Commentary on Theories of Mathematics Education

Appreciating Scientificity in Qualitative Research 387
Qualitative truth has emanated in the preceding discussion as a necessary part of
epistemology, in so far as a dynamic piece of epistemology which revolutionizes the
observer’s viewpoint, only in the sense of incorporating a reflexive element in the
observer’s qualitative mechanisms.
Methodological Rigor—Is Truth Rigorous?
As we attend to a standard in qualitative research, we must observe a methodological
practice and ‘scientific’ examination of such a process. Many standards aspire to an
objective ideal whereby the observer does not rely on any pre-conceived ideological
interrogatives. A pre-disposed philosophy towards an incorporation of a minimalobservational
ideology in a phenomenological agenda can hope to aspire to no more
than a pessimistic agenda in social research.
Firstly, we attend to methodology, which in its own self-conception is a process
of assessing the methods it attains to. As we incorporate a system of ‘scientific
examination,’ we look to a process that incorporates our style and procedural envelopment.
It is whereby one assesses the style of this incorporation and the effect
that oneself has in a self-situating environment that one incorporates a sense
of methodological ideology. Abusing that process, which subsumes our self into a
pathological process, alleviates a sense of methodology. From a method of observation,
one might now be able to assess the true potential that an analytical process
might have an associated truth to any established facets. To return to Popper, we are
not extinguishing any matter of self in making claims about essences of truth; it is in
observing a self-acknowledgement of truth that we might be engaged in a scientific
qualitative methodology by attending to falsifying the appearance of the essence of
observational material. It is the pure individuality of the essence of the observed
that gives rise to truth in its own sanctity. By the very nature of an enlarged self, via
reflection, in the observation of essences of how a sociological system might appear
in a paradigmatic setting, we make a scientific observation. In a reflection of such
an occurrence, we envisage what is called a meta-constructionist interpretation of
the phenomenon of an entity.
It is rigor, for me the essence of reflection in which observation of ourselves
within a social process is self-evident that becomes a mediating factor in our premeditated
work. From there on, we accept a methodological process that is defined
in qualitative terms in this essay. In searching for truth, we are establishing a truth set
up in a self-reflective methodology. To establish a ‘rigorous self’ in the qualitative
dimension calls for a social substance of a virtuous nature to assess the assimilated
process. Understanding the self in a reflective practice has been interpreted as a dual
between intentions and attentions. Sriraman and Benesch (2005) outlined a model
to interpret meaning through an “observer, interpreter, explainer” semiotic structure.
They draw on Shankara’s idea of “superimposition” to provide a methodology to analyze
and interpret the dialectic between the knower, the observer and the interpreter
and the inter-relationships between such. Again, aspects of essentialism are deeply
important in addressing “truth.”