Saxon Advanced Mathematics, Second Edition, is the third book in a three-book high school series designed to prepare students for calculus, chemistry and physics. It is intended to follow Saxon Algebra 1 and 2 and to come before calculus and physics. (Saxon does not have a separate geometry course. Geometry is spread throughout Algebra 1, Algebra 2, and Advanced Math.) The homeschool packet includes the student text, test forms, and test and problem set answers. An optional solutions manual is also available, and I strongly recommend that you purchase it.

Advanced Mathematics begins with a review of algebra and geometry. Topics covered in Advanced Mathematics include trigonometry, logarithms, analytic geometry, and advanced algebra concepts. Advanced Mathematics has 125 lessons and 31 tests. The following information is contained in the preface: "For high school students who complete Algebra 2 in the ninth grade, this is a three-semester book. These students can begin their study of calculus the second semester of their junior year. The book is a two-semester book only for the top third of high school students, i.e., those who complete Algebra 2 in the ninth grade and are highly motivated. They can begin their study of calculus in the fall of their junior year. For high school students who complete Algebra 2 in the tenth grade, this is a four-semester book. This will assure high College Board scores and will prepare these students for calculus as college freshmen." After a thorough examination of Advanced Math, I think that many students will need three semesters to finish the course because numerous lessons will take two or more hours to complete. A student who finishes Saxon Advanced Mathematics with a test average of 85% or better will be well prepared for college level mathematics.

Saxon math is taught in a spiral cycle. Students are introduced to small bits of a concept at a time. They are not required to master the material at the first introduction. Initially I loved the approach; it let us move on when we did not get it. At the higher levels this will be a problem for some students who need to see the whole picture at once. For this reason it is essential that students DO NOT skip problems in the problem set. Learn from my mistake and don't do only odd or even problems to shorten a lesson. Use two days if it takes too long! In an interview with Art Robinson, John Saxon Jr. said this about his math program, "Understanding more often than not follows doing rather than precedes it. If I'm going to teach you how to drive, I don't lecture you on the theory of the internal-combustion engine. I get you behind the wheel of the car and drive around the block." It is this presupposition that is the driving force behind each Saxon Math course.

I like the Advanced Mathematics curriculum. The lessons are presented so that most students will understand them with minimal outside help (this does mean Mom or Dad needs to go over the lessons too). Saxon math programs were originally written for the public school math teacher who presented the lesson to the student before the student read the book and were not intended to be do-it-yourself programs. Saxon recommends that parents do not allow the student to do independent study. I realize that many parents cannot teach at this level of math, so a tutor may be a necessity to help your student succeed. A cheaper alternative than a tutor is a DIVE CD by Dr. David Shormann. These CDs ARE NOT produced by Saxon, nor are they necessary for every student. But most students will benefit from Dr. Shormann's explanations on the later lessons, and I believe many students will benefit from his explanation for each lesson.

Another thing I like about Saxon Advanced Mathematics is that it is still available in the homeschool kit as a hardback book. The lower level paperback textbooks look and feel cheap. My hardback Saxon books have withstood the use of three to four students and still look good. While this is not a reason to buy or avoid Saxon, it is something every family with multiple students must consider.

In my ten years using Saxon Math, I have never regretted using what many consider the Cadillac of math programs. Saxon Math is the winner of many awards, including Cathy Duffy's Top 100 Picks of 2005 and The Old Schoolhouse 2005 Award of Excellence in Education as the best math company (again!). A few years ago there were few competitors in the high school math market for Saxon, and now there are many who claim to be better. I can't say if they are or not, but I do know that they do not have Saxon's track record. After comparing Saxon Advanced Mathematics to VideoText, Singapore New Elementary Math, Math-U-See, Jacobs, and Teaching Textbooks, I find it to be a first-rate program that will prepare most students for success in college (see the table below on areas I looked at). Does this mean that all students will succeed with Saxon? NO! Not all students need the repetition or drill, and some students need to hear or see the lesson in a video format (the reason I love the DIVE CDs).

This said, would I change anything about Advance Mathematics? Yes. There are too many problems per lesson. I call this drill and kill. From past experience I know you should not skip problems, so I won't even suggest doing only odd or even problems; but the amount of time for a student to complete the required work is excessive. Even a highly motivated student will find that he rarely finishes in less than 1 1/2 hours. A student who does not like math will most likely be turned off by the amount of work involved in each lesson. What I did to counter the amount of time involved was to take two days to do most lessons. I know this takes a lot longer than most families want to spend on advanced math, but after an hour of math my brain begins to make careless mistakes and my frustration level goes way up when working difficult problems. Some lessons could be done in that hour window. I suspect this is why Saxon advises Advanced Mathematics as a three-semester course.

Will I recommend Advanced Mathematics to most of my homeschooling friends? YES! It is affordable, fairly easy to use, covers the standard advanced math scope and sequence, is a tried and true program used by thousands of students for more than 20 years, and was written by a man who had a passion for teaching math to his students. I think that most unschoolers will dislike Saxon Advanced Mathematics, so I would not recommend it to them. It is well suited to a Classical Educator and the visual student. If you did not use Saxon for Algebra 1 and 2, you will need a geometry program before beginning Advanced Mathematics because Saxon covers geometry in Algebra 1 and 2. "Saxon works" is my motto.

Product review by Tina Rice, Contributing Writer, The Old Schoolhouse® Magazine, LLC, July 2006