This research addresses the theme of the area of Mathematical Education, with regard
to the said Trends in Mathematical Education, which in our perspective are Theories
in Development of Mathematical Education. The purpose of this discussion is to make
reflections that allow us to have a more integrated look at the Theories in Development
in Mathematics Education. Supported by Lakatos' Epistemology (1979), we take
Mathematics Education as a research program and theories in development as the
research subprograms. For this, we developed a Study and Research Pathway (PEP).
The Courses were carried out with professor-students of the Postgraduate Course at
the Master and Doctorate level of the Postgraduate Program in Education in Science
and Mathematics (PPGCEM), from the Institute of Mathematical and Scientific
Education (IEMCI) of the Federal University of Pará (UFPA). We assume as a research
question: What is the Firm Core of the Mathematical Education Program that would
articulate the Theories under development as Subprograms? In this perspective, we
understand that some of the so-called Trends in Mathematical Education, as
considered by many researchers in this area in Brazil, are nevertheless constituted as
Theories in development, being Research Subprograms that are articulated in a larger
context, the deque program is Education research Mathematics, which is organized
from a firm core to be revealed in a Study and Research Course. In these terms, we
developed the construction of this thesis, where we assume that the developing
theories of Mathematics Education are contextualization in a broad sense of this field
of research, and are constituted as research subprograms.
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