First one is to be proficient in explaining in written form how a student solves a math problem. I think this is a good skill to have but preventing a student from moving on to higher, above grade-level math because this isn't mastered is frustrating to the student.
There may be another perspective here. If a student can't explain how she solved a problem, it's possible that she doesn't fully understand it. If this is the case, the lack of understanding can appear later and cause problems. I've seen this with my kids. I remember my DD doing percent-to-decimal conversions easily. She got lost a few days later when the same kind of problem was presented in a very different way (e.g. with different wording or from another perspective). I didn't understand why she was tripping up, until I went back to basics with her and realized that she hadn't internalized a concept. It's possible to be, err,
algorithmically fluent while not understanding the concepts. If the base of poorly understood concepts gets to be too big, algebra and geometry can be very difficult.
Second, being able to learn multiple ways to solve/tackle/approach a math problem. Why do students who are mathematically talented need to learn multiple ways to solve problems? Why can't they just do what works for them?
It's important for students to have to
perform different methods and then pick which ones work for them. It's good to know that there are other ways of doing something. But...forcing them to master them all seems to be extreme. It also seems like a waste of time to force mastery of 3 different ways to multiply 82*13. IMO, if the kid can consistently and coherently explain what she did ("I put a 0 on the second line because the 1 in 13 is really 10"), it's time to move on.
Remember that your daughter's teacher might not fully understand the concepts of K-8 math herself, and that she's under a lot of pressure over test scores. If the scores are too low, the school can get into trouble and the teacher's job might even be at risk. I agree that it's a bad system, but right now your DD and the teacher are stuck with it. The teacher may be stressed out that the kids won't pass the test and is making
extra extra sure that they will. She might also not understand gifties. I agree that your description makes the situation sound bad for the kids, though. I'm just trying to explain where it came from without necessarily defending it!
Have you talked to the teacher and/or any of the other parents with kids in this class? It might be good to hear her perspective and if other people are unhappy, it's easier to create positive change.
