I'm not sure what point you are at in terms of the school knowing what is going on. You just had her tested privately, right? Forgive me if some of my suggestions aren't relevant. Based on my experiences with both full grade and subject acceleration, here are my thoughts:
1) do not start anything by email. It is too easy to misread, assign "tone" and start misunderstandings and offend people via email. I would contact for a face to face discussion. If they are already aware of the situation, then definitely something in writing as well that outlines your concerns.
2) begin the discussion by establishing that you and the school are a team, working on behalf of your child. Always use "we" and speak under the premise that the school IS interested in doing what's best. You want to establish a good working relationship with the school, not an adversarial one.
3) be prepared to identify the problem: DD6 is unhappy and unchallenged in math. She is capable of more and needs the "room to run" (aka: cheetah analogy here). Better to NOT identify the problem as the school, teachers or curriculum. They get a little defensive at that point!
4) be prepared to offer multiple solutions: provide the school with a list of the options that you see as available. This could include subject acceleration, whole grade acceleration, private tutoring at school with programs such as ALEKS or EPGY or whatever, etc. Make sure you offer the one or two options you like the best as well as one or two that are really not likely to be feasible. That way the school can make the decision - they feel more in control when you ask for two things and, even though you didn't want option B they get to tell you how option B just won't work and so THEY insist on option A (which is what you wanted anyway!)
5) Be prepared to back up your options with documentation about why those options will work. I used information from Developing Math Talent by Susan Assouline. Great resource. I photocopied some of the info, especially the Myths about gifted math learners. Be sure to offer the school reasons why each option, or the option you prefer, is going to be easy for them as well as good for your daughter.
6) Be patient: you might need to wait for those test results and then be able to present them as part of your discussion. Is the private tester going to make recommendations for educational planning? That certainly would help.
7) If they are unwilling to consider your options, request that they do curriculum based pre-testing for next year. Or, better yet, test with the *following* years curriculum. When we wanted subject acceleration in math to 3rd grade, the teacher put together a curriculum based test of 3rd grade material and the principal administered it to our son himself. He discovered that our son actually had already mastered the first 3 months of 3rd grade BEFORE even starting 2nd! It was HIS idea to put him up a grade level then!
And here's my thoughts on whole grade acceleration. It isn't right for every child in every situation. You need to consider your daughter, her needs and abilities, your school, her peers, the curriculum, etc, etc. (Use the Iowa Acceleration Scale - helped us "come to peace" with it!) We were a bit panic stricken with the thought of our school skipping our son. But then we had him tested, looked into research on acceleration, and decided that not only would his needs be met by grade skipping, but by doing it BEFORE he started school. He is twice accelerated in math now. Still one of the top students. He does NOT struggle with anything at school yet. Now, that may be due to his ability and/or the rural public school he attends. Your situation may be completely different. I'm just suggesting that you consider the acceleration option with an open mind. Sometimes it actually HELPS the emotional issues, which I know it did for our son. We freaked out at first at the idea, because I was sure he would be ostracized, stand out, not make friends, etc, etc. But nothing is further from the truth. We've had to deal with his age - ironically his friends call him a liar! They don't believe that he is a year younger than the rest of them! And someone called him a nerd this year - but, heck, he's going to get that sooner or later no matter what grade he's in. So, overall, the grade skipping has worked for him.
HTH.Best of luck!
