If your teen becomes secretive and doesn't want to chat even about how her way went in school, should you consider it normal? Why or why not?

This is a normal behavior during this particular stage of life. At one point, we were also a teen before. We tend to keep some issues from our parents having the thought that this could either make them mad or overreact in a way. But later on, we'll realize that it would be better to have shared it to them. This is a part of learning and development for every individual. The best thing to do would be to assure them of your presence and support all the way. Never fail to encourage them to open up. This way, they will realize that they are never alone every step of their way.