"Cultural capital" refers to Pierre Bourdieu’s concept that certain forms of cultural knowledge are the equivalent of symbolic wealth. These cultural (and linguistic) knowledge bases and skills are socially inherited and are believed to facilitate academic achievement. (Bartolome 1994)
Norms are rules of social interaction. Norms are prescriptions of conduct and are a subset of values. Values are beliefs about what is important.
Socially constructed rules unlike physical laws can be broken. To enforce dependable social interactions social rules come with incentives for compliance and sanctions for noncompliance.
First norms can become values. For example a norm of giving up a bus seat for the elderly can become a belief about how the elderly should be treated. For disciplinary norms checking scientific claims against evidence can eventually become a belief that ideas should be checked against evidence.
Second norms can produce a sense of belonging. One example is how colleagues shake hands when they greet each other.
Belonging is the perception of being accepted valued and included. Belonging can help learning by increasing effort and decreasing negative distracting thoughts.
Third norms contribute to identity development. Different cultures have different norms so partaking in a set of norms increases identification with the given culture. Inversely if one wants to maintain an exclusive identity with one cultural group they take an oppositional stance to other norms (Schwartz et al. 2016).