### Have algebra books changed?

Recently I've gotten started with the project of writing algebra worksheets for Spidersmart tutoring company.

To guide me, I have table of contents from one book many of their students are using, plus two algebra 1 books I have at home.

The one is Algebra 1 by Houghton Mifflin, from 1989 & 1986.

The other is Merrill Algebra 1 Applications and Connections by Glencoe / McGraw Hill, 1995 & 1992.

So in essence there's 6 years in between the first publications of these books. But the books are quite different.

I've been wondering if it has been a general trend among algebra books (I don't know), or I just happened to use two very different books.

The first is black-and-white with red, the second is full color and sprinkled with photographs.

But the main difference is how much more advanced mathematically the first book is.

I've been especially looking at the second "chapters" or parts, where both books practice the four basic operations and their properties.

The Houghton Mifflin book talks about axioms and theorems, and proves a few properties of real numbers, such as (a + b) + (−b) = a, or asks the student to supply reasons for steps of proof in proving a(−1) = −a or a(b − c) = ab − ac, and even asks students to do such proofs.

It also has plenty of "easy" calculation exercises, but each lesson also has some more challenging problems, such as proofs.

The latter book has Critical Thinking problems, and easy word problems following the typical calculation problems.

I'm not saying either book is bad; it seems both are well-made, just a little different. However I would guess that axioms and proving are difficult topics for an eight- or ninth-grader.

But did all algebra 1 books used to be that way in the past? Do you know? Is algebra easier today than it was in the past?

Also an interesting phenomenon is that nowadays you don't have to be a prominent textbook author or mathematics professor to write an algebra book.

You've probably heard of Teaching Textbooks - especially designed for homeschoolers. These products supply FULL solutions to EVERY single problem in the book. It's a massive amount of data. So this way a homeschooling parent or student can never get 'stuck' in a problem.

It says on their site that "Teaching Textbooks was founded by two brothers, Shawn and Greg Sabouri (a Harvard graduate and former Harvard math tutor). "

I also recently ran across another Algebra 1 in workbook format written by Christy Walters - apparently a tutor as well.

So while I'm making algebra worksheets, I've kept thinking if I would ever write an algebra book... Not this year for sure. It certainly would be a challenge.

Even while making algebra problems only, I constantly face challenges. I have to constantly think about the order of topics and how they relate to each other, and how mature/advanced or how easy to make the problems to suit today's audience... I don't know. I hope to get feedback on these some day, after they're available.

To guide me, I have table of contents from one book many of their students are using, plus two algebra 1 books I have at home.

The one is Algebra 1 by Houghton Mifflin, from 1989 & 1986.

The other is Merrill Algebra 1 Applications and Connections by Glencoe / McGraw Hill, 1995 & 1992.

So in essence there's 6 years in between the first publications of these books. But the books are quite different.

I've been wondering if it has been a general trend among algebra books (I don't know), or I just happened to use two very different books.

The first is black-and-white with red, the second is full color and sprinkled with photographs.

But the main difference is how much more advanced mathematically the first book is.

I've been especially looking at the second "chapters" or parts, where both books practice the four basic operations and their properties.

The Houghton Mifflin book talks about axioms and theorems, and proves a few properties of real numbers, such as (a + b) + (−b) = a, or asks the student to supply reasons for steps of proof in proving a(−1) = −a or a(b − c) = ab − ac, and even asks students to do such proofs.

It also has plenty of "easy" calculation exercises, but each lesson also has some more challenging problems, such as proofs.

The latter book has Critical Thinking problems, and easy word problems following the typical calculation problems.

I'm not saying either book is bad; it seems both are well-made, just a little different. However I would guess that axioms and proving are difficult topics for an eight- or ninth-grader.

But did all algebra 1 books used to be that way in the past? Do you know? Is algebra easier today than it was in the past?

Also an interesting phenomenon is that nowadays you don't have to be a prominent textbook author or mathematics professor to write an algebra book.

You've probably heard of Teaching Textbooks - especially designed for homeschoolers. These products supply FULL solutions to EVERY single problem in the book. It's a massive amount of data. So this way a homeschooling parent or student can never get 'stuck' in a problem.

It says on their site that "Teaching Textbooks was founded by two brothers, Shawn and Greg Sabouri (a Harvard graduate and former Harvard math tutor). "

I also recently ran across another Algebra 1 in workbook format written by Christy Walters - apparently a tutor as well.

So while I'm making algebra worksheets, I've kept thinking if I would ever write an algebra book... Not this year for sure. It certainly would be a challenge.

Even while making algebra problems only, I constantly face challenges. I have to constantly think about the order of topics and how they relate to each other, and how mature/advanced or how easy to make the problems to suit today's audience... I don't know. I hope to get feedback on these some day, after they're available.