This report has its origin in the research project: «Characterization of the student-teachers conceptions on the natural number concept», done at Universidad de La Salle in Bogotá. The project’s goal is to characterize the conceptions the students in the BA have on that mathematical topic. To inquiry about the mathematical conceptions of the students allows us to know about the mistakes they make, either in problem solving and mathematical exercises or when they have to defend procedures, algorithms and theoretical aspects linked even with practical problems. The research project this article is based on, belongs to the qualitative methodological perspective, with a descriptive type design, it is also a basic, microsocial and sectional work (Sierra, 2001). As a result, the students of the BA in Teaching Mathematics and Computing Sciences have the following conceptions of the natural numbers: «the natural numbers as representation of quantities» and «the natural numbers with field structure». Although, these conceptions are not correct since they do not correspond to any definition formally established in mathematics for the set of natural numbers, they show the ideas that the students have about this mathematical topic.

Initially, this article presents an approximation to two conceptions about Mathematics and its teaching. Then, the author describes the semantic field of the term “conceptions”. Finally, Restrepo Becerra makes an approximation to diverse approaches about what is the actual interpretation of the Didactic of the Mathematics.