Most math classes present the subject as a series of isolated, increasingly complex problems. Students who answer the difficult problems the quickest get rewards from the teacher. The rest develop a sense of failure, and fall into the ranks of the mathematical illiterate.
In the real world, mathematics plays a completely different role. Problems no longer exist in isolation. Real world problems are usually part of a broader context. If you choose to become a geneticist, you will spend most of your time learning to master the mathematical description of DNA. If you hawk hot dogs from a street corner, you will need to throw a great deal of effort into counting change and making sure the books balance. Day to day mathematics is part of a larger system.
In most real world situations, you will find that the individual problems are not that terribly difficult. They usually exist within a definable mathematical model—a model in which the same problem is repeated multiple times. In these situations, the challenge resides in defining an efficient mathematical model.
Professional mathematician spend most of their time honing models, and not on the grunt work of solving problems. In the computer age, we are very fortunate to have small electronic beasts sitting on our desk tops that are happy to perform the grunt work. A smart person will take advantage of these devices. Humans get to work on a higher level. They examine information, and work on developing the meta logic that describes the system.
Mathematics at this higher level is far more interesting that the grunt work. At this higher level, people get to think in broader terms, and make greater use of their imaginations than in the problem solving scenarios given in math class. Real world mathematics is much closer to an art form than a pure science. A mathematician who masters this ability to create models will start to see the aesthetic beauty of a well designed work.
Which brings me to the most important distinction between mathematics in a classroom and mathematics in a real. In the classroom, students compete with each other. The do their homework on their own, and take tests in isolation.
In the real world, people do not work in isolation. They work in companies and broader communities. In these communities, the ability to work with others and communicate your findings is far more important than problem solving skills. A clever solution means very little unless it adds to the broader context of the organization.
Developing this ability to communicate your ideas is often far more difficult than learning the problem solving skills. To communicate you need to learn how to interact with your audience. Being the smartest kid in the class means everything in school, but means squat in a conference room when you have not developed the skills to communicate your ideas.
The goal of descriptive mathematics is to focus on the two issues of creating mathematical models and in using mathematics to communicate ideas. Since I work as a computer programmer; so I will spend a good deal of time working on ways to use computers and telecommunications to help in these two efforts.
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