On the Sequentiality of Ordinality and Cardinality

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Abstract
Some research with Brainerd-like number tasks is reported. 266 subjects (from kindergarten and from primary school grade 1) completed 4 tasks: concrete ordinal correspondence tasks, abstract ordinal correspondence tasks, ordinal number tasks, and cardinal tasks. Results revealed no differences in difficulty level between concrete and abstract ordinal correspondence tasks. The ordinal number tasks were more difficult than the ordinal correspondence tasks. The data also suggest that the child acquires ordinality prior to cardinality. The last finding confirms the conclusion of Brainerd (1978, 1979). Nevertheless, these conclusions are rather weak because of serious differences in psychometric qualities between different kinds of tasks, because of poor operational definitions of cardinality and ordinality, and because of uncontrolled differences in task sensitivity. Only with more refined analyses of task variables will the future of a theory of number development be promising.

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