Also, there are other math books that use the repetitive learning approach. Rod and Staff (which, unfortunately, only goes through 8th grade, but is a good pre-algebra book at that level) not only reviews continuously, but notes, with each review problem, what lesson the concept was originally taught. In addition, it has WONDERFULLY comprehensible explanations. When my son was in 4th grade and struggling with adding fractions with different denominators, I turned to the 8th grade Rod and Staff book. There were 2 pages of explanation, which my son instantly understood. We'd spent hours and hours and pages and pages trying to get this through his head (and I'm a good explainer). So I was impressed.
University of Chicago's math program puts out another continuous review higher math series. Their book is preferred over Saxon by many public schools. It is more colorful, more engaging, and it doesn't neglect showing kids a REASON for learning all this stuff.
Which brings me to another drawback/asset (depending on the kid) of Saxon's books. Saxon is intensely effective on training kids to follow steps to a solution. They memorize the steps. They do not always get the concept behind the steps, unless they are naturally geared that way. My son very conceptual. He does Saxon math problems in his head and skips the steps. (We race to a solution, and he sometimes wins.) But he HATES writing down the steps, passionately. We still use Saxon, but we adapt it.
If you have a kid who whines, "But why do I have to LEARN this? What use is it?" and you are attempting to use Saxon, be forewarned that you will have to supplement the text to answer those questions. University of Chicago's stuff answers them while it teaches.
Saxon also neglects practical math. Its problems touch richly on scientific applications, but not on day-to-day mathematical uses. Your child will not learn to balance a checkbook, read a meter, complete an income tax form, calculate interest on a loan, or maintain a revolving credit account wisely. These things are easy to teach in a homeschool setting, but remember you will have to do it; the text won't fit it in neatly between percentage calculations and factoring polynomials.
Saxon teaches geometry, but barely touches on proofs. I ran across a description somewhere of classical education's main reason for teaching Euclidean geometry: It was a LOGIC course. So... if you want THAT kind of geometry for your kids, you'll need to use another geometry text. And if you are like me, wanting your kids to have exposure to constructing proofs, but not be buried in them, you may find that the Bob Jones geometry book is a happy compromise, with clear explanations and just the right dose of fun. Be warned, however, that BJU does NOT do repetitive review. They expect you to get it the first time around and then be able to use it.
All this said, there are definite instances where I'd recommend Saxon. For kids who don't mind tedium, are geared learning steps before concepts, and appreciate John Saxon's dry humor and don't miss the "why I have to learn this" explanations, Saxon sets mathematical technique FIRMLY in the student's head. For kids who can learn from anything, anywhere, Saxon works well, too, and it's admittedly readily available and easy to resell.
We use A Beka for almost all of our work. We are now starting our 5th year of use and I have found that for my eldest it is just what she has needed. The first 3 years were very colorful and had a wonderful way of explaining the concepts. It has the concept of building math one step upon each previous step with just a touch of review in each lesson. We have now reached a point that she is able to teach herself. I just set the lesson schedule and she knows what she needs to do. My youngest is flying through her math and seems to have a grasp of what it is all about. One of the things I have liked is how they work their way through basic math and gently work a child to beginning algebra with a introduction to the first skills needed in 3rd grade. I have looked at Saxon and it appears to be similar and we should be able to easily switch if we decided to at any point now. I would highly recommend the A Beka for the first 3 years at least. From there it appears that the two are fairly equal.
We use a fair amount of A Beka, but have always avoided their math. I can't say we tried it and didn't like it. We never tried it because the pages looked too busy and they seemed to jump from one concept to another without enough practice in between for the younger grades. However, I have not looked at the upper grades and look forward to hearing the other responses.
