He's averaging about 85% on the second grade tests, and about 60% on the third grade tests. And, to be honest, I've never taught him most of the things on those tests, and I know he hasn't learned it in school. So I have no idea how he learned a lot of it.
Okay, but he's getting 85% with essentially no prior exposure to the material? So much of elementary curriculum is repetitive, and the first few months of school are actually review, I'm betting he could learn that 15% very quickly in third grade. Also, look at the type of questions he's missing and see if there's a pattern. It could just be due to a lack of vocabulary or exposure to a topic. When the GT coordinator gave assessments to my DS, he would miss things like questions that wanted him to use "tally marks". He didn't know what that meant. When the teacher showed him, then he got all the questions correct. He had a similar issue on the reading test because I've never taught him any "reading skills" (LOL) and he didn't know what a prefix or root word was. Lots of "circle the root word" questions, and he got some of them right, but not the ones that were purposely tricky. So you might just have some gaps to address. And what I've been told is not to worry about the gaps when you're talking about a kid who needs to be exposed to something once to learn it. They'll fill in the gaps quite easily. Just make sure you help them find them and remind them to ask when they don't know something.
