This investigation used a clinical interview technique to identify the difficulties of kindergarten children who are unable to develop models or representations of simple arithmetic story problems. It is hypothesized that effective human problem solvers first generate some type of "physical model" and use this model to create a mathematical one. Further, the development of a model requires children to make three types of abstractions from a story. These are: making an abstraction of the (1) objects described, (2) locations or possessors of the sets, and (3) operations or relationships described. The type of physical model involved in the study is "operations on sets." The focus of the research is on student attempts to answer addition and substraction problems. Four components identified in tasks of abstraction are: set identity, set numerosity, operation on sets, and identity of answer set. The study results review each identified component, identify some pupil difficulties, and support several specific conclusions concerning pupil success with each aspect of abstraction. Also included are suggested steps for aiding students experiencing specific difficulties. (Author/MP)