Mr. Gradgrind summons Louisa to his room, and informs her that Mr. Bounderby has asked for her hand in marriage. She doesn't react at first, then responds that she doesn't love Bounderby. Gradgrind recommends that she substitute Fact for sentiment in their marriage. Louisa replies that she accepts this, but for a moment seems to be wavering on the brink of releasing all her pent-up feelings. Because there is no history of confidence or the sharing of emotions between her and her dry father, though, she says nothing, and instead assures him that thanks to his education, she has never received nor looked for romantic attention.
Louisa's dull reaction to the marriage proposal (from a man she has shown dislike for in the past) shows how distorted of a young woman she has become. Instead of revealing the feelings of her heart, which her father has taught her not to do, she goes along as usual with her father's wishes. Her education of facts has not taught her how to deal with a situation so difficult as this. She takes Gradgrind's advice to replace sentiment with fact in her marriage, which to the reader is obviously ludicrous advice and forebodes bad things for the couple-to-be.
She then says she will marry Mr. Bounderby, which she knows is her father's wish. Taking her downstairs, Mr. Gradgrind announces the news of the betrothal to his wife and Sissy. Louisa sees the look of shock, sorrow, and pity on Sissy's face. From then on, she places a cold distance between her and Sissy.
Sissy, unlike Louisa, does not try and hide her reaction at the news of the proposal, and the reader can assume that Louisa strongly resents Sissy's open feelings—perhaps because she herself is unable to express those same feelings. Louisa resents it so deeply that she tries to cut herself off from Sissy completely.