Why does Jess keep drawing supplies hidden under his mattress? And why does he not want or dare to show his father his drawing supplies?

Jess keeps his drawing supplies under his mattress because he knows that his father doesn't approve of his hobby. He also doesn't dare show his father his drawing supplies because he does not want his father to be angry with him.

When he was in the first grade, he remembers telling his father that he wanted to be an artist when he grew up. His father had gotten very angry upon hearing his son's words. Jess remembers how painful the exchange had been; his father had basically implied that the teachers at school were turning him into a wimp.

The irony of it is that none of Jess' regular teachers actually support his artistic endeavors. In fact, they 'would screech about wasted time, wasted paper, wasted ability' when they caught him drawing. The only one who supports him is his music teacher, Miss Edmunds.