M’Choakumchild is the name of a schoolteacher assigned to instruct Sissy Jupe in the fact-based education that Gradgrind supports. His name sounds like his role as a teacher: he is Mr. Choke-em-child, tasked with "choking" the "fancy" or imagination out of his charges.
The narrator describes him as a product of factory thinking and factory education, likening he and his 140 fellow teachers as the identical products of utilitarian educational philosophy, produced as if they are identical "pianoforte legs." M’Choakumchild knows innumerable facts and figures and plans to impose these and only these on the children in his grasp. The narrator is critical of him and his kind, stating,
If he had only learnt a little less, how infinitely better he might have taught much more!
The narrator also states that M’Choakumchild will either outright kill or "maim and distort" the imagination lurking within each child. His view on education is so rigidly mechanistic that all it has room for is facts and figures. In a play on a saying attributed to St. Ignatius of Loyola, who is purported to have said, "Give me a child to the age of seven, and I will have him for life," Dickens's narrator states,
Bring to me, says M’Choakumchild, yonder baby just able to walk, and I will engage that it shall never wonder.
Sissy Jupe has a hard time with M'Choakumchild, as she has, in his opinion, a "dense head" for figures and is slow to learn dates. She is a failure in his system of education, as her focus remains emotional and empathic, not factual.