my kid is the "shine your light under a bushel basket" type, and keeps his skills really private. I know that for my son, a lot of it was not wanting to draw attention to himself and not trusting the adults around him related to how they might react to his skills and abilities.
We talked to him about how if he didn't let them know everything he can do, they would give him boring work, and how if he showed them what he knows, they would give him work that was more interesting.
A week in, your son may not trust his teacher enough to let her in to his secrets.
