I have a 6 yr. old grand-daughter that has been lashing out,and when confronted about her behavior she goes into this cold distant stare and will not make contact with your eyes,recently I was contacted by her teacher who told me she was trying to get her to read a word that she was pointing to and my grand-daughter,physicly pushed her hand off her paper, and she is being mean to other kids on the playground.
The good news is you're asking the right question! So many people start off my saying, "This is what my child's doing - what should I do?" They skipped the most important part, which you remembered - before asking what to do, asking "Why is this happening?"
Unfortunately, there are a lot of possible explanations, and you'll probably want to find someone who has experience with behavioral issues to help figure it out with you, such as a guidance counselor at school or a mental health counselor. There are tens if not hundreds of different things that could be going on, and someone with experience who can work directly with your grand-daughter will be in a good position to help you with that answer!
She may be presenting with an undiagnosed mental health condition such as depression. She might be presenting symptoms of Autism, ADHD, need social skills therapy, a number of issues that a professional in pediatric development can help identify.
Folk become defensive or fearful of "mental illness," but STRESS is a form of mental illness. I suggest a psych-ed or neuro-psych eval which can be done, for free, at her public school. Parents may opt to fund this privately AND request the free eval through school.
If she has a mood disorder it will affect her behavior; if she has a sleep imbalance it will affect her behavior; if she has other socio-emotional challenges or PDD, (pervasive developmental disorder) she requires support and patience. I encourage the family to begin with an evaluation, for the little one's sake. The teacher could have requested an evaluation, if this is a public school. If the school is private, parents may go with a private eval which insurance should cover. Good luck, god bless!