The present study aims to investigate the existing institutional conditions and restrictions that
impact on the immediate need to understand the functions of the role of non-mathematical
knowledge present in mathematical models related to situations concerning Fiscal Education,
using as an example the Income Tax for Initial and Continuing Teachers. Our main theoretical
framework is based on the Anthropological Theory of Didactics (TAD), with the aim of
answering the following question: “what institutional conditions and restrictions exist and how
do they impact the understanding of non-mathematical knowledge present in mathematical
models, in situations involving tributes and taxes, with the Individual Income Tax (IRPF) as an
instigating element for the initial and continued training of teachers?”. From this perspective,
the investigation focuses on the reason for the foundation of the IRPF and Tax Education,
considering the bibliographic reference, contributing to the focus on teacher training with their
skills and competences in the use of mathematical modeling, resulting in the production of the
Model Epistemological Reference (MER). To answer the study question, we developed a Study
and Research Path for Teacher Education (PEP-FP), through the unfolding of seven study and
research sessions with students (students in initial and continuing education) of the Integrated
Degree course in Education in Science, Mathematics and Languages, from the Federal
University of Pará (FEMCI/IEMCI/UFPA) and other institutions in the country. It is understood
that research from the perspective of TAD shows its relevance to study and analyze teaching
problems, which often come from the Current Epistemological Models (MEV). A qualitative
investigation was carried out, with a methodological approach of the bibliographic documental
study, analyzing the new curricular bases, the curricular parameters, laws and norms,
dissertations and theses, based on the praxeological model of TAD, in the sense given by
Castela and Romo Vázquez, which deals with the participation of other knowledge, including
practical ones, in mathematical models about practices that, in our case, involve tax law,
accounting and Mathematics, constituting an essential tool to provide an answer to the
questioning posed about mathematical modeling , from the praxeological model that was
presented. We also used the dialectic of questions and answers that arose in a natural way, and
the dialectic of media and means, for the analysis. We verified, in the research results, that the
PEP-FP favored the initial and continued formation of the teachers, since the participants
managed to elaborate didactic proposals related to the object of research, the Fiscal Education.
Considering the procedures used in the research, we observed the production of favorable
conditions in the use of the Epistemological Reference Model during studies. Analyzing the
Current Epistemological Model, we highlight the restrictions that cannot be omitted and studied
for the construction of our Alternative Epistemological Model.
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