This study sought to determine whether a number of specific counting and numeration behaviors emerge within children in a fixed developmental sequence; at what point in the development of mathematical behavior the use of numerical representations normally appears; and what relationship holds between development of counting skills and development of one-to-one correspondence operations. The subjects were 78 kindergarten children in an urban public school. They were given a battery of tests, each assessing the ability to perform a specific task involving counting, use of numerals, or comparison of set size. The test scores were subjected to scalogram analyses. Results suggested: (1) a reliable sequence of skills in using numerals; (2) the dependence of learning numerals upon prior acquisition of counting skills for sets of the size represented; (3) acquisition of numeral reading for small sets before learning to count larger sets; and (4) the independence of counting and one-to-one correspondence operations in young children. The implications of these findings for designing an introductory mathematics curriculum are discussed. (Author/CT)