Middle school and high school math texts

[The|M|onster]

This question is aimed primarily towards educators teaching math to grades 7-10. I am a math major doing some research in math education for a summer project I am working on. What are some of the standard texts currently in use for the subjects of pre-algebra, algebra 1, and geometry? Also, what are the "best" texts for teaching these subjects? Again, my question is mainly for teachers, but all responses are appreciated.

 

[qntty]

I'm not a teacher but my high school uses the "Discovering [subject]: An Investigative Approach" series from key curriculum press in some of it's classes

 

[Tobias Funke]

For algebra 1 and 2, we use Martin-Gay's Beginning Algebra and Intermediate Algebra, respectively. I like them because they usually have decent explanations and plenty of examples. However, there is not too much theory and the section on complex numbers is very weak. They're good for average students, although I've found that for many students the book doesn't matter. A lot of them just aren't mature enough to learn from a book.

For Geometry we use some book by Larson (I'm not teaching it this year). I don't care for it too much, but it's probably typical in the sense that everything they ask you to prove is pretty trivial.

The best books, or so I've heard, are Gelfand's.

 

[Howers]

+1

https://www.physicsforums.com/showthread.php?t=307797

 

[symbolipoint]

The|M|onster asked:

Also, what are the "best" texts for teaching these subjects?

Really, the best were written about 20 to 30 years ago. Many of those older ones were not worsely written nor more difficult to study from compared to modern books for Pre-Algebra, Algebra 1, Algebra 2. My impression after reviewing the courses from the older books is that they are less cluttered on each page and easier to understand. Some of the most impressive authors were Wright, Write & New, Lial & Miller, Aufmann, Aufmann & Barker, Drooyan. There also was an author, Dolciani, but I have not found many copies of that author's books and when I did, never bought any. I can't remember the quality of the books of this author so many years after having used them - it's the other authors' books I mention which I had more recent access.

 

[The|M|onster]

I'm not a teacher but my high school uses the "Discovering [subject]: An Investigative Approach" series from key curriculum press in some of it's classes

Thank you, qntty. How do you like using this series of textbooks? Also, how would you rate your own ability as a student and your relative interest in mathematics?

For algebra 1 and 2, we use Martin-Gay's Beginning Algebra and Intermediate Algebra, respectively. I like them because they usually have decent explanations and plenty of examples. However, there is not too much theory and the section on complex numbers is very weak. They're good for average students, although I've found that for many students the book doesn't matter. A lot of them just aren't mature enough to learn from a book.

For Geometry we use some book by Larson (I'm not teaching it this year). I don't care for it too much, but it's probably typical in the sense that everything they ask you to prove is pretty trivial.

The best books, or so I've heard, are Gelfand's.

Thank you very much, Tobias. Do you know if the texts by Martin-Gay are standard nationwide or not? If not, do you know if there is a text that sees to dominate across the country? I do not know very much about what is used in middle school and high school curriculum as my focus has always been on pure math. However, I think I need a change of pace during the summer break, which is why I'm looking into math education.

+1

https://www.physicsforums.com/showthread.php?t=307797

Thanks, Howers! That's exactly the type of thread I tried searching for earlier. It's a big help.

The|M|onster asked:


Really, the best were written about 20 to 30 years ago. Many of those older ones were not worsely written nor more difficult to study from compared to modern books for Pre-Algebra, Algebra 1, Algebra 2. My impression after reviewing the courses from the older books is that they are less cluttered on each page and easier to understand. Some of the most impressive authors were Wright, Write & New, Lial & Miller, Aufmann, Aufmann & Barker, Drooyan. There also was an author, Dolciani, but I have not found many copies of that author's books and when I did, never bought any. I can't remember the quality of the books of this author so many years after having used them - it's the other authors' books I mention which I had more recent access.

Yeah, I sort of figured that the quality of older books would be much better than what is currently out. Unfortunately, I want to target current high school students using newer texts. But I will definitely check out the authors you recommended, symbolipoint, because one thing I would really like to do is compare and contrast current and older texts to see why the quality seems to have deteriorated.

 

[yeongil]

Thank you very much, Tobias. Do you know if the texts by Martin-Gay are standard nationwide or not? If not, do you know if there is a text that sees to dominate across the country? I do not know very much about what is used in middle school and high school curriculum as my focus has always been on pure math. However, I think I need a change of pace during the summer break, which is why I'm looking into math education.

The Martin-Gay books IIRC are college textbooks for remedial courses, so I doubt that they are standard nationwide. I would imagine that books from the following companies are used more often in high schools:

http://holtmcdougal.hmhco.com/hm/series.htm?l1c=3&level2Code=AG"
http://www.pearsonschool.com/index....utionid=&PMDbCategoryid=806&&filter_423=6732"
http://www.glencoe.com/catalog/index.php/catalog?c=1670&v="

Go http://mathematicallycorrect.com/algebra.htm" to see some reviews of Algebra I textbooks by Mathematically Correct.

I'm also a member of a homeschooling forum (though I don't have any children, go figure), and the most popular Algebra I books by homeschooling moms are the following:
http://high school.bfwpub.com/high school/newcatalog.aspx?disc=HS&course=Mathematics&type=Algebra&isbn=0716710471"
http://www.pearsonschool.com/index....6&PMDbSubcategoryid=933&&PMDbProgramID=21021"
http://holtmcdougal.hmhco.com/hm/detail.htm?ID=1005500000030772"
http://www.pearsonhighered.com/educator/academic/product/0,3110,0321557131,00.html" (note that this is a college book for remedial courses)01

 

[symbolipoint]

yeongil,

What opinion if any do you have about the Dolciani book of Algebra that you listed? My guess is that is it good or better, probably a good choice - just based on experience when I was a student at that level.

Is "Lial", the same author who made the various Algebra books, sometimes with "Miller" during several years of the past? If this is the same Lial, then I would say those books are at least good or better, just based on association with past textbooks by the author.

 

[symbolipoint]

yeongil,
Would you tell us what homeschooling forum you read?

 

[yeongil]

What opinion if any do you have about the Dolciani book of Algebra that you listed? My guess is that is it good or better, probably a good choice - just based on experience when I was a student at that level.

I find the Dolciani books very solid and thorough. I used them for Algebra 1 and Algebra 2 when I was a student. However, I understand that the earlier editions (1960's) were even more rigorous, more challenging, and more abstract.

yeongil,
Would you tell us what homeschooling forum you read?

Sure, it's http://www.welltrainedmind.com/forums/index.php" . I only read their high-school subforum, though.


01

 

[The|M|onster]

This is great. Thank you, yeongil, the list of the big suppliers is very much appreciated. You mentioned Jacobs Algebra book as a top choice for home schoolers. This book also came up in the link Howers posted. Is Jacobs geometry text, Geometry: Seeing, Doing, Understanding just as popular?

Also, is there a place where I could obtain a 60's copy of Dolciani? I would like to get a copy of the newest version as well so I can see exactly what rigor was lost.

Also, does anyone have experience with Serge Lang's book Geometry that he co-wrote with Gene Murrow?

 

[Howers]

This is great. Thank you, yeongil, the list of the big suppliers is very much appreciated. You mentioned Jacobs Algebra book as a top choice for home schoolers. This book also came up in the link Howers posted. Is Jacobs geometry text, Geometry: Seeing, Doing, Understanding just as popular?

Also, is there a place where I could obtain a 60's copy of Dolciani? I would like to get a copy of the newest version as well so I can see exactly what rigor was lost.

Jacobs is definitely the homeschooling choice as is Saxon, but Jacobs is much more preferred by students and teachers. I was hesitant to bring it up at all because it is not a standard book you'd see in high schools these days. I'm in Canada, and here the books are sort of made by the government and MG. Therefore I don't know what books are used in US schools outside of a few I've seen and well, found awful.

Jacobs Algebra is good because the reading is short and to the point, and the exercises are your routine ones. It explains algebra really well and all concepts are explained intuitevly. Its ideal for a first exposure to algebra. Regarding geometry, the seeing/doing one is the third edition. It is significantly dumbed down. Proofs are omitted, the proof exercises have way too much hand holding, and its too colorful. Its still a good book if the focus of your class is not on rigor. But I would try to get the 2nd edition if you can, although at the quantity you need I don't think that will be possible.

In conclusion, I think Jacobs meets your criteria for algebra: it is modern, includes everything from pre-algebra to quadratic equations, with chapers on sequences and inequalities. I've had great success teaching it to grades 7-9. My only criticisms are that its a little on the easy side and some sections should be removed. Geometry is very good if you can find 2nd editions, but because that is out of print you might need to look elsewhere.

 

[The|M|onster]

wow, proofs omitted from a geometry text seems like sacrilege. However, I would actually only need two copies of the textbook so it may be feasible to try to find the 2nd edition.

 

[Howers]

I guess I sort of said they are omitted :p

I didn't mean all of them. Proofs are still there. But some have been removed. The exercises are also much easier now, because in proofs he basically tells you what to do. Overall its a lot more application driven rather than axiomatic, which kind of defeats the purpose of geometry.

 

[The|M|onster]

It's good to hear not all the proofs have been taken out. I'll probably look for a 2nd edition before I look at the newest one. What is the consensus on this book:

https://www.amazon.com/dp/071672426X/?tag=pfamazon01-20

and would it have material that would be suitable for grades 7-10?

 

[Howers]

It's good to hear not all the proofs have been taken out. I'll probably look for a 2nd edition before I look at the newest one. What is the consensus on this book:

https://www.amazon.com/dp/071672426X/?tag=pfamazon01-20

and would it have material that would be suitable for grades 7-10?

I haven't read all of it but from what I remember, its a book that teaches basic algebra and discreet math (ie. combinatorics, probability, some geometry, some modern math). Its real purpose is to spark interest in math by showing real life examples, rather than teach any kind of high school course. Depending on what kind of course you are planning to teach, and what kind of students you have, it could be either good or bad. I would recommend knowing some algebra before doing it though. On the whole, its kind of like an algebra II / precalculus book at an easy level.