Gradgrind calls himself a "man of facts and calculations." He wants his pupils to know nothing but the facts. He calls Sissy Jupe girl number twenty, because he believes education is primarily a matter of learning arithmetic and numbers.
Gradgrind also finds her name, Sissy, ridiculous, saying it is not a real name. He tells her she should call herself Cecilia instead. He is not pleased that her father rides horses in the circus and tells her not to talk about that in the classroom. He humiliates her when she cannot define "horse."
In fact, Sissy and her family, as circus performers, are the polar opposites of Gradgrind and his utilitarian philosophy of efficiency. Their career is based on exciting people's imaginations, entertaining them, and bringing joy into their lives with no other value attached to the experience than pleasure.