What kind of child is Paul? What are his motivations?

Paul longs for his mother's love. We learn early in the
story that his mother "felt the centre of her heart go hard" around her children. She
tries to hide this, but her two daughters and Paul sense she doesn't really love
them. 

Paul's mother, a proud woman, yearns for more money
and likes to keep up appearances. She feels disappointed that her husband has not been
more successful. Paul, a sensitive child, feels an "anxiety in the house" that haunts
it. The very walls seem to cry out, "There must be more money." Everyone feels the
"grinding sense of the shortage of money."

Paul
internalizes his mother's desire for money. Like her, he is proud. He wants to please
her, but his pride is injured when she doesn't believe that God told him that he was
lucky: 

The
boy saw she did not believe him; or rather, that she paid no attention to his assertion.
This angered him somewhere, and made him want to compel her
attention. 

Later, he again
reveals his pride and desire to be taken seriously:

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 And then the house whispers, like people
laughing at you behind your back. It's awful, that is! I thought if I was
lucky—

Paul is also
secretive: "He went about with a sort of stealth, seeking inwardly for luck." When he
wins 5,000 pounds betting, he doesn't want his mother to know he is the source of the
money. He lies to her about why he has his rocking-horse moved to his
bedroom.

He is an angry child too, as might be expected
from someone who senses his mother really doesn't love him. We see this in his eyes. For
instance, "his eyes had a strange glare in them." His eyes "glare" and "blaze." His
voice shows his anger as well: he speaks "fiercely" and at one point his voice "flared."
He rides his rocking-horse "furiously." We see his anger in his determination to "force"
the horse to do his bidding:

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He would slash the horse on the neck with the
little whip he had asked Uncle Oscar for. He knew the horse could take him to where
there was luck, if only he forced
it.

There is also something
odd about this little boy. His eyes "had an uncanny cold fire in them." The word uncanny
is used twice to describe him.

We also learn in the story
that Paul is "frightened."

Despite being a proud, angry,
driven little boy, we feel sorry for Paul at the end, for he is most of all a frightened
child who dies trying to earn his mother's love and approval.