It is of great importance for mathematics teachers to use tools to describe, explain and improve the teaching and learning processes. Consequently, the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA) has tools to carry out this type of didactic analysis of mathematical objects. In this sense, the reconstruction of the global meaning of the inequalities object is presented, where some of its reference meanings are identified, from the semiotic analysis of problem-situations, found in the 3 periods of humanity and from these the reconstruction of the epistemic configurations present in the solution of the problem-situations which emerge from the historical-epistemological study carried out for the reconstruction of the referential global meaning. This work is the result of an investigation carried out as a case study to teachers from public and private institutions in the department of Boyacá (Colombia) to answer the research question: What knowledge do mathematics teachers have of the inequalities object, with respect to the intended meanings in the teaching processes, according to their conceptions and beliefs? As categories of analysis, those exposed in the model of the teacher’s Mathematical Didactic Knowledge are taken and among the results of the study it is concluded that teachers find it difficult to recognize the importance of identifying and knowing the different types of reference meanings for the inequalities object.