An exploratory study of the relationship between young children's understanding of randomness and Piagetian developmental level

The purpose of this study was to bridge the research gap concerning the linkage between probabilistic understandings and Piagetian developmental level in young children and to shed light on the conflicting data that have been gathered concerning young children's probabilistic understandings. Specifically, a portion of a study by Kuzmak and Gelman was replicated in order to determine if children between the ages of 4 and 7 are able to differentiate between a determined outcome and a fortuitous outcome. In addition, the same children were tested concerning their ability to differentiate between random and regular patterns of outcomes. Furthermore, tests of conservation, classification, and sedation were administered to detect evidence of the existence of concrete operational structures. This study was deemed to be important because of the recent trend to introduce the concept of chance into the early elementary classroom. There was evidence that some children as young as 4 can distinguish between a determined and a fortuitous outcome when the criterion for understanding is judgment as opposed to judgment-plus-explanation, which was in agreement with the study of Kuzmak and Gelman. However, no children age 4 and few children ages 5, 6, and 7 provided adequate explanations. These percentages are considerably lower than those Kuzmak and Gelman found. There was little evidence that children age 4 or 5 have the ability to distinguish between a random and a regular pattern of outcomes. However, most children ages 6 and 7 had this ability when the criterion for understanding was judgment instead of judgment-plus-explanation, while approximately one-third and two-thirds of the 6- and 7- year-olds, respectively, provided adequate explanations. Finally, Piaget's theory that children must show evidence of the emergence of concrete operational structures in order to exhibit the first understandings of chance was supported using methodology which required that subjects formulate verbal explanations. As little evidence was gathered to investigate Piaget's linkage between understanding of randomness and reversibility, which is supposedly inherent in children who are in the concrete operational stage, the instrumentation needs to be revised in future studies to directly address this issue.