Reverse Mathematical Modelling

Background: Research in mathematics education shows that mathematical modelling is a practice that seeks to “translate” problem situations into possible mathematical models without, however, explaining the complexity involved in the reverse formulation, starting from the mathematical model to delimit the type of situation. Objective: To highlight the problem of reverse mathematical modelling, in the sense of a reverse formulation that goes from the mathematical model to the situation. Design: For this, a course of study and research was carried out guided by the investigative cycle of mathematical modelling that is based on theoretical-methodological resources of the anthropological theory of the didactic. Setting and Participants: Pre-service teachers of a teaching degree at a public institution were faced with a problem in an unusual context about the decimal number system and, more broadly, the positional number system. Data collection and analysis: We present an empirical approach based on research carried out by Ferreira (2020) with teachers in initial training. Results: The empirical results observed confirm the hypothesis of the existence of the problem of reverse mathematical modelling, even in the face of normative models, in the sense that they can faithfully describe a real situation. Conclusions: Ultimately, the study of a type of problem in an unusual context, in addition to highlighting the encounter of teachers with different objects of knowledge, revealed the remarkable difficulty in delimiting the type of quantification situation that can be associated with the mathematical model of the number and as stimulate future research on the teaching of reverse mathematical modelling.