Three studies were conducted to assess the abstraction processes involved in the development of the ability to associate numerals with sets of the appropriate size (numeration). Experiment 1 examined the sequence of the ability to discriminate relative numerical magnitude, numerical equivalence, Arabic numerals, absolute size of a set, and numeration, with 90 children, aged 3 1/2 to 5 1/2. Quantity and numeral discriminations and the magnitude concept were significantly easier to learn than numeration, but the equivalence concept was not easier than numeration. Experiment 2 was designed to determine if the lack of familiarity with numerical symbols accounted for children's failure in the numeration task. The subjects, 63 children aged 3 1/2 to 4 years, 11 months were trained to associate either geometric shapes, realistic pictures, or numerals with sets of objects. Both the realistic figures and the geometric shapes were significantly more difficult to associate with the appropriate numerical set. Experiment 3 compared performance on numeration tasks with linear homogeneous, non-linear homogeneous, or linear heterogeneous sets, using 90 children, aged 4 - 5 1/2. Numeration was significantly more difficult with heterogeneous stimuli than with the other stimulus arrays. (Author/ST)