This research project focuses on identifying the difficulties that children between 6-7 years-old have in learning natural numbers, when working a teaching model with a Von Neumann formal mathematical basis. In this study, we present the analysis of the experimentation with a first-grade class in the construction of zero and one numbers, contrasting the results with a case of the clinical interview. Our methodological theoretical framework is the Local Theoretical Model (LTM) and its four components: Formal, Cognitive, Communication and Teaching. With the theoretical contribution of each component, the categories of analysis are designed to observe and explain difficulties in the use of the Mathematical Sign System (MSS) involved in the construction of the first natural numbers, using iteration and the recursive process. [For the complete proceedings, see ED629884.]