1. ## Geometric Proofs

There are two types of geometric proofs:

1. Direct
2. Indirect

Both direct and indirect geometric proofs make zero sense to me. I did have to worry about proofs in high school because most of classes were remedial. I took MODIFIED courses except for gym and art. In terms of art, I took regular classes but ended up taking a modified art state exam as a prerequisite for high school graduation.

Anyway, back to geometric proofs.
Four questions for you:

1. Why is the study of geometric proofs needed at the high school level?

2. If you took geometric proofs in high school, how well did you do?

3. Are you familiar with the STATEMENT VS. REASON method of geometric proofs?

4. What is the basic difference between direct and indirect geometric proofs?

As far as I am concerned, I care more about "regular" geometry questions than I do proofs. For example, if I can find the perimeter and area of shapes, the circumference of a circle, the arc length of a circle, etc, this is more valuable and important to me. What do you say?

2. ## Re: Geometric Proofs

Originally Posted by harpazo
There are two types of geometric proofs:

1. Direct
2. Indirect

Both direct and indirect geometric proofs make zero sense to me. I did have to worry about proofs in high school because most of classes were remedial. I took MODIFIED courses except for gym and art. In terms of art, I took regular classes but ended up taking a modified art state exam as a prerequisite for high school graduation.

Anyway, back to geometric proofs.
Four questions for you:

1. Why is the study of geometric proofs needed at the high school level?

2. If you took geometric proofs in high school, how well did you do?

3. Are you familiar with the STATEMENT VS. REASON method of geometric proofs?

4. What is the basic difference between direct and indirect geometric proofs?

As far as I am concerned, I care more about "regular" geometry questions than I do proofs. For example, if I can find the perimeter and area of shapes, the circumference of a circle, the arc length of a circle, etc, this is more valuable and important to me. What do you say?
You're missing the major point of the teaching of Geometry. It isn't just to draw pretty pictures or poke holes in your paper. It is to teach you to THINK LOGICALLY and SYSTEMATICALLY. It is the PROOF that is most beneficial in teaching this. The most important realization, in my opinion, is that there are many ways to think, but many of those ways do not result in logical and consistent results. For those not disposed toward Linear Thinking, it is your chance to learn this foreign language. Many a geometry student has groused and sputtered at the course as it is the first they have encountered where memorization and repetition simply are not sufficient. The student must learn to THINK!

I believe you have exposed your admitted impediment with mathematics. Linear Thinking is a foreign language to you. Maybe that is where you should begin your studies. Stop trying to dive into things that don't make natural sense to you (translating problems into algebra expressions). Stop trying to do easy things that interest you ("perimeter and area of shapes...more important to me"). Find a High School geometry book and do EVERY PROOF in the book! This is likely to give you the background you are missing. You must learn to THINK DIFFERENTLY than you do. If you have a desire to learn anything of mathematics, the most important thing, in my opinion, is to learn to think linearly. I am NOT saying that you should abandon how you normally think. Just learn that at times in your life, the linear and logical path will be of more benefit to you than any other kind of thinking. Whatever your natural style of thinking, please bring it with you, but do not for a moment believe that just one way of thinking will do.

Having said that, let's recall this:

You are surprised at my working simultaneously in literature and in mathematics. Many people who have never had occasion to learn what mathematics is confuse it with arithmetic and consider it a dry and arid science. In actual fact it is the science which demands the utmost imagination. One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit. It goes without saying that to understand the truth of this statement one must repudiate the old prejudice by which poets are supposed to fabricate what does not exist, and that imagination is the same as “making things up”. It seems to me that the poet must see what others do not see, and see more deeply than other people. And the mathematician must do the same.
— Sofia Kovalevskaya

** End of Philosophy Lesson **

3. ## Re: Geometric Proofs

Originally Posted by TKHunny
You're missing the major point of the teaching of Geometry. It isn't just to draw pretty pictures or poke holes in your paper. It is to teach you to THINK LOGICALLY and SYSTEMATICALLY. It is the PROOF that is most beneficial in teaching this. The most important realization, in my opinion, is that there are many ways to think, but many of those ways do not result in logical and consistent results. For those not disposed toward Linear Thinking, it is your chance to learn this foreign language. Many a geometry student has groused and sputtered at the course as it is the first they have encountered where memorization and repetition simply are not sufficient. The student must learn to THINK!

I believe you have exposed your admitted impediment with mathematics. Linear Thinking is a foreign language to you. Maybe that is where you should begin your studies. Stop trying to dive into things that don't make natural sense to you (translating problems into algebra expressions). Stop trying to do easy things that interest you ("perimeter and area of shapes...more important to me"). Find a High School geometry book and do EVERY PROOF in the book! This is likely to give you the background you are missing. You must learn to THINK DIFFERENTLY than you do. If you have a desire to learn anything of mathematics, the most important thing, in my opinion, is to learn to think linearly. I am NOT saying that you should abandon how you normally think. Just learn that at times in your life, the linear and logical path will be of more benefit to you than any other kind of thinking. Whatever your natural style of thinking, please bring it with you, but do not for a moment believe that just one way of thinking will do.

Having said that, let's recall this:

You are surprised at my working simultaneously in literature and in mathematics. Many people who have never had occasion to learn what mathematics is confuse it with arithmetic and consider it a dry and arid science. In actual fact it is the science which demands the utmost imagination. One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit. It goes without saying that to understand the truth of this statement one must repudiate the old prejudice by which poets are supposed to fabricate what does not exist, and that imagination is the same as “making things up”. It seems to me that the poet must see what others do not see, and see more deeply than other people. And the mathematician must do the same.
— Sofia Kovalevskaya

** End of Philosophy Lesson **
I plan to learn the basic of geometric proofs in the near future but right now, I am reviewing/studying algebra applications. I understand what you said about linear thinking but tackling many ideas at the same time leads to additional confusion.