Why Learn Geometric Proofs?
Date: 02/27/2002 at 18:44:35 From: Sarah Burdick Subject: Geometric proofs I am writing an analytic paper for my college writing class on how students are taught things that they will 1) never remember and 2) never have any use for in their lives. I believe learning geometric proofs is one of these topics. So my question is, why are we taught geometric proofs if the vast majority of us will never use them?
Date: 02/27/2002 at 22:26:56 From: Doctor Roy Subject: Re: Geometric proofs Hello, Thanks for writing to Dr. Math. The fact that you are writing an analytic paper is proof that geometric proofs are useful. But I'll start with other examples. One could argue that teaching English in high schools is equally useless, as few people use obscure grammar rules in their daily lives (standard American spoken English is a good example). So why do we teach it? Why do we teach foreign languages in schools when the vast majority of people will never have a need to speak a foreign language? Why teach history or science or anything else when the vast majority of people never use the subjects? One simple answer is that you never know when you may need skills you learn in school. For instance, if schooling was about simple rote memorization of facts, we would not really need high schools or universities. We could read almanacs filled cover to cover with all the knowledge we could ever hope to memorize. To become a doctor, one could simply read Gray's anatomy. To become a physicist, one could read a fact sheet about relativity. Of course, this is not the case. The purpose of education is really one of brain-washing, even as early as junior high school or high school. Educational institutions seek to indoctrinate students into different modes of thinking. Most first- year college students expect classes to be rote memorization of facts, equations, etc. However, we hope that students will progress to realize that these facts and figures are really tools to be used in some creative process. Of course, facts and figures are important to anybody in a given profession, but they are not the essential element. The key aspect of higher education is the atmosphere created by several minds concentrating on a few topics. Students develop modes of abstract thinking vastly different from their previous experiences. Of course, the first point is subjective. Students remember or choose not to remember on an individual basis. Some people do not feel the loss heavily. I, for example, am pained that I cannot recall several facts about American history. The second example is simply wrong. You really can never tell when you will use some topic. It is an alarming trend that fewer and fewer people vote. However, ideally, the informed voter will understand key political issues and vote responsibly. This is not possible without an understanding of the electoral process. This, in turn, is based on American history. And the current trend in society is toward the technological. Those who do not have a firm grounding in science and math cannot expect to be in any position to influence any change in such a culture. But back to the point. The idea of an analytical paper is one of analysis. Analysis implies some ordered process, some type of reasoning based on evidence and logic. The notion of logical reasoning is the basis for teaching geometric proofs. If a person can reason through a geometric proof, then he or she can be expected to learn how to reason logically in areas other than math. Often, this is the only exposure most people have to an orderly thinking process. Logical reasoning certainly isn't taught in any of the other traditional high school subjects. And the ability to reason logically is essential to functioning in society. Of course, we aren't usually as rigorous in everyday life, but the concepts are there to be exploited. - Doctor Roy, The Math Forum http://mathforum.org/dr.math/
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