In "The Rocking-Horse Winner", how does Paul's behavior compare to other kids?

In the short story "The Rocking-Horse Winner" by D.H. Lawrence, the author presents a boy who,to all intents and purposes, is like any other small boy. But soon the author shows us how Paul is under stress. He is suffering the terrible strain of his mother's expectations snf hid family's limitations in meeting them. He becomes unchildlike when he internalises responsibility for all this financial pressure and tries to take satiating his mother's ambition for money and materialism and social status on his own young vulnerable shoulders. He is childlike in his belief that he can make his mother love him more, and in his belief that he has some influence over what happens in the life of his parents. For example, some children believe that a divorce happens because of them.

In "The Rocking-Horse Winner", how does Paul's behavior compare to other kids?

Paul, like all small children, seeks for approval and love from his parents.  So, he does things in order to please them.  This is what prompts the rocking-horse riding in the first place.  He senses his mother's "cold" heart, and in a conversation with her, learns that she wants to be "lucky," or rich, more than anything else.  He figures that if he can get her money, then her heart will soften, and she will finally love him.

Paul is also like a small child in the way that he trusts people.  He trusts the gardener and his uncle to work with him in winning these huge amounts of money; that is pretty trusting, if you ask me.  An adult would expect scamming to occur, but Paul just innocently lets the gardener handle all of the money, and deal with it.  Very child-like and naive.

One other way that Paul is like other children is that he doesn't really express greed or desire for a lot of money--his desire for the money is to win his mother's love, not to get things for himself.  He is very selfless and childlike about money and what it means.

Despite these traits, Paul is really more serious than most children.  He is calm, serious, earnest and mature for his age.  He doesn't seem to play or take things lightly.  Also, he is very focused and determined.  Most kids can't focus on one thing for more than ten minutes.  Paul spends hours on his horse, focused and determined.  Kids also tend to give up pretty easily and get frustrated when things aren't going their way--not Paul.  He rides and rides until he gets the right answer, even if it takes a very long time.  He is also unduly  burdened with the cares of the world; his parents' desire for money weighs on him, and he takes the responsibility on himself--that is not like a child at all.

I hope that those thoughts helped; good luck!

In "The Rocking-Horse Winner," how do Paul's actions reflect a child's response to a stressful situation beyond their control?

Although D. H. Lawrence's story, "The Rocking-Horse Winner," reads much like a fairy tale, there is a perversion, rather than a reinforcement, of values as the obsession with money overrides the natural value of love:

Although they lived in style, they felt always an anxiety in the house.  There was never enough money....There was always the grinding sense of the shortage of money, though the style was always kept up.

Confronted with the demand in his home that "there must be more money,"  young Paul asks his mother about their situation.  When she tells him it is "because your father has no luck," Paul asks her "Is luck money, mother?" In response, she explains that luck is what causes people to have money, and she is unlucky.  Paul, then, "stoutly" replies that he has luck, without knowing why he has said this. But, in a typical childlike reaction, Paul feels that if he can be lucky, things will be better. 

So, unknowingly, Paul tries to please his mother; he thinks if he can be lucky, then he can "compel her attention," attention that she does not give him because she is incapable of loving.  Moreover, Paul feels that if he can be lucky and win money for his mother she will be happy, and then he will win her love.  And, so, Paul begins his "mad little journey" of riding his rocking-horse "in full tilt."  After winning horse races with the help of the gardener, Bassett, Paul indirectly gives his mother five thousand pounds.  This, he hopes, will silence the house, silence the demand for money and let his mother love him.  But, Paul's mother squanders the money and does not silence the house by paying off her debts.  Even when she works, Paul's mother is disastified because she does not get paid what she feels she is worth.  Money, not satisfaction in her art, is the only compensation for Paul's mother.

In his efforts to quiet the house and make his mother happy, Paul continues to try to make more money by finding the winners to bigger horse races such as the Derby. However, Paul later grows extremely tense from his great efforts, and becomes terribly nervous; nevertheless his mother goes out one night to a dance instead of staying by him.  When he falls ill, she feels her heart has "turned actually into a stone."  As he lies dying, Paul utters his desperate preoccupation to gain her love by repeating, "Mother, did I ever tell you?  I am lucky!"

"No, you never did," his mother says, ironically, because Paul has said these words to her much earlier.  That she does not remember indicates the futility of Paul's obsessed riding of the rocking-horse in order to silence the house and win enough money to win his mother's love.

What is Paul's behavior in "The Rocking-Horse Winner"?

Paul is an innocent young boy who tries desperately to help his family. His mother's manner (her outward behavior) towards the children is "gentle and anxious." So, it appears that she loves them, but inside, she really has no love for them. Paul's parents do not make enough money and Paul's mother attributes this to bad luck or lack of luck. She says luck is what causes a family to have money. She says this instead of pointing to hard work as a means to making money. 

Paul takes it upon himself to obtain the luck the family needs. He doesn't realize it, but he essentially becomes like a parent to his parents. In picking winners of the races, he is the one bringing in the money. His mother spends it frivolously, proving how she is the immature, irresponsible one while Paul is the responsible breadwinner of the family. Their roles have reversed. His mother and father do not know of this role reversal until it is too late. Plus, with the money coming in, they don't want to change their newfound luck. When Hester, Paul's mother, spends the money and requires more, Paul pushes himself even more. Some critics also claim that Paul is acting out a sexual desire. As he is on the verge of adolescence, he conflates the ideas of sexual desire and the desire for luck/money as rites of passage en route to adulthood. In the end, Paul sacrifices himself for the sake of his family.