It seems that most people misunderstand
the real purpose of mathematics in higher education. Sure, math
is valuable to scientists, engineers and math teachers. Technologically,
we'd still be stuck in the Middle Ages were it not for the graphing
on the *x* - *y* plane that people begin to learn in
their first algebra. The United States has the most and best mathematicians
in the world, which has helped our country lead in high-tech innovation.
About a hundred years ago the application of mathematics to aiming
naval guns made the U.S. a world power.

But most students will not become scientists, engineers or mathematicians, and they won't even consciously use algebra in their careers! Math skills above arithmetic have no meaningful value to most people and are eventually, if not soon, forgotten. So why bother?

Higher education traces its
roots all the way back to Socrates. Until specialization took
root about a hundred years ago higher education consisted of studying
the *liberal arts*. The list varied by time and place, but
the liberal arts normally included languages, literature, philosophy,
sciences and, invariably, mathematics. Mathematics has held a
prominent role in higher education from the very start. Why has
the accumulated wisdom of centuries held math as one of the key
ingredients in producing the educated person?

The educational purpose of high school is acquisition of sufficient knowledge to produce productive citizens. Acquiring knowledge still plays an important role in higher education, but the emphasis now shifts to learning how to think. That is why college degrees are valued. Earning a degree demonstrates that you have followed through on completing a challenging long-term commitment and have experience at concrete and abstract thinking, and creative problem solving.

Let's survey the *how to
think* roles of several subject areas. (Beware, these are the
opinions of the author, who is a mathematician.)

In English Composition you learn how to communicate in the written form. In order to write clearly you must be able to think clearly and organize your thoughts.

In Literature you learn how to analyze the written word and uncover the great thoughts of perceptive writers.

In History you learn why people and societies made decisions leading to important events. Understanding this helps society learn from experience.

In Science you learn scientific, deductive and inductive reasoning.

In Economics you learn how people communicate wants and needs through financial transactions, and how certain patterns or policies affect the whole.

In Humanities you learn to how to appreciate and discriminate between different forms and eras of the visual and performing arts, and how these are greatly influenced by culture.

Superficially, it may appear that your math classes are all about learning a laundry list of math skills, learning acceptable techniques on how to manipulate numbers and symbols in order to solve problems. But learning all this stuff provides valuable experience at an important form of thinking, analytical thinking. This is learning how to dissect problems into their key ingredients, processing this information, then arriving at insights or conclusions in an orderly, rational way.

For example, when you are given a math problem to solve you must be able to recognize the key processes at work in the problem, and then draw from your knowledge and experience the appropriate methods to solve the problem. In essence, this is analytical thinking.

Almost every aspect of mathematics flows from logical thinking applied to mathematical ideas. (The only rare exceptions are the issues mathematical language, such as in what order we perform calculations from an expression.) Anything you can learn about such logical thinking will help you become a better thinker. It is so important to focus on the "why" questions about mathematics. These are the concepts of mathematics, and learning them will help you do much better and improve your speed.

The experience gained from intense practice at analytical thinking in math courses will help you to better analyze problems and solve problems in real life. It may be a little hard for you to appreciate that or even to believe that at this point, but wise educators through the centuries consistently kept mathematics as one of the core elements in producing good, well-rounded thinkers able to handle responsibility. In the past century colleges diversified their degree offerings into many specialties, so some math courses have been tailored to fit these specialties to further give examples of how math can be used to analyze within those specialties.

Here's a dirty little secret about math skills. No one really cares if you have them. Computers and even very sophisticated calculators can do about any math manipulation, and they do so more quickly and accurately than any human. If taking math was only about acquiring math skills then it would be pointless to do so. But computers cannot think, reason and analyze like humans.

So math is required in college because you need to learn how to think at deeper, more effective levels, and like almost anything else, that requires practice. And you will learn other ways to think in other subject areas.

*To contact the author by e-mail click on this link: Jon Davidson*