This paper analyzes Brainerd's work in assessing the developmental sequence or ordination and cardination concepts of number, and describes a study which investigated the hypothesis that task-specific difficulty could explain Brainers's data. Three new tasks were designed for the assessment of ordination and cardination and administered to a sample of 42 children from preschool, kindergarten, and first grade classes. Each child was given a total of six different types of tasks; one counting task, two strictly ordinal tasks, two strictly cardinal tasks, and one task with both cardinal and ordinal aspects. Results indicated that (1) the Brainerd cardination task was significantly more difficult than any other ordination or cardination tasks; (2) generally, no other tasks were significantly different from one another, and (3) some a posteriori analyses were in the opposite direction predicted by an ordinal theory of number. These results were interpreted as supporting the task-specific difficulty hypothesis. (Author/GO)