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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/   
    
Associated Topics:
High School About Math
High School Euclidean/Plane Geometry
High School Geometry

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