Here’s Martin Doherty (2009) with a nice introduction to the empirical study of verbal false belief tasks:
“… According to Piaget’s theory, young children are profoundly egocentric: They are only able to consider things from their own point of view until they are about 7 years or older. What is now known as theory of mind was considered to emerge as part of a general escape from the confines of egocentrism in middle childhood. This diverted attention away from the surprisingly rapid development of the ability to understand others’ beliefs around the age of 4 years. Researchers driven by a powerful theory can sometimes miss the blindingly obvious.
“The change was brought about by an influential paper by two primatologists, David Premack and Guy Woodruff (1978): “Does the Chimpanzee Have a Theory of Mind?” This question of chimpanzee theory of mind remains hotly contested, but in a commentary on the paper, the philosopher Daniel Dennett suggested a way of determining the answer. He briefly sketched what has become known as the false belief task, taking as one example a Punch and Judy show. Children squeal with glee as Mr Punch prepares to throw a box over a cliff. Although they have seen Judy escape from the box while Punch’s back was turned, it is “obvious—obvious enough for four-year-old children—that Punch believes (falsely) that Judy is in the box” (Dennett, 1978, p. 569). Dennett’s reference to 4-year-olds is a notable piece of foresight. The method was put into developmental practice by Heinz Wimmer and Josef Perner soon after. They found that 4- to 5-year-old children can indeed predict the actions of someone with a false belief.”
Doherty, M. J. (2009). Theory of Mind: How Children Understand Others’ Thoughts and Feelings. Psychology Press.