat. One teaspoon (5 milliliters) of mustard easily converts to 2.3 teaspoons (11.5 milliliters). And so on. Beef stroganoff, anyone?

What Disadvantages?

As might be expected, an electronic calculator is not all advantages. There are disadvantages, and it is wise for you to consider them. For one thing, having a calculator is going to involve some money, time and attention. How much would you use it? In your case the few occasions when you would really be helped by having a calculator might not justify the cost, even with the recent low prices. Do you want to put money into something that you may not need, or that may be just a toy for a few days?

Also, it will take you some time to learn how to use a calculator. You will have to think about repairs if it breaks. And what about getting batteries for it periodically if it is of the type that requires such? Good questions to consider.

Another thing, how might having an electronic calculator affect your present ability to do mathematics? One man from Illinois got into the habit of using his even for simple addition or multiplication of a few small numbers. Later he observed: ‘When I had to figure something out without my calculator, I found I was much slower than before. It was harder to do simple calculations, things I had learned as a child and formerly could do easily.’ Hence, he decided to use his electronic calculator only when he faced long, tedious mathematics, such as adding columns of figures, when working out many percentages or averages, or when speed and accuracy were vital.

Calculators in School?

With more and more families having a calculator available, many educators are debating the question of whether schoolchildren should be permitted to use them. And if so, when? That is, how early in a youth’s schooling?

In this ongoing debate, a common point of agreement is that calculators should not be introduced too early. A child should first learn and be quite comfortable with addition, subtraction, multiplication and division. It is particularly important for a child to have learned by memory the normal multiplication tables. Frank S. Hawthorne, of the New York State Education Department, observed: “If introduced too early, before a child has developed some ‘number sense’ and familiarity with the basic operations of arithmetic, calculators could do great harm. . . . They do not help students to gain the understanding of basic number concepts.”

In this same vein, a January 1976 newspaper report stated that “senior officials of the Austrian Education Ministry have declared war on [calculators] on the ground that they threaten to cause ‘arithmetic illiteracy.’” They want to ban electronic calculators from the classrooms on the elementary level. This is “to encourage children to use pencil-and-paper calculations, [and] to protect from unfair classroom competition those youngsters who cannot afford to buy their own calculators.”

On the other hand, some authorities feel that mini-calculators are not a menace, that they merit a place in education. Once a student has learned well the fundamental procedures of mathematics, a calculator may make the subject immensely more interesting for him. By taking the tedium out of routine figuring, a student may have more zest for working out problems and doing his homework. At a school in California students use calculators during one or two classes a week. One teacher there commented: “Kids who weren’t all that eager to come to math class now ask, ‘Is this the computer day?’”

Certain experts even feel that pocket calculators can be particularly helpful to slow learners. In what way? If a student can quickly check his answers on a calculator, it may improve his confidence and sense of accomplishment. Calculators may increase a student’s motivation by enabling him to solve more interesting problems or to work out large calculations that would otherwise be discouraging. Whereas the complexities of solving a problem on paper might result in a student’s losing sight of the problem he is trying to solve, the speed of a pocket calculator might overcome that.

Despite these beneficial aspects, it bears repeating that if a student is to be allowed to use a calculator, he should first have shown that he has learned the fundamentals of mathematics. In that way he will never be a mathematical illiterate if his calculator battery goes dead.

It is estimated that sales of pocket calculators may soon reach 40,000,000 a year. So there is no doubt that they are finding a role in modern life. How about your life? A mini-calculator could be helpful, simplifying your life and speeding up things. But an electronic calculator could also be just another needless gadget that takes up your time, money and attention. You are the one to determine whether a pocket calculator should be in your pocket.

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