The question was from an elementary school teacher. She wanted to tell students why they would need math and algebra. I proposed a lame English-teacher kind of explanation (is the teacher or the explanation lame?) and then thought I ought to consult a math teacher. Floyd Haupt has invested a life gently nudging those of us who misuse, misunderstand, misappropriate or just plain miss mathematical concepts. Here is his answer:

Elementary students view the world with wonder, excitement, ignorance, fear and laziness. Their questions about mathematics may spring from a love of the subject, fear or simply from a desire to be told they won't need it - an excuse for avoiding effort. Many will change lifetime goals and realize too late it is easier to revise them downward than make up mathematical deficiencies.Within a few years elementary students will become adults whose use of math will range from almost zero to extremely high in fields where math is essential. Some will be in the minority that along with the majority will need not only the facility of arithmetic, but mathematics to make sense of life. These are some ideas for this average person.

One may ask, "Is it possible to get through life without using math?" Yes. It is also possible to do without a car, dental care, underwear and a higher income. The question should not be "Is it possible?" Rather, one should ask "Is it a good idea?" Anyone who wants to avoid math could copy the primitive tribe whose entire number system was "one, two, three, heap." Since they could not distinguish between integers larger than three, dialing a telephone or delivering the mail to an address beyond three would be impossible. Do math-haters want to sink that low?

Many see a need for arithmetic but not algebra or geometry. The spirit of math is thinking, not just calculating. Mathematical proofs teach logical thinking - a skill that can be useful in life.

For example, a logical proof involves the concepts of necessary and sufficient conditions. A condition is necessary if no other condition can take its place. All of the necessary conditions taken together are sufficient. For instance, to get a driver's license it is necessary to pass the written test. This is not sufficient because there are other necessary conditions. A single necessary condition may or may not be sufficient in other situations. Granted, one does not turn getting a driving license into a math problem, but the logic illustrated applies in any discipline.

Other useful skills acquired in math include the ability to manipulate and interpret formulas and graphs. Applications are just a matter of recognizing opportunities. For instance, a simple equation relates power, voltage and current. Understanding it can save your life. Ignorant people die every year in fires caused by overloaded circuits. The rule of thumb, one plug per socket, can result in a burned thumb. Better to understand a mathematical relationship.

The author once used algebra in rearing a baby daughter. Her formula did not agree with her, so we called the doctor. He changed the mix. It was too late to buy more supplies, so it was necessary to use the remaining old formula, a little more canned milk and water, to get through the night. This involved solving a "word problem." We got some sleep.

Average people need to know when advertisers are trying to fool them. A common trick is to omit or redefine some variable in an equation. Saying an item is "only $100 a month" while "forgetting" to stress how long, may be a tricky way of charging $2,400 for a $100 product.

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When a utility announces a $5,000,000 "rate increase" they are redefining an amount as a rate. This conceals the real rate. It also puts the issue in terms that don't translate very easily into individual wallets.

Two products may be 93 percent and 94 percent efficient, so it appears that there is little difference, but if the origin is moved to 92 percent and only greater values are displayed graphically, one seems to be twice as efficient as the other, at a much higher price. Seeing is not always believing.

All this and we haven't considered those who are elementary students now and will someday work where math is required. Perhaps at this point the best thing they could know is that math is not a dead subject. We still need pure mathematicians at the top of the heap who work far ahead of applied science. The point is that these new discoveries require mastery of the old.

It will be for another day to explore all the careers that require math. Perhaps for now this will be enough to keep one energetic math class working hard. A good exercise for the class may be to discover other ways we use math in our everyday lives.

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