J.G.
As a former 3rd grade teacher- and 2nd and 5th grade in Texas (and mother of only one 22 month old), I do need to tell you that it's near impossible for a teacher of 20plus kids to work one-on-one with your daughter while the rest of the class works on their own. A classroom of kids can sit still for maybe 5 minutes before needing a teacher to redirect or intervene in something. But of course, a teacher's job is to help all of their students to be successful! And if your daughter is not being successful, then her teacher MUST address it. She should be finding ways to help your daughter - a small group, a private lunch with your daugther once a week to work on math during lunch time, tutorials afterschool. I would be surprised if this close to TAKS, there is not a pull out group for math (a math specialist makes a schedule to come and get all 3rd graders that are struggling, or takes at least the ones that if pushed a LITTLE bit more, will pass TAKS). Perhaps ask the teacher or grade level chair or principal if the teacher is not cooperative with you.
I think a tutor is a great idea right now, as it will give her the one-on-one that she needs. I hope that you have found someone who will help teach your daughter why and when to use a certain operation (adding, subtracting, etc) and not just how to add, how to subtract.
Something I don't think most parents know is that old TAKS tests are online with the answer key. I do not like teaching 'to the test', but it would be a great eye-opener for YOU to see the test so you know what your daughter is up against. Open GOOGLE, type in TAKS TEST and the first link is the 'release tests'. Scroll down and click on anything that's 3rd grade math in English.
It's tough to figure out just WHY a child doesn't get the math idea. In other kids I've seen, they need to draw the picture of what's happening (which is VERY GOOD to do!!!) yet they need help figuring out how to turn what they read into a picture. Other kids struggle with understanding what they're reading, such as "How many more cookies did Joe have than Sarah?" They don't know if they're supposed to subtract or add or do WHAT with that kind of question - so I recommend drawing a picture and I ask "Joe has more, right? Well how many more, How many extra?" One student I dealt with understood the math well, but rushed. He didn't want to be the last one through (the kids can't talk ALL DAY (except for lunch) until the last kid in the room finishes - it's stressful for that last kiddo - the pressure on them. So I gave him practice tests in bunches of 10 questions. 10 questions one day, 10 the next, 10 the next. He passed when he stretched it out. So taking a break is important. Your daugther should be able to go to the restroom, get a drink of water after 10 or 12 questions. Teach her to do that. Talk to her teacher ahead of time.
As you can tell, I have a lot to say and I LOVED teaching. I now love being a stay at home mom, but my passion for helping kids learn will always be a part of me. And I especially love math too. Message me if you have more questions or anything.
Oh and as for private school - see if you can talk to any parents to find out what you're getting into before enrolling. I have heard both bad and good. I do think though, that there is no TAKS - YEA!