How much time should the student practice?
I recommend that students practice at least the length of their lesson time daily. So if your child takes a 30 minute lesson every week, he or she should aim for practicing at least 30 minutes every day. The goal is to set up consistent practice routine. It's more important that they spend time with their instruments on a daily basis than a big chunk of time every two or three days. It is also a good idea to break up the practice time for younger children. For example, you can practice violin hold after school, a bow exercise before dinner, and "soaping the arm" with "mystery rhythm" before bed...etc.
It seems to take a long time before my child starts playing the violin. Why?
How fast the child starts to play the violin (with violin and bow) varies greatly on their age, learning style, coordination, home environment and many other factors. Just like learning to speak a language or picking up a new sport, our job is to create the best environment for the child to learn, and leave the rest to them. In my experience, building a good foundations at the beginning is the best and most important thing we can do to start the child on the road of a happy music journey. It may seem to take a while, but a few months of solid foundation building is worth all the remedial works down the road. (Trust me, I had to do some serious remedial works when I was in graduate school after playing the violin for 17 years. I really wished I had taken care a lot of that beforehand.)