Scout and Calpurnia have a teacher-student relationship:

Like Atticus, Calpurnia is a strict but loving teacher, particularly in regard to Scout, whose enthusiasm sometimes makes her thoughtless.

Calpurnia disciplines Scout, and at times, Scout rebels against that teaching. Scout shares her feeling with Atticus who wisely sides with Calpurnia. During one of the times that Calpurnia disciplined Scout, Scout wanted Atticus to get rid of Calpurnia:

'She likes Jem better'n she likes me anyway,' I concluded, and suggested that Atticus lose no time in packing her off.

Scout reacts as a typical child would when she is scolded. In reality, Scout truly loves Calpurnia. Scout is learning. She has to be disciplined, and discipline is grievous. No one enjoys discipline. Calpurnia balances her discipline with affection which often gratifies Scout:

Calpurnia bent down and kissed me. I ran along, wondering what had come over her. She had wanted to make up with me, that was it. She had always been too hard on me, she had at last seen the error of her fractious ways, she was sorry and too stubborn to say so. (3.75)

Truly, Scout is too young to realize that Calpurnia is doing the right thing in disciplining her. Nonetheless, Calpurnia is fair. She scolds or disciplines Scout. Then she will show her tenderness at the right moment.

After Calpurnia had scolded Scout for making negative remarks about the Cunningham boy, the next day she makes a treat for Scout--crackling bread. In a tender moment, Calpurnia shares how lonely she was while Scout was at school:

'I missed you today,' she said. 'The house got so lonesome, 'long about two o'clock I had to turn on the radio.'

Truly, Scout and Calpurnia have a balanced relationship. Calpurnia is balanced in teaching Scout. She scolds using tough love. Then she showers Scout with tenderness and affection. No doubt, Scout will grow up to appreciate Calpurnia for her firm teaching and tender love.

Explain the relationship between Scout and Calpurnia and how it has developed through the book.

Calpurnia has raised Scout and taught her many things (how to write in cursive, for example). As her caregiver, Calpurnia is loving and yet strict with Scout. When Scout goes to Calpurnia's church, Scout is amazed at the way Calpurnia talks - shedding her "white" way of speaking. Calpurnia explains that she is being respectful and sensitive towards the other people in her congregation.
When Scout asks if she can visit Calpurnia at her house, Cal agrees.
Scout begins to understand that Calpurnia has a life outside of the Finch household. This realization is part of the maturation process for Scout (an all people, really).

Explain the relationship between Scout and Calpurnia and how it has developed through the book.

Calpurina helped raise Scout and Jem, and at first Scout sees her only as an extension of herself, which the novel allows for by having Calpurina scold Scout in the beginning. Scout can't imagine Calpurina outside of her household, as being anything other than her Nanny. As Scout slowly begins to grow she realizes that Calpurina is her own person, that she has a life outside of her and Jem. This really comes to a head when Calpurina takes them to her Church. At the Church Calpurina takes on a persona that Scout has never seen, she uses a dialect and voice that is unfamiliar to Scout. Calpurina becomes the link between the black and white world for the children.