by PATRICIA G. LAUBER
A WEEK ago Henry was telling us about his basic training in the Army.
“What kind of things do you do?” I asked.
“Well,” he said, “there’re things like clean-up duty. Other day, ten of us were sent out to pick up pieces of wood lying around a building. Two men could have done it in half an hour.”
With lightning rapidity I covered several sheets of foolscap with formulae and calculations. “So,”I said, glancing modestly at my mathematics, “it took the ten of you six minutes.”
“Naw,” Henry said.
Without hesitation I seized another sheaf of paper and started afresh. Fifteen minutes and seven pages later I said, “Five minutes?”
“Naw,” Henry said. “Three and a half hours.”
I was again the victim of the great hoax. The hoax, I might add, has nothing to do with the Army, it has been thought up and perpetrated by the writers of mathematics books. While their thinking may be algebraically sound, the fallacies and misrepresentations they put forth to permeate innocent young minds are little short of rapscallion. My life is now dedicated to exposing them in their duplicity.
Mind you, I have no objection to pure algebra. If “4x equals 8” means that “x equals 2,” that’s all right with me. But how many algebra-book writers stop here? They go on and make x stand for bananas or horses. And as soon as problems are built around people or things in real life, misimpressions are created. Those the student absorbs along with the method of solving the problem. Very often his life is seriously impaired.
Take, for example, this familiar problem: If peanuts cost 33 cents a pound, walnuts 87½ cents a pound. and pecans 73 cents a pound, how many pounds of each must a grocer use to get a mixture worth 69 cents a pound?
You’ve met this problem under many guises — sometimes it concerned nuts, sometimes dried fruit or dog biscuits or buttons. But it always conjures up the same picture of the honest storekeeper silting behind his shop after a hard day’s work. The doors are bolted, night has fallen, his dinner is cooling on the table, but the storekeeper labors on. Before him lie his scales, piled with nuts or cookies or buttons. He himself is bent over a scrap of paper, a stabby pencil clutched in his fingers, working away in the trial-and-error method. As the church clock tolls midnight, the man at last stumbles into bed. He has found the right proportion of buttons and nuts to sell for 69 cents the next day.
Meanwhile we students have calculated the exact proportions in a matter of minutes (never mind lammany minutes it took me) and stepped out to buy a pound of assorted nuts. The price is 69 cents — but the contents are nine-tenths peanuts, as anyone except an algebra student would know. The conditioning process of mathematics has just cost us some 36 cents.
Or take this problem: A leaves a summer resort at 5 A.M. and drives home, a distance of 263 miles, at 30 miles per hour. B leaves the resort three hours later. How fast will he have to drive to reach home at the same time A does?
On first encounter this seems like a useful sort of problem to be able to solve. While few of us will ever have to mix nuts, we rnighl well be in B’s position.
A clear-eyed second glance, however, shows that the problem is simply another hoax. B can’t possibly arrive home at the same time A does.
The student, of course, doesn’t realize this. Knowing that Rate times Time equals Distnnce, he works out the number of hours it took A to get home, applies the necessary information to B, and comes up with the answer.
Now let’s look at poor B. A didn’t tell B he was going to drive at 30 miles an hour. So B couldn’t possibly compute how long it would take A to arrive, even if he wore able to — which is dubious.
B is a good sport, though, and willing to make a slab at arriving at the same time, just for the sake of the problem.
But at this point a human factor enters the situation. All the people who were going to ride home with A decided to go with B when they heard what time A was leaving. This meant it was closer to 10 A.M. than 8 when B got under way. Then he had to go back to the hotel because Aunt Sally had forgotten her suitcase. (It turned out to be in the trunk of the car all the time.)
Having left at a civilized hour, B has to buck I raffle and stop at a restaurant for lunch. He loses still more time because of people being carsick, people wanting to stop for drinks, a flat tire, a ticket for speeding, stopping to look at the scenery, and slopping for more drinks. If B (or you or I) can gd home before midnight, he’ll be doing well. A, by this time, has arrived home, taken a nap, eaten dinner, gone to the movies, and is fast asleep in bed.
Realizing the truth about algebra problems isn’t enough. You have to re-examine all your thinking and straighten out the parts that have been distorted. This is easier said than done, for it must be accomplished in a world of unreconstructed algebra students. Just yesterday I was busy dropping different-sized rocks out my window to see if they hit the ground at the same time, when my mother interrupted me. “it will take me an hour to clean downstairs,‘’ she said. “But if you would help me, we could do the job in half the time.”
“If that is true,” I said, “then 60 of us could do it in one minute, and 360 of us in one second.” I think she got the point, though older people are more set in their ways.
Well, I have to go out now. Cousin Mary says that the sum of her age and her sister’s is 56 and that 10 years ago she was twice as old as her sister was 13 years ago. If this is true. Mary is only 32. She doesn’t look a day under 40, and I want to get down to City Hall before the Records Office closes and check up on her. I’m late now. But I think if I run twice as fast as I usually walk to the corner and take the bus, which travels three and a half times as fast as I can walk, I should be able to make it.