Final answer:
The American researcher who classified the five types of play is Mildred Parten, not Jean Piaget, Sigmund Freud, Lev Vygotsky, or Maria Montessori.
Step-by-step explanation:
The American researcher who identified five types of play, including solitary, onlooker, parallel, associative, and cooperative, is Mildred Parten. While Jean Piaget, an eminent psychologist specializing in child development, is well-known for his theories regarding cognitive ability changes as children mature, he is not the one who categorized these types of play. Return to Mildred Parten's work to explore these classifications of play further.