Customer Reviews

Algebra I: Expressions, Equations, and Applications

5 star:		(11)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

I searched long and hard for a text like this. It is well organized, well illustrated, and has plenty of example and practice problems with solutions to odd problems found in the back of the book. It is not like some of the newer algebra texts, which take an inductive approach and rely on "group discovery" of mathematical concepts. It delivers a thorough explanation of concepts in a logical and intuitive fashion, and proceeds at a deliberate pace that ensures a mastery of each concept before moving on to the next.

As a home schooling resource:
I use this for home schooling. It explains things so well that my 12 yr. old daughter is able to read a section and work the homework problems with little or no help from me. I supplement it with more drill and explanation found in the Key to Algebra workbooks from Key Press Curriculum. We proceed at a comfortable pace and have covered the first six chapters in one year. I plan to use Geometer's Sketchpad (also from Key Press Curriculum) as a supplemental graphing tool beginning in chapter seven.

I don't mean to infer that home school parents with no knowledge of algebra can successfully use this book. It does not have a teacher's guide and one probably is not appropriate. As with any home school scenario, you will need to understand the topic yourself so that you can answer questions. I far prefer this text to Saxon and other texts designed for home school use.

I spent over a year looking for a good algebra textbook and was surprised and disturbed to find that most are poor examples of how to explain a concept to a student. This book stands out as a wonderful exception. Compared to other algebra texts, it beats all I have found hands down.

Here is the table of contents:
1 Expressions and Equations
2 Operations with Negative Numbers
3 Distributing: Axioms and Other Properties
4 Harder Equations
5 Some Operations with Polynomials and Radicals
6 Quadratic Equations
7 Expressions and Equations Containing Two Variables
8 Linear Function, Scattered Data, and Probability
9 Properties of Exponents
10 More Operations with Polynomials
11 Rational Algebraic Expressions
12 Radical Algebraic Expressions
13 Inequalities
14 Functions and Advanced Topics

Foerster's text provides the student with a strong foundation in algebra. Topics are introduced incrementally. Before Foerster introduces a new idea, he first makes sure that the reader has a strong understanding of the concepts on which the new idea is based. His exposition, which can seem pedantic at times, is clear and effective. The numerous examples he provides are explained in painstaking detail. He also warns the reader of potential pitfalls. The exercises are designed to build both the reader's algebra skills and conceptual understanding. Each chapter concludes with a section in which the reader applies the material learned in the chapter to real world problems. This material, which is a particular strength of the text, demonstrates how and why algebra is used.

The book begins with basic algebraic concepts that are sometimes covered in pre-algebra classes. Those concepts include operations on numbers, variables, constants, algebraic expressions and equations, signed numbers, and the rules of algebra such as the commutative, associative, and distributive laws.

Foerster then discusses linear equations in one variable. Rather than discussing equations of lines next, as many authors do, he defers that topic in order to cover operations on polynomials. That allows him to discuss quadratic equations before the midterm review. While he later discusses how to factor by grouping, in this chapter he treats the factoring of quadratic polynomials as a series of special cases. The chapter concludes with a discussion of the quadratic formula, the derivation of which he leaves as an exercise. If this book has a weakness, it is that Foerster teaches you how to do algebra without always justifying the methods he uses.

Following the midterm review, Foerster discusses equations of lines and systems of linear equations. This leads to a brief discussion of probability and statistics. Probability is revisited in the exercises later in the text.

The following chapters address exponents, operations on polynomials, rational expressions and equations, radical expressions and equations, and inequalities. The last chapter, which is followed by a final review, introduces concepts such as functions and right triangle trigonometry that are explored in more advanced algebra classes. The final sections of this chapter, which address quadratic inequalities, provide a capstone to the text because they tie together many of the concepts introduced earlier.

The exercises, which are numerous, vary from drills designed to develop the reader's facility with a particular type of algebraic manipulation to challenging application problems. For instance, Foerster poses the following problem: In some states, your state tax is based on your net income after your federal tax has been deducted and your federal tax is based on your net income after your state tax has been deducted. How do you determine how much tax you owe each entity if the tax you owe depends on the amount being collected by the other entity? The difficulty of the problems Foerster poses makes this text suitable for an honors course.

The text is quite comprehensive, discussing topics not found in other texts. For instance, one topic he introduces is a system comprised of a linear equation and a linear inequality. As is the case with other topics, he also introduces applications of such systems. Consequently, there is more material here than can comfortably be covered in one year. Instructors will need to be selective in their choice of topics. However, the text's clear exposition, detailed examples, and the provision of answers to the odd-number exercises make it suitable for self-study.

A less challenging alternative to this text is Harold R. Jacobs' Elementary Algebra. It is engagingly written, provides a strong foundation in algebra, and will not overwhelm the average student.

Until I met Mr. Foerster, I thought I desperately hated math. I scored well in it, yet I just hated the whole subject.

Mr. Foerster is truly an inspiring man; the whole high school was in awe of him. His courses were reputed to be extremely tough. But the hallway gossip was soon dispelled. Although Algebra isn't always "easy", I was quite surprised and delighted to discover that Mr. Foerster's classes - and especially his textbooks - were extremely user-friendly! Mr. Foerster writes clearly, and is able to address Algebra from the beginning, rather than talking several levels over students' heads. His kindness, humor, and gentle personality show through in the books. Wow! Math is fun after all!

I am now homeschooling my three kids, and Foerster's books are the texts of choice in this family.

I am a Math major and I have tutored Algebra for many years. This is the best text I have ever seen from a wide range of both public and private schools in my area. I am ordering a personal copy to have on my reference shelf. The text is extremely thorough and not at all watered down (as many of the texts I have recently seen). It covers each topic completely and in depth. An ample set of problems is given and the author builds the student up to the challenge of more difficult problems. Word problems are written with a sense of humor that even gets a chuckle from the eighth grade boys. This author strives to develop an Excellent student not just an adequete student. Highly recommended.

We homeschool most of our children. I search carefully to find school materials that I believe are of high caliber. When algebra appeared on the teaching horizon, I read reviews of Mr. Foerster's algebra texts from both the homeschooling press and from the public/private school sectors. Having read nothing negative about this textbook, I went ahead and purchased the textbook, teacher's guide, and tests. I could not have chosen a better textbook for my son! As a ninth grader, he worked his way through the textbook completely, asking for assistance only a handful of times. The explainations are clear, and the range of problems assigned is both wide and in-depth. My son made an "A" in the course (on the 90-100 scale), despite my "picky" grading. I will not use Mr. Foerster's textbook with my next-down son, because mathematics is difficult for him. But I recommend the book unreservedly for anyone who is comfortable with math.

Our school district has misguidedly adapted one of those fuzzy math curriculums, and I have chosen to teach my mathematically talented daughter at home rather than have her lose her love of math entirely. This book has made the job easier! Clear, elegant reasoning that doesn't skimp on rigor, plus problem solving with a humorous bent. It also covers all of the topics that I think "should" be covered. I am not finding the lack of a teacher's guide to be a problem, however, I do have a strong math background. I compared several math books before settling on this one. A close second, or maybe first, depending on your taste, is the Houghton Mifflin Algebra text. I have both, and sometimes it is enlightening to a non-teacher to see the different ways material can be presented.

I had no particular affinity and no particular aptitude for mathematics when I first embarked on this book. Note that I said "had." After nearing completion of this book, not only is my mathematical ability greater than ever before, but so is my liking of mathematics. The vast majority of math textbook authors have a penchant for teaching math as nothing more than a horrid compendium of formulas (a glaring example of this banal pedagogy is the Saxon math series). Little wonder then that most students find math dreadfully boring.

Paul Foerster takes a delightfully different approach. In this gem of a book, mathematics is not merely something to be memorized, but something to be digested and savored - and most importantly, understood. Consider the addition property of equality, that is, if a, b, and c are real numbers, and a = b then a + c = b + c. Simple enough. Yet in the Algebra 2 Saxon text, John Saxon writes that "it is important to understand why we do things in Algebra, but it is also important not to let the emphasis on understanding interfere with our ability to do." And then he proceeds to illustrate his point by giving a very shallow presentation of this very simple - and very important - property of mathematics. He simply tells students - literally - "change sides, change signs." Paul Foerster, however, writes that "a transformation such as adding 3 to each member can be thought of as adding equal weights to both sides of a balance. If it was balanced before, it will still balance afterward. But if you add weight to only ONE side, it no longer balances!" And then he follows by giving a pictorial representation of what he means.

Again, a very simple, almost trivial example, but it represents one of the fundamental differences between Foerster's pedagogy and the pedagogy of the vast majority of textbook authors. Here's another example. Consider the definition of negative exponents. x^-3 is defined as 1/x^3. Saxon tells students that there is nothing to understand about this because it's merely the result of a definition. What he fails to tells students is that this is the only LOGICAL definition of a negative exponent, and is NOT merely arbitrary or conventional. Foerster, however, explains the logic behind the definition of a negative exponent and shows how it follows NECESSARILY from the ratio of two positive exponents. For example, if you go from top to bottom in this following expression, you go x^3/x^4 --> xxx/xxxx --> 1/x (you've cancelled all the other x's); however, if you go from bottom to top, you end up with x^-1, but negative exponents are meaningless, so we are FORCED to define x^-1 as 1/x^1 = 1/x.

Foerster thus shows that mathematics is a LOGICAL system, that it makes *sense*, and that it is *not* just a collection of formulas to be memorized, whereas Saxon - along with most authors - does quite the opposite.

Some parents and some students might opt for another text because this text has some challenging problems. But if you **carefully** read his explanations, the challenge problems instead of becoming the rough meat of a meal, become the delicious desert that follows it. Rest assured that there is no challenge problem in his book that cannot be deduced from Foerster's explanations. In fact, I even wish more such problems were included!

Foerster's books *will* prepare you for the rigors of any acclaimed college math program (e.g. Harvard, MIT, Cal Tech); you cannot go wrong with Foerster.

This book is wonderful. Not only can I use it every day, the explanations and methods covered by this text are exemplary. My entire district now uses this book, and we have had nothing but success with it. Five Stars!

I am a mother simply trying to help out my 9th grader to to better in algebra I. I saw that this algebra book was rated pretty well on amazon, so decided to buy this book used. In a nutshell, the reviews were indeed accurate. This is a very good beginning Algebra book to have on hand. If you think equations are complex and difficult, this book goes step-by-step in explaining those equations. The book explains concepts very easily for my 9th grader to comprehend, and so far no complaints. I sure wish daughter's school would buy this book for the 9th grade class, as both my daughter and some of her friends in this same algebra class have been using this one book to study from. If several kids in this class turn to this one book for guidance, then you know it must be pretty good. Saxon math book writers should take lessons from this math teacher's algebra I book on how to explain concepts, for sure!

This book was recommended through a web site that selects books by clear and concise instruction. We have just started with the lessons and find it to be an easy way to introduce algebra to a student who has not had pre-algebra. You do not have to have the teachers book if you assign the odd numbered problems, answers are in the back. I have looked for the corresponding teacher book, but have yet to find the correct edition. Other editions of the teachers book have been in the 150-200 dollar range.

There is a video that supports this book if the student needs help. It does not follow exactly on the older edition, but does cover the subjects. The video is for the 2006 edition. [...]

Depending upon the child's learning style, this book works well with the current child I am teaching. It keeps moving forward building on what you have learned. This book does not do the continual review of old information.