Master of Arts Thesis, 2010

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Rethinking Developmental Transitions in the Acquisition of Number Concepts and Cardinality
                Barry Finder

When children begin counting they do not fully understand the meanings of number words. This understanding comes sequentially; for "one," then "two," then "three," then "four." These children are called "subset-knowers" because they have exact meanings for only a subset of their count list. Children become "CP-knowers" when they induce the cardinal principle (that the last number counted in an array indicates how many objects there are). Approximately six months later, children become "CP-mappers" and map the number words to non-verbal representations of approximate quantities.

In two studies, we examine these developmental transitions. What do subset-knowers understand and what do they need to become CP-knowers? Study 1 examines the possibility that subset-knowers (incorrectly) use number words to refer to discrete objects (e.g. "this truck is the five") while CP-knowers (correctly) refer to sets (e.g. "there are five trucks here"). We found that subset-knowers do not systematically make this error, but they have more stable understandings of sets after the one-knower stage than previous research has indicated. Study 2 attempts to train three-knowers to become mappers. All children became four-knowers but did not induce cardinality.

Taken together, these results are important for understanding conceptual changes in number development. The one-to-two-knower transition brings with it an understanding that number words refer to sets. This understanding does not appear to be sufficient for inducing the logic of counting and cardinality: training to support children's mapping of numbers words to sets did not promote an understanding of counting.

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