The dynamics of children's counting: The role of actions and gestures

Date of Completion

January 2011

Keywords

Education, Mathematics|Psychology, Developmental

Degree

Ph.D.

Abstract

In this dissertation, two experiments investigated the role actions play in the development of children's conceptual understanding of number. Experiment 1 examined how small changes in the perceptual properties of items being counted (i.e., whether the items alternated in color) impacted the microstructure of the actions associated with counting those items. Further, this study explored whether these changes in the microstructure of actions were related to changes in participants' conceptualization of basic number principles. The results showed that the differences in the items being counted created different across-scale interactions in the microstructure of counting and that different patterns of interaction were associated with conceptual gains in understanding counting principles. Experiment 2 tested whether the differences in across-scale interactions associated with conceptual change were a function of the manual motion itself, as opposed to a more general property of the self-organizing system. Half the participants were asked to inhibit their hand motions during a counting task; the remaining participants were free to gesture. In both conditions, the motion of the head and the hand were tracked. Results showed the same systematic pattern of across-scale interactions associated with conceptual changes found in Experiment 1 emerging from the motions of the hand (when the hand was free to move) and the head in both the inhibited and free-motion conditions. These experiments were the first to use Gottlieb's theory of probabilistic epigenesis, in conjunction with theories of self-organization, to address conceptual changes in children's understanding of basic number concepts. ^

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