Commentary on Theories of Mathematics Education

388 S.J. Hegedus
The Basis of Truth-Finding: What Is the Smorgasbord of Truth,
i.e., Do We Have an Establishment of Processes Which Announces
Our Universal Set of Truths?
Effectiveness is vitally a sense of overseeing the smorgasbord of eventualities. We
are sanctioned into a society and prove ignorant if we do not ignore wily virtues
and seek for a more instructive problem in our methodological environment. In doing
so, we might assess a degree of rationalized scientific discovery in ourselves,
which is sociological rather than mindful. This report attends to abusing the philosophical
mindfulness that Popper alludes to and Hammersley intellectualizes. We
are attempting to describe what is not itself an image. A symbolic painting; an indexical
representation or an iconic demography of what might/should have been
experienced in a sociological setting can be experienced more effectively in a scientific
discovery with a three-fold doctrine which this essay has attended to throughout
its entirety.
In assessing a reality by assessing someone else’s reality in a sociological scientific
discovery—a reconstructing reality by a reality if you may—we might attend to
being confident that we are in a self-sufficient system of assessment. 1 This involves
itself with the nature of knowledge—in an objective manner; also, a reflexive identification
of the self and, a dynamic evolution of the self-perpetuating knowledge
mechanism which is a part of itself in the environment being discovered.
Through this essay, I have implicitly attended to constructing a philosophical
three-fold doctrine, which is embedded in a circular process of scientific discovery.
Aspects of reflexivity, iteration of epistemological constructs, and dynamics
have been described as key aspects of substantiating rigor in the qualitative research
process. And, I propose that in generating a process for observing one’s identity in
an episteme constructed from a qualitative observation of a pedagogical or epistemological
interaction (researcher/respondent) the qualitative scientist might observe
the following three-fold doctrine.
The 3-fold Doctrine of Scientificity
The three-fold doctrine is described by three interacting processes which are part of,
and thus vital in assessing, the qualitative scientific discovery process:
(i) The epistemological identity;
(ii) Reflexivity; and
(iii) The dynamic.
A brief description of each is followed by a non-exhaustive list of questions, which
attempt to epitomize the nature of that part of the discovery process. The section
concludes with an illustration of how the doctrine is embedded into a circular
process of scientific discovery.
1 This adheres to Hammersley’s tentative absolution of the ‘ontological paradox’.