Analysis of the extract from Hard Times at page 348 - answering the questions at page 350 -

The setting of the extract is a classroom. In particular, a third person omniscient narrator describes what is happening during Mr. Gradgrind's lesson and guides the reader with interventions (and would have blushed deeper if she could have blushed deeper) , even if the writer adopts the technique of showing too (dialogues).
Mr. Gradgrind is testing orally "girl number twenty"; right from the start, her identity seems to be alienated: to the teacher, she is just a number and her name does not conform to the institutional context of school, thus making the child feel ashamed (blush) because of her modest social background.
Such a condition of discomfort, gets worse when the teacher asks her questions about her father's profession and, last but not least, he wants her to describe an horse. It seems as if the girl, Sissy, were paralyzed by fear in front of such an authoritarian figure and could not make the point of his requests.
Her total submission to the teacher is underlined by "curtseying" and the repetition of "if you please, sir". her discomfort is repeated many times by the use of the verb blush. The peak of embarrassment is reached by the girl when her classmate is able to answer the question about horse through a very detailed description of the animal and the teacher seems to insist on her poor figure.
It goes without saying that Mr.Gradgrind is the object of C.Dickens' indirect critique. He represents an education-system based on terror and derision. The character is a sort of caricature, whose most interesting feature is "his square forefinger": indeed, he stabs at students in order to desperately affirm his power.