Prior to his going to Miss Havisham's, Mrs. Joe and Pumblechook have felt that Pip would have the opportunity to gain some kind of fortune. However, after his visit, and the cruelty of Estella and his being simply used to play cards with the girl, and being ridiculed by her, Pip expects very little. Besides this low expectation, Pip is for the first time ashamed of his being "common," and ashamed of Joe's being uneducated and common.
So, Pip's decides that he will do everything he can to not be common; he asks Biddy to impart all her knowledge to him.
The felicitous idea occurred to me a morning or two later when I woke, that the best step I could take was to get out of Biddy everything she knew.
The obliging Biddy promises that she will help Pip. However, since the schoolroom is anything but traditional with Mr. Wopsle's great aunt has no control over the children, then falls asleep. Nor does Mr. Wopsle exert much influence over the children; consequently, Pip does not learn much. Nevertheless, Pip is determined and has Biddy instruct him per their special agreement.