I just found this article on math instruction in which 12 children ages 9 - 12 learned all the math normally taught in grades 1 - 6 in 20 hours. That is 20 teacher contact hours. The students worked hard on their own, because they wanted to. It is amazing what students can learn when they are ready and want to learn.
I had read a similar article in a magazine a few years ago.
In the November-December 2004 Home Education Magazine an article called "Just Do the Math!" actually quotes this article on the website. This article in the magazine was quickly added to my Stand Firm Kit because it helped to define my educational philosophy. I don't have to push education on my kids, if I provide love and support, when they are ready to learn something they will.
I do provide them with opportunities, we have pay day(they get an allowance) we have contracts ( they work to earn extra money), and I even have workbooks. They choose when and if they do them. Somedays Emily will do 6 or more pages in her math workbook just for fun. WE play games, ok - really, they play games with Grandpa Glasgow. Grandparents are a huge influence in our life and a wonderful addition to our education.
Right Start Math by Dr. Joan A. Cotter ( www.alabacus.com ) is my math program of choice because of the manipulative and games that are abundant. When we have used the textbooks we enjoyed them, but really, we don't use them much and only occasionally do we even play the games, but if I had to recommend a program this is the one I would recommend. Just buy the games and the book on how to play the games and you would have a great math program.