Well, Ron, you didn't list the five areas and I don't have a copy of Everybody Counts, so will you please list them, or do you want us to see if we can figure out what they are?
Interestingly enough in my experience in teaching math radically differently from the way my parents (and I) were taught, as long as I can intelligently discuss with parents WHY I'm doing what I'm doing, they are usually VERY pleased that we're doing math the way we do in my class. Most of them are actually embarrassed about their lack of understanding about math, some have asked me to teach them (the parents) mathematics, not just how to teach their kids at home. They ALL seem to consider math important and want their children to have success in math. They are often VERY impressed with the kinds of problems we do in 2nd grade. They do have trouble, though, when I give the kids problems that COULD involve "carrying" and "borrowing" because they feel they have to TEACH their children these processes. I ALWAYS include a note with these problems that the children CAN solve the problems in other ways and that it isn't necessary (or actually very desirable) for parents to teach the processes. The problems are always part of a situational story problem and either the exact one we've worked in class or one very similar. If they will ask their children questions, or get their child to talk about the problem they can usually get the child to come up with his/her own solution. I also encourage drawing pictures, using manipulative objects at home, etc. Anyway, my point is that although I think it used to be the way the question indicates, my experience with parents is that these attitudes are changing.
The one area parents have concerns about is mastering basic facts. I send lots of information on the importance of concept understanding and then lots of ideas how to help children learn basic facts and have the parents work on this at home. Parents feel they are doing something important and I don't have instructional time wasted in class. ANd, the truth is, some knowledge of basic facts is really helpful to children, as long as we've at least worked on the concept of the operation in meaningful ways in class--and certainly as long as we continue to do so. I have had difficulties with a student who had spent a lot of time in Kumon classes and had done a great deal of drill on basic facts with little or NO conceptual understanding. She's had a lot of trouble with the situations and contexts of true problem solving this year--couldn't apply her facts and saw math as merely procedures. But, as long as it isn't that extreme I think this partnership with my parents works pretty well.
It doesn require a LOT of communication with parents, though. I send weekly newsletters explaining what we do in class and why-- and a lot of that deals with math. I've held evening sessions for parents. It all pays off! Cindy