Using four large existing databases on student performance in the elementary grades, this study involves a task-by-task, year-by-year cross-sectional analysis of six topics in computation. Information about what students eventually learn and when they learn it is provided by the data analysis; information about when skills are introduced and expanded is determined by examining school textbooks. This information is seen as being useful in setting higher standards for elementary schools, which currently concentrate on teaching skills piecemeal over several grades. Specifically, topics investigated are addition and subtraction with regrouping, multiplication and division facts with numbers 5 through 9, and multiplication and division beyond basic number facts. Results show that the topography of student performance varies across topics and across grades within topics. Implications of findings are that efforts focusing on learning opportunities in the middle elementary grades will be more productive than efforts undertaken at the point of entry into secondary schooling. In particular, it is concluded that students learn most when topics are taught as part of regular instruction, that the margin for school improvement may be more promising in certain segments of a subject (i.e., subtraction and division), and that a dramatic loss of performance occurs when the first teaching of a topic occurs late in the school year. (CB)