Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were interviewed individually and in small groups to study how children use their knowledge about addition and subtraction to describe, predict, and explore situations of change. The paper is divided into five sections. Section 1 describes the authors' view on additive change and its relation to calculus. Section 2 presents a review of work related to the research on additive change. Section 3 uses the review to describe the goals of the study and the methodology utilized in the interviews. Section 4, the main component of the report, analyzes selected episodes from the interviews. Section 5 discusses the three themes that emerged from the study: (1) additive change: a web of relationships; (2) the many graphs of additive change; and (3) qualitative relations. The authors conclude that the interview episodes indicate that qualitative reasoning is not pre-quantitative or less sophisticated than quantitative judgments. (Contains 28 references.) (MDH)