My daughter is the same way; I believe it's related to her innate competitiveness. She doesn't care so much about being right, she wants to be done first! Her 2nd grade teacher suggested we wait to do WISC for her until 3rd grade, since she recognized the rushing would impact her score and she wanted to work on that with her first. Her 3rd grade teacher paired her with another gifted boy and so since they were both quick, the competition started to include not only being done first, but being done right, too. Loved, loved those two teacher.
Now in 4th grade, her teacher is so not the nurturing type and is very strict and thorough. DD has brought home numerous homework assignments with a "correct and return" stamp on them because she was not thorough in her answers. DD hates re-doing work, so this has REALLY helped her in the rushing/carelessness area. And to be fair to the teacher, if DD does the next homework assignment well/thoroughly, the teacher makes a point to note that on the homework as well. I love that "correct and return" stamp, LOL! I know it's so old-school, but it has really helped with DD.