That scary-looking man is Mr. Thomas Gradgrind. He proceeds to grill the children on what practical knowledge they possess (not much, with the exception of a pale, fair-haired boy named Bitzer, who gives Gradgrind the robotic, factual answers he wants). The first girl Mr. Gradgrind calls upon, whom he calls "girl number twenty" but who is actually named Cecilia "Sissy" Jupe, is unable to define a horse for him and is humiliated by him in front of the class; Bitzer, who Mr. Gradgrind then calls upon, responds correctly but in an unnaturally emotionless manner.
Mr. Gradgrind's way of calling Sissy "girl number twenty" instead of by her real name shows how he wants a factory-like school that cares only about stuffing facts into children. As Sissy, is unreasonably humiliated in front of her classmates for answering Mr. Gradgrind's questions as any child might be expected to answer them, Bitzer's mechanical answers demonstrate what an education of Facts can do to children.
Sissy goes on to make a number of similar innocent mistakes when called upon, but mistakes that prove she has an imagination. Mr. McChoakumchild, the actual schoolmaster of the class and a very learned one at that, then begins his deathly boring lesson on facts for the day.
Mr. McChoakumchild's name indicates in a less than subtle way what his teaching will do to his pupils. All the practical knowledge he possesses and teaches will only serve to suffocate the fancy, the imagination, of the children.