Preschoolers' Understanding of the Addition–Subtraction Inverse Principle: A Taiwanese Sample

Previous research, which typically overestimated competence, indicates that preschoolers have an unreliable or a localized understanding of the addition– subtraction inverse principle (e.g., 2 + 1 − 1 = 2). Forty-eight Taiwanese 4- to 6-year-old participants were tested with a relatively conservative measure to gauge when a reliable and general nonverbal understanding of this principle begins to emerge. After an uncountable collection was covered, a child saw 2 to 4 items added to the covered collection and then an equal number removed from the opposite side of the cover (or vice versa). Three-eighths of the 6-year-old participants, 1/4 of the 5-year-old participants, and a single 4-year-old participant were reliably successful. Younger children, particularly, may have “melted down” because of the large size of the original collection or because the task required unfamiliar algebraic reasoning. Qualitative and quantitative analyses indicated that an understanding of the inverse principle emerges gradually and that a general understanding of this principle is within the zone of proximal development of at least some 5-year-old children.