Hmm...math is so drastically different than every other subject, that it's difficult to think of a concrete solution.
I was much like your daughter in highschool...very gifted, never had to work hard (even though my "not working hard" was 150% more work than most people did), and frankly HATED math. My middle-school math grades were decent, 9th grade geometry was a waste of time, as was 10th grade Alg. II. The problem with me is that, in class, everything is simple. Watching the teacher do the problem, it all made sense. Doing it on my own - pfft, forget it. I was able to ace all of my math courses, but mainly through participation and homework grades - tests were typically B averages.
My junior year of HS, I had Trig. That, finally, was a beacon of understanding and enjoyment. Why? Because trigonometry is real. It can be seen, it has logic, and can be memorized through that logic. I couldn't find that in other forms of math.
I was an Economics major in college. First semester of my freshman year, I had to take basic Calc. It was torture. Again, eveything made clear sense when presented on the board, but I was stymied when it came to doing it myself. Part of that was that the course was at 8am. Part of that was that I didn't do homework because I didn't have to and that it's tedious and boring. Part of that was that the teacher was terrible. She was brilliant, but couldn't explain anything to kids that weren't as math-oriented as her. Oh, and I never learned to factor in high school. That might have had something to do with it, too.
As I explained to her, I could recite every therom, every step to problem completion. Ask me how to derive. Ask me how to find limits. I could define it all. I could even supply positives and negatives to each approach. But damned if I could factor an equation. Future calc. classes were better - I had a better teacher who explained things realistically and physically.
Back to your daughter. Retaking the course will most likely lead her to being even more bitter and frustrated. The reality is that she might get the same grade even if she takes it again. Now, what would look better on a transcript, one C or two? My suggestion is to let her advance, but encourage her to get extra help if needed. A different type of math course (like geometry or trig) might be better understood by her. I enjoyed both of those, but always hated Algebra. Might be the same for her.
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"I've made only one mistake in my life. But I made it over and over and over. That was saying 'yes' when I meant 'no'. Forgive me."
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