When I last wrote about math (on March 19th), I said that choosing this curriculum was the easiest for me, and I didn't even have to look around very much - Saxon just seemed like the best fit right away.
Well, I started looking around some more, just for fun, and now I'm rethinking my choice. Sigh. But it's probably for the best, since more knowledge about choices can only lead to the better choice, right?
Now, we're doing fine with Saxon 1 right now (on lesson 34), and I think the manipulatives are really good for my daughter. She enjoys all the different activities Saxon has us do, and seems to be learning some. A lot of it is still too simple for her, though, so I'm skipping through parts more often. The teacher's guide says to have her count from 1 to 100 every day, for example, and I think that's a bit overkill. She's been able to count to 100 since preschool, and she and I both get bored listening to the repetition every day. But she still asks to do math, if we're having a shortened day. She'd gladly skip handwriting, but she wants to do math every day.
But I started reading some reviews that talked about Saxon not teaching enough of the understanding behind math, and about it being geared more toward passing tests, and not understanding. I read that it will get your student quite far for high school, and is good for applied math, but it's not quite rigorous enough for someone who plans to enter a scientific field in college that needs theoretical math. Then I read a research paper, actually, not related to homeschooling, that studied mastery learning vs spiral learning in math, and found that mastery learning produced students who were far more knowledgeable about math, and comprehended the underlying truths much better. I know that I do better with a mastery approach, not leaving any details "to be learned later," and having to see the big picture before I can understand all the details.
Saxon is definitely not mastery. Its incremental approach is spiral learning to the extreme. I know people say that whether to use spiral or mastery depends on your student - some like one better than the other, or learn best one way. I'm all for utilizing your student's learning preferences to help teach things best, but I don't agree that all students will be universally happy with all subjects if you just find the right approach. Sometimes they just have to learn things they don't like, and sometimes they just have to work harder in order to learn something the right way. Spiral may be good in some subjects, and reviews and drills are good even in a mastery math program, but I'm leaning toward thinking mastery is best for math.
So I think I'm going to switch. I still plan to use Saxon K (for preschool) and 1 (for kindergarten), and I like all the manipulatives that we're using. In fact, my 2- and 3-year-olds love to play with the manipulatives we're not using during my 5-year-old's math class. I'm not sure yet if I'll use Saxon 2 or not, though I did already buy it.... The other math curriculums I like don't start until 1st grade, so I have no problem using Saxon for kindergarten still (since I already have the teacher's manual).
I liked Christian Light Education's math at first, with their workbook approach, but it is spiral too. I also read good things about Rod & Staff's math, which is mastery. But from the samples, it seems to be too classroom-focused, and requires more charts and/or displays which I don't really want to pay for or make. I had been looking at CLE and R&S for English curricula, which I'll talk about later, but I've decided to pass on their math choices.
What I think I will use for 1-6th grades is Math Mammoth, the Light Blue Series (http://www.mathmammoth.com/complete-curriculum.php). This curriculum is mastery based, rigorous, colorful (if you print it out in color), workbook format (electronic, actually, though you can buy it printed out too), and cheap. All good things for us, I believe. I plan to buy the whole set (it's cheaper that way), and can print out whatever pages I need for all 3 kids. I believe it's even going to be on sale later this month. It can apparently be quite independent starting even in 2nd grade (or 1st, for good readers?), though others say that the parent still needs to teach it. It probably depends on the child.
As for later grades, the author highly recommends getting a regular textbook, and has lots of recommendations on her website for what to use. In fact, the way I first came across her website was by looking for recommendations for upper level math textbooks. After deciding to look at things other than Saxon, I came to the conclusion that textbooks used in public schools and even in colleges were the way to go for algebra and higher. Saxon calculus doesn't cover much of what's needed for math-heavy college majors, and I found several recommendations to just go ahead and get a college-level calculus text and go through it slower. Several places offer "video teachers" for these levels, on DVDs, though not all are universally acclaimed. I may end up just teaching them myself, as needed, since the DVDs can get rather expensive. I realize that most homeschool parents don't have the extensive math background that I do, however, so that's probably not an option for most. But anyway, since I liked the Math Mammoth author's advice so much for the later grades, I decided I would probably like to use her 1-6th grade material as well.
For more motivation to teach math, I found this article today: How the U.S. lags in math, science eduation, and how it can catch up
Here's a few links that might be useful for upper levels:
Chalk Dust - very good reviews, a little pricey
Math Without Borders - companion videos for Foerster textbooks
Ask Dr. Callahan - DVDs don't have wonderful reviews, but might be ok; uses some of the texts listed below
Teaching Textbooks have a really nice format, very independent, but they are not as rigorous as I'd like and are probably at least a grade level behind - may be good for a student not going into a science or technical field, or for earlier years before switching to a regular textbook
Also, see this part of the Math Mammoth author's website for tons of useful information. My suggestions are really just a subset of hers.
Foerster's Algebra and Trigonometry: Functions and Applications (Prentice Hall Classics)