Everybody says their kid is really smart. My mom said that about me for the longest time, which made me feel uncomfortable, because I felt I had to live up to some weird expectation she had of me. I have to agree, I was smart, but I had a serious problem with numbers.
No one could wrap their heads around that fact, because I was reading and writing way above grade level, so how could this ridiculously annoying know it all factoids galore smarty pants kid actually have a *gasp* problem? "She's really smart! How come she won't do homework?"
I remember crying over my math homework, being very frustrated, feeling really angry, and just not "getting" it. And feeling sick and punished and the whole "why me" thing. And then I'd grab a judy blume book and stay up all night reading.
I am convinced I either had a learning disability that I eventually overcame, or I was not brain-ready for math at the time.
My homework and grades suffered intermittently in school. My teachers always reported that I was not very motivated for math and certain other related subjects. I was recommended for gifted classes but was ultimately rejected because of the crazy math issue. This really bummed my mom out, but I was glad because I already felt like a sore thumb because there was nobody who could read at a level high enough to be in a reading group with me.
Not sure if your daughter is picking and choosing which homework to complete, or if she hates a particular subject, or if she is really miserable in school and is like I was. I know I got into a rut where I would be forced to do math homework, would spend all my time on it, and be too exhausted or stubborn or frustrated to complete the rest. And it's very embarrassing. I felt almost cheated by my own self, but it self-perpetuated. Once I was convinced it was futile, I stopped doing it altogether. The grades would drop (except in reading) and my parents would come down really hard, which probably made me very depressed.
Have you checked into other teaching methods than what is already offered at your school? Your daughter may be in need of after school tutoring, or perhaps she would benefit from something like the Waldorf Method, which is geared toward meeting developing children as their strengths and maturity level as they occur instead of "forcing it", the way most schools do it. There is definitely something to the whole 'brain development' thing, and eventually someone will figure out a really cohesive and well rounded approach to educating children, but feeling frustrated, if that's what's going on with your daughter, is just going to make her current schooling regimen seem worse and worse.
The punishment for the behavior is also probably getting in the way of solving it on her end.
I applaud your looking at it as a motivational issue. Maybe that's all it is, and that all she needs is the right motivator. But as the adulthood version of your daughter, I hope you investigate some causes...and good luck finding out what's really going on! If it really is motivation, the one that worked best for my grandparents was to actually take their kids out of school for a whole day (they would surprise them and pick them up in front of all the other kids, they had to take a day off from work to do it, and this was a HUGE treat back in the 50s) if they got straight As, and sweep them off to disneyland. My dad went 4X a year from age 10-14! The best part was that the other kids in the family had to stay in school if their grades weren't up to par.
Now, if your daughter was 13 and into anime and was a gamer? I'd say she was just lazy and needed her ipod taken away until the history diorama was finished.