We have been using the Singapore Math program for about a month now. I guess the main selling point of this program is that it is the program used in Singapore schools, and children there consistently score high on math tests (much higher than children in the United States score). The program is said not to just teach math, but to teach how to think mathematically.
I started Tania at the beginning of the First Grade series, because the program is taught much differently than the program she learned from in school. In the first grade, students learn basics of addition, subtraction, multiplication and division. Most programs in the United States teach addition and subtraction, from basics to advanced, then move on to multiplication and division. This program seeks to show the relationship between addition, subtraction, multiplicaton and division by teaching them all simultaneously throughout the first few years.
The program uses kid-friendly pictures, but there are no manipulatives. Some children learn fine this way, but many children need manipulatives in order to learn math concepts. I think I would say that just about any child could use this program, but different children might need different supplements to fully benefit from it. Tania is a "logical-mathematical thinker," much like I am, so she doesn't really need manipulatives, but I have added addition/subtraction and multiplication/division tables for her to memorize. I know that a lot of homeschooling parents think those sorts of tables are useless, but I still use that memorized information most days of my life. Memorizing those tables made more complicated math courses easier as well. I didn't have to waste time figuring out components of math problems that I had already memorized. And I think that as long as children are memorizing the tables along with learning the mathematical concepts of what they are memorizing, the information doesn't become useless.
A lot of the contents of the First Grade series are extremely easy for Tania, but some of its contents are new material (like multiplication and division). She'll be finished with the first workbook next week, and finished with the second workbook and all of First Grade by the first week of August. Then she'll be where she needs to be in order to begin the Second Grade. We'll be able to take a couple of months off to just enjoy the remainder of our time in Hawaii, then set up in and get to know Portland without the pressure of schoolwork.
Tania actually really likes working on math. She always asks to do math before doing any other subject. I think she likes it because it's sort of "schoolish," what with the workbook and all. She likes to get graded. It's bizarre. I think she also likes the coloring she gets to do in the workbook. It's really set up to be attractive to children.