What is a good geometry textbook that teaches proofs?

[happycc]

I know there is a number of geometry texts out there and some are really good and some are really bad. Some are homeschool friendly and some are not. Some teaches proofs and some don't. I would like a good homeschool friendly geometry textbook that teaches proofs.

[regentrude]

We love Art of Problem Solving. It proves everything and it is easy to use for homeschoolers, but it is designed for strong math students who thrive with a discovery based approach and will not be a good fit for all students.

[Julie of KY]

I also love Art of Problem Solving, but agree that it is not for most students. It teaches proofs as a paragraph explanation style rather than two column proofs that some people are looking for.

[happycc]

Any textbook that teaches with a two column proof?

[WishboneDawn]

I just ordered Harold Jacob's Geometry for next year. From what I've read it's a good text for a self-directed student. I bought the second edition rather then the current third because the third is lighter on proofs. My daughter enjoys math but the doing of it rather then the discovery part so I'm hoping it will be a good fit. Foerster's Algebra 1 has been an absolutely perfect for her.

[Arcadia]

Any textbook that teaches with a two column proof?

 

California Geometry: Concepts, Skills and Problem Solving does cover two column proofs. It is a 9th grade geometry textbook in some school districts (call number J516 California).

ETA: California Geometry, Holt 2008 (ISBN:978-0-03-092345-6) covers two column proofs too and satisfy UC A-G requirements.

McDougal Littell Geometry California 2007 (516 Larson) does as well.

[HS Mom in NC]

My husband used Jacob's Geometry with Euclid's Elements to teach our older two girls. I used Martin Cothran's logic books from Memoira Press (Traditional Logic 1 and 2, Material Logic and Rhetoric) while they were doing proofs in Geometry-they both specifically said the logic books and geometry books reinforced each other for the thinking required to do proofs.

[quark]

 

Jurgensen's Geometry teaches the 2 column format.

[AK_Mom4]

Saxon Geometry is very good as well. Definitely homeschool friendly and DVD lectures are available.

[Farmgirl70]

We've used both Teaching Textbooks and Jacobs' Geometry. I found both of them to be easy to use at home and effective. Both have proofs.

 

Jacobs' took a little more time investment from me, which is why, with #3, we chose to go with Teaching Textbooks this time. I simply don't want to teach Geometry again. I'm more of a back-up with Teaching Textbooks. So, either is a good resource, in my opinion. Good luck!

[Candid]

I also love Art of Problem Solving, but agree that it is not for most students. It teaches proofs as a paragraph explanation style rather than two column proofs that some people are looking for.

 

 

Singapore's NEM series does this sort of thing as well. They usually do it as part of a "classroom exercise."

 

I've read that two column proofs are not what real mathematicians use: http://www.maa.org/devlin/lockhartslament.pdf

[regentrude]

There is no need to squeeze proofs into the "two column" format. It is a teaching tool, makes proofs easier to grade (which I suspect is why it is so popular in public schools) - but there is no reason why this particular format should be preferable over a narrative proof. Proving is important, but drilling the two column format is not.

Mathematicians do not use two column proofs, and proofs in higher math courses are not in this format either.

[regentrude]

I've read that two column proofs are not what real mathematicians use: http://www.maa.org/d...hartslament.pdf

 

THANKS for posting the link to this wonderful piece about mathematics!

If you are pressed for time: p.21 deals with the "two column proof" in a very succinct and blunt manner.

I love this guy.

[Teachin'Mine]

Another vote for Jurgensen's. They teach the two column proof and paragraph proofs. The teaching and level of rigor of the text is excellent. The solutions manual is more like an answer key. The problem with proofs is that there's often several correct ways to approach the proof, but only one way is listed for each "solution". But this is a problem you will find with most geometry texts, so it helps to have some geometry background when checking over the work. The consolation is that the year of geometry is followed by Algebra 2 where once again there will usually be only one right answer.

[Maureen]

What a great article! Thanks for posting Candid.

[Susan of Croton]

_{Regentrude, does the AOPS style of instruction, in your family's experience, develop the "creative" side of math problem-solving? Secondly, are the students able to solve problems using the traditional formulae and techniques as well? Forgive my ignorance of this program. I would want to develop the creative side of math problem solving while also being able to perform ordinary problems. We use NEM from Singapore.}

[regentrude]

_{Regentrude, does the AOPS style of instruction, in your family's experience, develop the "creative" side of math problem-solving? Secondly, are the students able to solve problems using the traditional formulae and techniques as well? Forgive my ignorance of this program. I would want to develop the creative side of math problem solving while also being able to perform ordinary problems. We use NEM from Singapore.}

 

 

Developing creative problem solving is definitely the strength of the program. And if the student has learned to THINK about math, can solve complex problems and understand why an approach works, of course he can also solve simple, ordinary straight forward ones.

[happycc]

Well then I guess I will teach both ways in case my kids end up in school. Sigh!

[jennynd]

What is 2 column proof.? I don't think I have ever see it. Is that "required" in US high school?

 

[regentrude]

What is 2 column proof.? I don't think I have ever see it. Is that "required" in US high school?

 

I have never seen one either in my entire math education; in my home country we use the paragraph format. Seems to be a US thing.

(I have never written a five paragraph essay either).

 

If you click on the link to Lockhart's Lament in this thread and scroll to page 21, you'll find an example. Pretty self-explaining: one column has the statement, the other the reason why the statement is true (given, xyz theorem, whatever)

[Arcadia]

What is 2 column proof.? I don't think I have ever see it. Is that "required" in US high school?

 

There are a few ways to do proofs. I had not done 2 column proof or paragraph essay proof. Page 19 and 21 of the pdf are examples of 2 column proof. It is easy to write a proof in that format if required to. Any school textbook has the 2 column proof chapter/unit if you want to see more examples.

[Arcadia]

Well then I guess I will teach both ways in case my kids end up in school. Sigh!

 

As long as your kids know the axioms/theorems/ postulates, it would take less than a morning to teach them to write in the 2 column format. I won't worry about the format so much but concentrate on the understanding of geometry.

[Luckymama]

Let me tell you, after going through geometry with two-column proofs three times (me+2 kids), I find paragraph proofs with youngest dd to be so easy------simple and intuitive.

[Candid]

_{Regentrude, does the AOPS style of instruction, in your family's experience, develop the "creative" side of math problem-solving? Secondly, are the students able to solve problems using the traditional formulae and techniques as well? Forgive my ignorance of this program. I would want to develop the creative side of math problem solving while also being able to perform ordinary problems. We use NEM from Singapore.}

 

If you read the whole essay I posted you'll see that he doesn't think many math programs do this. I can tell you my husband graduated with a math degree but knew his junior year of college he was not a mathematician. If you read the essay, Lockart refers to people not learning this until graduate school.

 

I say this because my oldest is doing great with AoPS this year, but I have strong doubts about his true mathematical skill set. Like both his dad and I he is not creative in that way.

 

I think what AoPS can do is give those who do have this skill a breath of what math can be. But teaching it to those who don't have it, I'm not sure you can.

 

This does not mean that someone who doesn't have this skill can't be a fantastic engineer, etc. Just not a theoretical mathematician.

[Pamela in VA]

I didn't see anyone recommend Holt Geometry 2007, but I am very pleased with it. It teaches traditional 2-column proofs, paragraph proofs, and flow chart proofs. We use either the 2-column or abbreviated paragraph proofs. Alot of times, I just have ds explain his reasoning to me and not necessarily write it down. I'm following Jann's suggestions and use the One-Stop Planner to generate worksheets and tests. It is very nicely laid out and there is a ton to choose from.

 

Note: It is a bit expensive.

 

Good Luck!

Pamela F.

[Pamela in VA]

I didn't see anyone recommend Holt Geometry 2007, but I am very pleased with it. It teaches traditional 2-column proofs, paragraph proofs, and flow chart proofs. We use either the 2-column or abbreviated paragraph proofs. Alot of times, I just have ds explain his reasoning to me and not necessarily write it down. I'm following Jann's suggestions and use the One-Stop Planner to generate worksheets and tests. It is very nicely laid out and there is a ton to choose from.

 

Note: It is a bit expensive.

 

Good Luck!

Pamela F.