Customer Reviews

Elementary Algebra

5 star:		(25)
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This book is a kinder, gentler approach to first year algebra. Harold Jacobs actually writes math texts that are fun to read.

The sequence of this book is a little different than most algebra books. Jacobs starts off with one of those "Think of a number" puzzles, and shows with diagrams how it works, and then translates it into algebraic notation. This is the point of algebra: How do you say with numbers what you can diagram? This leads quite naturally into Cartesian coordinates and a discussion of some basic functions. Exponents, polynomials, factoring and quadratic equations follows a full treatment of linear equations and systems.

I use this book with homeschooled students, because they can actually take it home and study it. The homework problems come in four sets. Set I is review problems. Set II applies to the lesson and has all the answers in the back of the book. Set III is similar to Set II problems, but does not have the answers in the book. Set IV is some logic puzzles and brain teasers for students who love math. Answers to sets other than Set II are in the teacher's guide to Elementary Algebra, along with some wonderful extra material and teaching suggestions. Amazon, why don't you carry the transparencies for this text?

I highly recommend both this and Harold Jacob's text on Geometry, a good, old-fashioned approach to Euclidean geometry and proofs. Enjoy! Really.

I began using this book to teach my own children after using Saxon Algebra I and II. I was amazed to discover that Jacobs covers ALL the algrbra from both Saxon Algrbra books in only one book and in much more simple language. (No Geometry is covered in Jacobs Algebra-- but Jacobs Geometry covers it more completely that Saxon.) Each lesson starts with a comic strip or interesting picture and builds the lesson on the comics. After one year with Jacobs my children understand how to find the formulas they need and why problems are solved the way the are. Problems that were complex with Saxon are explained simply and visually with Jacobs. Test scores are way up and math is fun again.

The question last summer was, "What next, for a younger child who's mastered all pre-algebra mathematics?" Was it too soon for algebra? And could a parent who hadn't seen algebra in the last twenty years help the child cope? We ordered Harold R. Jacobs' text, encouraged by reviews mentioning self-study, and began work in the fall, prepared to stop any time if the child found it difficult or stressful. Quite the contrary, it was mentally very stimulating -- the lessons took us carefully from familiar arithmetic concepts to equivalent algebraic content, and presented each new subject one very manageable bit at a time. It was exciting to watch skills developing, and to see the child's enjoyment and growing sense of competence. The little cartoons and often-intriguing Set IV exercises added fun and interest throughout, and made it easier to keep going, especially during those mid-school-year doldrums. This book was perfectly suited to our schedule, which allowed only three lessons per week, after school -- we needed only about half an hour per lesson at first, then near the end, about an hour and a half. We're looking forward to Jacobs' Geometry book next year!

At the time I started homeschooling my sixth grader last year, I was completely math-phobic. I had forgotten every bit of algebra I ever learned (and any math I did learn in high school, more than 20 years ago, was just barely learned at that). My now seventh grade son and I are learning algebra together with Harold Jacobs's Elementary Algebra book.

This is really an exceptional self-study guide. We will read a chapter, then independently try to solve the problem sets given. We then compare our answers. If our answers don't agree, I will either explain to him how I solved a problem that he got stuck on, or vice versa.

The delightful thing about this book is that I am learning to enjoy a subject I always thought I detested. Harold Jacobs makes everything clear, comprehensible, meaningful and often humorous. I am learning that I am not left-brain impaired, as I've thought I was ever since second grade, and actually look forward to my algebra time with my son! My son, too, has overcome his own math phobia, and become a math lover. I can't recommend it highly enough.

I homeschool my kids & have taught them through geometry so far, including Algebra I for two of them, using the Saxon series, which we've liked for the most part, but haven't liked as much for the later grades than for the earlier (say through about 7-6). I've started with the third child using Jacobs instead, since he seems to present many topics in a more understandable way, at least a more visual way. He also structures the problem set in each lesson exclusively to deal with the topics of that lesson, rather than using a spiral review method or other method that presents problems from lots of previous lessons. This makes for more concentrated treatment of the lesson at hand, which the third child likes more. Jacobs's method of presenting is, as I said, more visual, with helpful diagrams and graphs that illustrate the point of a lesson. My favorite is his use of a two-dimensional matrix to illustrate multiplication, and later division, of polynomials. The step by step addition of information to the matrix illustrates the steps and the concepts of polynomial multiplication and division quite well. I'm looking forward to using this book with this child and having it available for the others for reference on topics on which they need refreshers.

I have used Jacobs Algebra (and Geometry) for a homeschooled audience, in a once a week classroom setting of 8 - 16 students. I love the way the material is presented, especially the "boxes" which are used to multiply and divide polynomials and lead to an elegant method of completing the square. His emphasis is understanding WHY, instead of HOW, and my students enjoy it. I do have parents repeatedly request a "Solutions Manual" - the teacher's guide only contains the answers, not the solutions to the problems.

Jacobs' book has a lot of really good, interesting problems to do, and that is the most important thing in a math book. The probems are unsurpassed by any other Algebra book that I know of.

I bought 7 copies of this book so far for people who are self-teaching this Summer. Or at least half-self teaching, because the reading level is a little high (many large words). Some people have a spouse, parent, sibling, or frient who are helping out by reading some of the problems to the self-learner, without doing them.

It would be good to come out with a version of the problems in this book with, say, a seventh grade vocabulary to open it up to people whose reading skill is not that high yet. This would SEPARATE the reading work from the algebra work.

In the end, of course, one must master language in order to master math. In the beginning, however, it is still good if one has the motivation to self-learn some Algebra, even before becoming am master-level reader.

Harold R. Jacob's text is a lively and clearly written introduction to elementary algebra. Jacobs engages the reader through puzzles, including the number trick with which he starts the book, humor, and references to actual persons and events. He finds intriguing ways to introduce topics, then explains the concepts well. Concepts are introduced incrementally. Often, Jacobs introduces a concept in a particular context so that the student gets the idea before reintroducing it later in a broader context after the student has learned additional material. This reinforces the concepts and contributes to the student's conceptual understanding of the material, as do his problem sets. While Jacobs makes sure that the student can perform the algorithms presented in the text, the problems that he poses are designed to reinforce the concepts by exploring all aspects of the topics that he covers.

Each section concludes with four problem sets. The first set is a brief review of earlier topics (aside from the first five sections of the first chapter). The second covers the topics in the section. Jacobs provides answers to the problems in the second set in the back of the text, making the book suitable for self study. The third set is a variation on the second. The fourth set consists a puzzle or a problem that extends the concepts learned in the section. I particularly enjoyed these problems, often turning to them to see what Jacobs was asking before I finished the other problems. Each chapter concludes with a chapter summary and two sets of review problems.

Jacobs begins the text with a review of arithmetic, including the order of operations and properties of integers and rational numbers. He introduces algebraic concepts gradually as he does this. This leads to a discussion of functions, linear equations, lines, systems of linear equations, and exponents. Jacobs pauses for a midterm review. Then he covers polynomial, rational, and radical expressions and equations. He also discusses the properties of the real numbers, inequalities, and number sequences before finishing his text with a final review.

If you enjoy this text, and I think you will, you may wish to explore Jacobs' text Geometry: Seeing, Doing, Understanding next.

This book is the best textbook for a series of courses in pre-algebra and basic algebra that I have ever encountered. There is no assumption of initial knowledge other than some familiarity with basic arithmetic. Even that is very limited, a student in late elementary school would understand the material of the first few chapters. The pedagogy is the correct one for the middle and early high school student. A few, generally three or less, pages of new material followed by a large set of exercises. Diagrams are extensively used, and children will love the inclusion of the cartoons. Most of the cartoons are from the Wizard of Id and Peanuts strips. Solutions to many of the exercises are included in an appendix.
If there is a criticism that can be leveled against this book it is that it moves too slow. There are times when it can be argued that a couple of sections could be combined. However, that does not prevent the instructor from combining them if they wish. Therefore, I consider the point to be weak; it is always better to move too slowly than to move too fast.

...and I have found this to be a good course. We had tried several algebra programs before we tried this one. For the most part this is an excellent course. One drawback is that the author often does not mention key principles, in the assumption that the student will pick it up while working the problem, which is not usually the case! Overall, however, this is a good course. An optional supplement to the course: it helps to have a dad around who knows algebra...