I would like to begin this post by sharing our homeschool experience with mathematics. When we began homeschooling, we used Saxon Math. Why? I really don't have a good reason. Unlike other curriculum, I didn't really research a lot of different math curriculums, maybe because I never really did well with math in my own schooling. Therefore, I purchased what the majority of the homeschool families I knew were using at the time. They all seemed happy with it.
Now, lest I sound negative toward Saxon Math, I would like to say that it served us quite well through elementary and junior high school. I liked the way that each lesson built upon the previous lesson and the boys seemed to be doing quite well. Saxon is a bit more advanced than some of the other math curriculums, and I don't feel they give you, the teacher, enough explanation to help the student grasp the concept, but, as I said, my boys did fine through elementary and junior high.
We hit a major roadblock when our oldest son reached the pre-algebra level. He didn't understand it and I, not being mathematically inclined and without enough explanation, couldn't help him. Math was not his strongest subject nor his favorite, either, and with the frustration of the pre-algebra, he began to cry over math. Now, this is a child who absolutely loved school and learning and had never shed a tear over anything academically related before or since, so I knew we needed to start looking at other math curriculums and make a decision.
We found Math-U-See. We were impressed with the demonstration we saw at a homeschool convention. We liked the fact that it included video instruction by the man who created the curriculum, Steve Demme, and it had manipulatives to help reinforce what your student(s) had to do.
We purchased Math-U-See and our oldest son was happy and relieved because watching Steve on those videos was extremely helpful. He understood and he did well in pre-algebra and algebra. I am sure that he could have done more with Math-U-See, but he didn't need any more math credit to graduate and wasn't going into a field that required any more math.
We decided to follow the same path with our second son since he was already working on Saxon Math and doing well also. We switched him to Math-U-See for algebra I. He didn't need pre-algebra. He is more mathematically inclined than our older son and he likes math. He will be doing Math-U-See's Geometry this next school year.
For our youngest, we decided simply to start him with Math-U-See and simply let him go all the way through it. He loves the videos with "Mr. Steve" and he really grasps each concept before we move on to a new one, and he can do math problems in his head pretty quickly for a second grader. We have become big Math-U-See supporters, and though, the Saxon worked okay for the other two boys through elementary and junior high, and they are competent in their math skills, I do think they may have fully grasped the concepts better if they had used Math-U-See all the way through.
Oh, and for the record, Saxon Math has been used in public schools.