Rebecca,
I intended to reply to this earlier, and then it went down the board without me getting back to it in time. So, I apologize, and I appreciate your patience!
Math is one of those areas that we are weighing carefully by working through things with our own two oldest kiddos prior to making recommendations. My oldest son has done much of what is out there for math, except he was always beyond the Singapore series as the U.S. editions weren't out for his age as he went through his school years (and I wasn't comfortable with Singapore until the U.S. editions arrived). So, this makes my oldest son a trial child in the math area, but also means we must lean on son number 2 when weighing where to go next after Singapore math (as my son number 2 has used Singapore since he began in kindergarten).
In the past, we had pretty much ruled out New Elementary Math as a follow-up after Singapore 6B, as it seems to take pretty huge leaps in understanding without significant explanation (and also does not have answer keys for the books 3 and 4).
Now though, Singapore has come out with a Discovering Mathematics series (new in 2008, I believe) that is definitely worth a look. My understanding is that it is somewhat easier than the New Elementary Math Series, has better explanations, is designed more similarly to the Singapore Primary Math Series books 1-6 (that we carry and schedule), has answer keys for all 4 levels, has an A and B level each year, and has problems that begin more basic and move toward more challenging in the lessons. It also now has a workbook with additional practice problems.
One concern with the series is that it integrates Pre-Algebra, Algebra I, Geometry, and Algebra II concepts within each of the 4 books in the series. This is different than the traditional scope and sequence here in the U.S. It does seem to give much of the needed coverage, but is not conveniently divided into each of the various maths for transcript purposes. How far it goes into geometric proofs would be something to look at more closely, as this area may not go as far.
It would appear that the series would leave off at a Trigonometry/Calculus type level, which would come next if desired.
One possible thought if one wished to continue with the Singapore method, by using the Discovering Mathematics series, would be to add a program such as Life of Fred to each of the Discovering Mathematics years. Using Pre-Algebra with DM1, Algebra with DM2, and so on. I have to really get into looking through the series more thoroughly to see whether this would be a possibility.
As the years pass, I am becoming more of a Singapore math fan each year. I'd hate to forego the thinking found within Singapore to do something completely traditional instead, if there is a viable Singapore alternative. So, I like the thought of exploring this option more deeply.
Singapore also carries a New Syllabus Math, which I think appears to be light on explanation, requiring leaps in understanding (more similar to the reasons we did not like the looks of New Elementary Math). Singapore also carries a New Mathematics Counts series, which is a revision that seems easier in its problem sets to the point of not including much of what people love about the Singapore method. But, I have only looked at samples and so do not know if this impression is fully correct.
Anyway, those are my current thoughts.
I will be receiving all of the Discovering Mathematics series to take a good hard look.
Blessings,
Carrie
