Your story is eerily familiar. In fact, last year (2nd grade) my son came home saying he hated math and was no good at. This caused HUGE alarm bells for me and my husband as we were already struggling with the school and my son's clear lack of joy there. We immediately got him a tutor who works specifically with gifted children (yes, big $, but we saw it as our only option). She does no drilling. Instead what we discovered is that our son is what she calls a "non-linear learner"...so the ideas that he has jumps YEARS beyond his abilities, and then he has to go back and fill in with all this rote stuff.
You may just be dealing with someone who needs that stimulation that they are only going to get from exploring algebra, physics, astrophysics, calculus etc. etc. and all the stuff that the school dist. does is just back-fill.
Take a look at the Kahn academy online or take a look at Zaccaros books. They might inspire your child.
Another thought is that my son has a VERY high IQ, but an average processing speed. My understanding from others is that this is not uncommon...so your child might be having very deep, bit thoughts, but "spitting them out" is difficult.
I would explore on your own what is going to work best for your child and then offer that as a solution to the school (obviously some schools/teachers will be more receptive than others). My son's teacher's for the last 3 years were not receptive AT ALL. This year's teacher challenges him to be just as smart as he is. So let your child know you support him fully and will make his learning opportunities outside of school as wonderful and exciting as possible. And continue to go to bat for him behind the scenes. This "minute testing" might really tie into a sense of perfectionism that many gifted kids have. This may to real damage. Talk to the school from that perspective.