I think this is what I tried to accomplish with the last teacher and it didn't go so well. At the beginning of first grade I asked if she would give him an above-level test. She never seemed to do it and said she's working on it. Finally at conferences like 6 weeks after school started, she said that she gave him a second grade level CBM test and he scored 89 percent. She said she can't send him to second grade for math because of the class schedule. She said she'd give him a second grade workbook. I said "Ok, so maybe you could have him do the 11 percent he didn't know on the CBM assessment and then go onto third grade." She agreed. Turned out she never gave this workbook AT ALL...she didn't even enrich the first grade material. When I emailed her three months later nicely asking her "how's the workbook going--did he move onto third grade yet?" (I knew full well he wasn't doing it) she never emailed me back and ignored my request for a conference. When confronted later she admitted she never gave him anything. Who knows if she even gave him an above-level test. She was a jerk about other things and we got in an argument. She told me I'm a bad mom because I don't inital DS's planner (where he wasn't writing anything half the time!). That was when I gave up and took him out, and he got the decent teacher who actually tested him and his overall math score was very high, like the upper 90's percentile-wise, but with all the gaps. I'm not sure if he's been tested again.
If the new teacher tests him maybe she can give him only the things that he isn't getting and move on, but that's exactly what the current teacher is doing. And it presents as kind of a mish-mash of random stuff. I'm not sure if there's anything left of third grade standards that she hasn't given him yet. So in a way, he raced through the second and third grade curriculum in a few months.