The conflict between Mama and Beneatha is related to respect for family and family history.
Beneatha desperately seeks a way to self-respect in A Raisin in the Sun. Her pursuit of education, which Mama supports, is a large part of her character, as is her interest in creating an African identity for herself.
Mama only disagrees with these interests where they constitute an intentional break with the family, family history and entrenched family values. Mama believes that her children have been raised to respect themselves (and God), as she herself does and as their father did. The family is not something to be escaped or broken from.
Beneatha's self-makeover becomes a betrayal and a significant source of disrespect to Mama, as she sees it.
It is not too surprising that mother and daughter are in opposition a bit in this play. The mother/daughter conflict exists in most of humanity. In A Raisin in the Sun, Mama’s dreams only conflict with Beneatha’s dreams when those dreams oppose traditional ideas of family life.
Any (and only) Beneatha’s dreams that oppose family are the dreams that Mama is against. Because Mama’s generation considers the man to be the “natural” head of the family, many of Benetha’s dreams oppose this older idea of the woman as subservient. (Some say this has to do with Mama being a Southerner who moved up north in the chaos that followed the Civil War.) In regards to education, Beneatha only conflicts with Mama in the extent that her upper level of education teaches her to show disrespect to family and/or to move further away from family. (Otherwise, Mama supports Benetha’s attempt to better herself in this way.) Beneatha also conflicts with Mama over another family tradition: religion. Mama is devoutly religious and the tension is high when Beneatha proclaims, “There is no God.” This conflict bleeds deep into Beneatha’s desire to visit Africa (which, of course, is traditionally not Christian). Not only would these visits to Africa be taking Beneatha away from home but, as Mama suggests, further away from her Christian religion as well.
In conclusion, it is important to note that we would be in error to say that Beneatha’s dream of a formal education betrays Mama. Mama is, in fact, in support of this dream, but only to the extent that it doesn’t conflict with the traditional family values that Mama supports. Mama and Beneatha, then, are unified in at least one desire: to succeed in The United States of America. Mama simply wants this success to be within the realm of family values. Beneatha wants this success in any way possible and, especially, in the “new” way including more significant roles for women.
The conflict between Mama and Beneatha contains multiple parts. It is obviously generational. In most stories in which an older character must interact with a younger one, there is generational conflict. However, more importantly, this play involves religion, access to education (Beneatha's access vs. Mama's lack thereof), and black American traditions vs. an increasing connection to African themes and traditions (common in the 1960s and 1970s).
Beneatha is a university student in Chicago. Not only is she in college, but she has access to one of the world's most sophisticated cities. She is taking advantage of its art, music, and architecture -- not to mention all of the changes of the late 1950s and 1960s, which were most strongly felt in major cities. She is able to do this because Mama moved the family to Chicago long ago. Lorraine Hansberry intended for Mama to represent someone who had migrated "up North" from the rural South. She is one example of someone who would have come to Chicago during the Great Migration of the early 1900s, when many former slaves and their descendants moved North from the South in search of work in Northern factories.
However, Mama still follows the traditions that she learned "down South": she is devoutly Christian; she is committed to believing that her son knows what's best for the family (she still sees a man as a head of the household); and she refuses to accept the possibility of Ruth getting an abortion when Ruth gets pregnant during a time of financial difficulty.
Recall the scene in which Beneatha proclaims: "There is no God." Her mother slaps her and assures her daughter that, as long as she is alive, her children will believe in God. Beneatha had learned to question religious faith in the classroom. Mama, however, is steeped in the Southern Baptist Church. Christian faith provided many Southern black people with peace and hope throughout slavery, during the sometimes terrifying years of Reconstruction, and thereafter, when they went North into "unknown" territory. When Beneatha says, "There is no God," she indirectly dismisses her mother's values, and her mother's system of coping with a world that is not welcoming to black people.
These Southern Christian values also conflict with Beneatha's desire to "go back to Africa." She dresses in West African clothing and listens to West African music, in an attempt to get closer to her ancestors. Yet, her insensitivity to her mother and other members of her family contrasts with this. It is her West African boyfriend (it is never clear which country he comes from), Asagai, who reminds her to have respect and sympathy for them.
Really, Mama and Beneatha have the same dream: they both wish to make it in America. For a black American, This was no easy task in 1959 (the year the play was written), and it is no easy task now. They seek to go about it in different ways: Mama wants to be more conventional and do things the "American way," while Beneatha seeks to create a new way to exist as a black person in America. Both, however, want the best for their families. Both want to be happy and prosperous.