Commentary on Theories of Mathematics Education

386 S.J. Hegedus
In such a dilemma, though, one must still attend to what a world is. And in
attributing truths about one’s cognition in a learning environment to an observer, one
might not be able to describe what is part of a newly constructed phenomenon of
describing a naturalistic phenomenon. What is naturalistic is not always naturalistic
to the respondent. Hammersley (1989) highlights the paradox as:
[A] conflict between his realist account [Blumer] of the process of research in which the
nature of the world is discovered, and, as using, my terms, the phenomenalism of symbolic
interactionism, in which meanings are portrayed as constructions, not reflections of some
independent reality. (p. 194)
Hammersley (ibid.) goes onto to revoke the paradox slightly by offering the idea
that resolution can represent the same phenomenon in people in multiple, noncontradictory
fashions.
In summary, how can scientific inquiry be based upon a world which is our
dataset—whose very nature depends on us reflecting upon it—but at the same time
our very existence in it causes us to reply with a commonsensical response to the
very phenomena which one is required to assess objectively? We do appreciate that
the field of Naturalistic Inquiry does present some answers to this line of inquiry
(Lincoln and Guba 1985).
In seeking truth, we make accounts of what we observe and meanings are made
from counteractions of our accounts. Critical objections of our observations give
way to portrayals of the phenomenon that is under investigation. With an aspiration
for seeking not the independent reality of the phenomena observed, we attain
to observing the psychical content of the entity and attempt to attain meaning of
it whilst attempting to reject any understanding of the phenomena by sub-topical
issues invested in an environment surrounding the entity. As humane scientists, we
might find it difficult to observe and question within a faculty where a sub-faculty
of issues affect and lead to a consequential truth-base of our own understanding of
the original system in effect.
A meta-constructionist phenomenology might well attain to a doctrine in a sociological
aspect and by which a qualitative researcher has established certain truthvalues
distinguished by separate constructions of observational facts. Such constructions
are in themselves qualitative aspects of philosophical truth, which are not truth
in an ontological setting but are in a paradigmatic setting. Here, one regards a sociological
setting of the interaction of students and a teacher, a sufficient paradigmatic
setting to establish theory and reflective practice.
In doing so, we might regard a reflective methodology as a superior mechanism
to observe the preceding constructs of philosophical delicacies. It is the very sense
of observing a sophisticated mechanism of interaction, which can only be obtained
by human neuronal-chaotic interactions giving rise to what quantitative mechanisms
would find combinatorially inept. A constructionist phenomenology is not suitable
in itself; it is a meta-constructionist phenomenology which desires a reflective element,
psychologically speaking, to the constructionist aspect of absolving some
physical interpretation of a psycho-social formulation.
In summary, no ontological, epistemological or methodological aspect of qualitative
research should be envisaged as a pedantry aspect of scientific discovery.