This study contributes to a growing body of research on the development of elementary teacher's content knowledge of mathematics. Individual clinical interviews were conducted with preservice elementary teachers (N=21) enrolled in a professional development course called "Foundations of Mathematics for Teachers." An instrument that allowed for the flexibility to probe and clarify participant understandings of elementary number theoretical concepts was employed. Questions were designed to clarify participants' understandings of procedures and concepts relating to divisibility and to investigate their abilities to make connections and inferences from them. A constructivist-oriented phenomenological analysis of reflective abstraction was adapted as a framework for interpreting data acquired in the interviews. Data analysis supports the general claim that teacher's content knowledge is "weak" and teacher's conceptual understanding is "insufficient" at times to teach arithmetic even in the elementary grades. Results provide a preliminary basis of a descriptive theory for the development of mental constructions involving elementary numbers concepts, their properties and relationships. An illustration of the model used to guide analysis and excerpts from the interviews are included. (Contains 16 references.) (LL)