Emergent Understanding and Attribution of Randomness: Comparative Analysis of the Reasoning of Primary Grade Children and Undergraduates

Abstract

In this study, I examined primary grade children's emergent understanding and attribution of randomness, as reflected in the classicist and frequentist forms of objectivist probability. Participants included kindergartners, 3rd graders, and, in order to address the complex issue of developmental versus nondevelopmental difficulties, university undergraduates (n = 36). The participants worked individually with me through three tasks: (a) an adaptation of Piaget and Inhelder's (1975) marble tilt box problem, (b) an analysis of spinners and associated game outcomes, and (c) urn-based sampling problems. My research assistant and I conducted a microgenetic analysis of the participants' videotaped performance at 2 levels of analysis, attaining an interrater reliability of 84% across 809 episodes at the most constrained level. Kindergartners' interpretations were typically either deterministic or altogether outside of the determinacy-indeterminacy frame. Only a minority of the kindergartners ever evoked randomness in any task domain. Comparison of kindergarten and 3rd-grade data revealed both conceptual and interpretative advances on the part of the older children. Most of the 3rd graders manifested some grasp of randomness, as evidenced by attribution of randomness at least once. Furthermore, their interpretations were less dominated by the false attribution of determinism than the kindergartners. Nevertheless, all of the 3rd graders interpreted at least 1 of the 3 random phenomena as deterministic.