From the beginning of time man has hated math. Fortunately, that was a long time ago and we have Harold Jacobs now. Harold Jacobs' premise is that everyone is a born mathemetician, and that, provided the proper instruction, anyone can do well in math. His texts appeal to students at all stages of mathematical competence due to their literate presentation of material, engaging illustrations and comics (including Peanuts, B.C., and the New Yorker), and comprehensive problem sets designed to reinforce and contextualize key concepts. Jacobs promotes creativity in learning, and his books are creative and even exciting.
The Elementary Algebra text has frequently been compared to the Saxon math curriculum for high school students. Both are incremental in approach (introducing concepts a little at a time and reintroducing them later as parts of larger wholes) and both emphasize constant review so that building-block principles aren't forgotten as students progress into more complex territory. However, Jacobs' text is far more engaging with its use of meaningful illustrations and references to culture, literature and art. It is also better written; whereas Saxon tends to write in a breathless, choppy style, Jacobs' prose is clear and to-the-point.
Geometry follows the same general pattern of Elementary Algebra, but offers more supplementary information. The author describes it as a "museum in a book" because of all the historical and cultural references to the various uses of geometry. It's also more colorfully illustrated than the other books, with photographs of famous artwork and architecture illustrating different concepts. There is more information in the teacher's manual than in either of the others, though full step by step solutions are not included. We don't think of this as a huge problem, since the point of geometrical proofs is proving them, and this can be done in many different ways.
Elementary Algebra and Geometry were meant for high schoolers (grades 9 and 10), although older students have found them useful, especially those who've struggled with math. A third text, Mathematics: A Human Endeavor (subtitled A Book for Those Who Think They Don't Like the Subject) is aimed at a less focused audience. While it can be used as a follow-up to the other two books it can also be used for remedial college students who need to be re-introduced to general math concepts. Some parents have used A Human Endeavor for earlier levels, but we probably wouldn't recommend that. The three books form a loose trilogy of some of the finest math textbooks available.
Each level consists of a student text, teacher's guide, and book of test masters. (Overhead transparencies are also available on CD-ROM for the classroom setting, but due to their cost we don't currently stock them.) The teacher's guides contain all the answers to the problem sets as well as suggestions for presenting the material, although Jacobs encourages teachers to find their own ways of teaching and to be creative.
The books are broken up into chapters focused on specific topics. These chapters are further broken down into lessons containing text which introduce and explain the topic and include a series of problem sets. Algebra has four sets: the first is review; Sets 2 and 3 relate to the lesson; and Set 4 is a special math or logic puzzle for advanced students who need more challenge. Geometry only has 3 sets: only Set 2 covers the specific lesson. Answers to Set 2 are always included in the back of the student text; answers to the other sets are in the teacher's guide.
In some instances, the text leaves it up to the student to understand aspects of a principle through intuition. Jacobs heavily encourages deductive reasoning, and presents several opportunities to put it to use. While this may seem daunting to the beginner, the course is designed to help students improve their reasoning and logic skills, thus preparing them to encounter such problems. To the uninitiated, however, there will appear to be certain gaps in some of the lessons.
Elementary Algebra aims at student competency, providing a solid framework of skills and concepts from which to move on to more advanced math. Geometry is Euclidean in approach and nearly exhaustive in scope—Jacobs criticizes other curriculums (like Saxon) for failing to devote an entire text to geometry. Mathematics: A Human Endeavor is much broader, providing more basic information and filling in gaps. Together they provide an excellent, consistent overview of high school math.
Jacobs designed his books for use in a classroom setting. Teacher involvement and instruction is expected, and so too is a measure of teacher competency in the subject matter; unlike other curricula, the teacher's guides are not exhaustive references. However, the student texts are comprehensive enough that students can work through them on their own. Solo work might not yield as full an understanding as teacher-led efforts, but there is enough content to at least generate competency if not mastery.
There really aren't much better math curriculums for upper-level work than Harold Jacobs'. The texts are engaging but not overly visual—there is plenty of content, and the pictures and cartoons are often used as illustrations for key ideas. Topics are easily referenced later on due to the logical structure of the books and obvious chapter and lesson breaks.
The student texts are excellent. Concise and witty, they present complex and difficult ideas in a way most students can understand. The teacher's guides from Freeman (the publisher) leave more to be desired: they offer minimal support for teachers, only rudimentary lesson plans, and no solutions manual. Happily, Dr. Callahan and his daughter Cassidy Cash have come to the rescue with video supplements, additional teaching aids and a solutions manual for Elementary Algebra. This helps us to highly recommend these books for high school (home school) students.
If you're looking for a curriculum that will make your kids sick of math this probably isn't the one you want. Many parents report that, after switching to Harold Jacobs, their kids did a lot better in math and started to actuallly enjoy it. Even professional mathemeticians and math teachers offer glowing reviews, and as far as we can tell this is definitely a curriculum that deserves high marks.