The school has said that a private testing would be beneficial to helping understand him better as they won't be able to test them for himself until well into the year.
Depending on how 'mysterious' your son is, the achievement test might be important for the tester to help sort out what is going on. Is the tester going to do a consultation with you and try and give some insight. If not, no point in doing the achievement until the school has had a chance to.
If a grade skip or subject accelerations are a possibility the achievement test information will help assure you that this will be a good thing long term when filling out the Iowa Acceleration Scale.
I think either way could work well, depending on what is uncovered.
Good Luck,
Grinity
