Your description of your child sounds almost exactly like mine when she was 8 and 9 years old. she's now 10. She spoke early, read early, asked deep questions and was bored to tears and headaches with school. in first grade she begged me to homeschool her. it took her a few months of begging, but after lots of research I took the leap. At home, with one-on-one instruction it became apparent to me that there is something seriously different/wrong going on with her. she was consistently inconsistent, a hallmark of ADHD. fro example, her strengths are in her math abilities, and at the time she was happily working through algebra, but would d be stumped when she need to do simple subtractions.
We had her tested by a grad student when DD was in kindergarten. the numbers were simlirar to yours, some very high, some so low, and an overall "average" IQ. By the tiem DD was in 3rd grade I had a her have a full nuerophysochologial battery of testing by a PHD with years of experience with children who are 2e specifically ADHD and gifted. The results confirmed what I knew in my guts for years. DD is profoundly gifted, and her giftedness was being masked by severed ADHD inattentive type. she's now a DYS and thriving with homeschooling and appropriate challenge and support.
My advice to you:
1- trust your mother instincts. if you think something is wrong, then something IS wrong.
2- Get your child testing comprehensively by an expert.
3- Till you get your child tested, keep track/notes of the strange inconsistencies you notice from your child.
HTH
