Last summer, I put together a 10 week math workshop for 5-6 year old kids entering first grade the following fall. My approach was math boot camp during the sessions, and to have the kids plod along with a math workbook during the week. I selected Every Day Math (University of Chicago) because it is used in school and I like the approach.
As I was walking around the neighborhood presenting this idea to parents, I stumbled across a sensitive issue. Those parents with older kids found that the new math fails in one respect - the kids forget how to add and subtract. The new math emphasizes problem solving, math applications, conceptual maturity - and drops altogether repetitive practice of the basics - unless the parent sticks to a regimen of 2 workbook pages per night with no skipping of problems. No teacher assigns 2 pages of math workbook per night to first, second, and third graders.
So we've got math for geniuses turning out dummies.
Of course, the problem with the old math which I grew up with is that the child doesn't develop a mastery of the concepts by exercising these under different circumstances. A child can multiple 5 x 3 but doesn't really know what it means, and sees a word problem begging for 5 x 3 and get can't solve it.
The new math is highly qualitative, and you're left to fend for yourself on the quantitative mastery. The old math was primarily quantitative.
The answer is of course you need both. If you use new math in a homeschooling setting, or your child does it at school, plan to supplement it.
I like the new math because it is consistent with gifted and talented programs and with my working theory about the super secret GAT test. If you are in a program that uses the new math, or you are teaching your braniac yourself using the new math, look for supplemental material to reinforce quantitative skills. There are plenty of workbooks that cover math operations without the confusion provided in the new math book.