Final answer:
Carson wants his sons to know him to instill a sense of familial responsibility, pride, and awareness of their family's reputation and prosperity. Fathers tend to be more involved when their sons engage in gender-appropriate activities. Carson's own upbringing and success also make him want to pass on his knowledge to his sons.
Step-by-step explanation:
Carson's desire for his sons to know their father stems from the poor man's deference toward the wealthy and well-born that Carson unconsciously manifests in his interactions with his son. By having his sons know him, Carson hopes to instill in them a sense of familial responsibility and pride, as well as to ensure that they are aware of their family's reputation and prosperity.
Fathers also tend to be more involved when their sons engage in gender-appropriate activities such as sports, which further emphasizes the importance of Carson wanting his sons to know him. Additionally, Carson's own upbringing in poverty and subsequent success makes him want to pass on his knowledge and aid his sons in their growth and development.