Commentary on Theories of Mathematics Education

Appreciating Scientificity in Qualitative Research 385
what is the nature of our inquiry; what form does it take? An ontological prerequisite
might well be necessary if we are to analyze the very necessity of what
we are attempting to discover in our qualitative philosophy.
The generation of truth for humans is a sordid and political philosophy. We might
seem more just to observe and synthesize what is possible whilst addressing the
polemic of the naturalistic method. In founding our investigation of the world on
assumptions about how knowledge is possible, we lock ourselves into an epistemological
formula as opposed to making algebraic investigations of the assumptions
about the nature of the world that we seek to understand. With such an approach, I
view that epistemology is purely a sub-set of ontology.
And so, in addressing a truth statement rather than a statement that denies truth
(meta-philosophy), one might seek to adhere to a scheme that analyses the very nature
of the sociological interactionism, which one observes. Interactional analysis
might well have its place, but an appreciation merely of an interactional process—
which is transcribed in a qualitative form—has its own ontological attributes which
we intend to make assumptions about its being, more so than question why it is in
existence. In order to make the subtle move of accepting the assumptions of scientific
discovery—e.g., why we see it necessary to religiously believe that an interaction
between a pedagogue and a student (or researcher and a respondent) is deemed
necessary and an interactive dialogue (to varying degrees of dialogue) might be
evident—it is necessary to accept why the nature of that incident is in effect, ontologically,
and then describe the epistemological facts inherent in these situations.
Research that focuses on classroom dynamics and flow of argumentation (Hegedus
and Penuel 2008; Toulmin 1958) or semiotics (Radford et al. 2008) are offering
theoretical and methodological perspectives to unpack the issues of interaction in
an educational setting. We note that we are not even addressing the complexity of
including more digital and transparent settings such as social networks.
In summary, it seems that the truth of the matter is based upon what we see, visibly
hear and record. The truth though extends to a degeneration of knowledge of
that event, in effect, reducing what that person had said into incomprehensible statements
about what the individual’s cognizing system might well have constructed. It
becomes a meta-philosophy where one achieves to return to the cognizing subject
and cause that subject to react to what he/she might well have constructed (Schoenfeld
1992). A meta-psychology is only evident when the subject can attain to reacting
to such philosophical occurrences (cf. Hegedus 1998).
The matter of one’s epistemological battle with oneself and what one is establishing
as a truth in society depends largely on what society regards as truth. Often
people view the world qualitatively, which includes society, in different ways. It
is this phenomenon, which leads to the ontological paradox (McPhail and Rexroat
1979). Hammersley (1989) summarises this by questioning where Social Science
researchers regard his common-sense interpretation of the social world as an imputation,
rather than reflecting on the nature of the world—i.e., in attending in an
epistemological fashion to a knowledgeable acclamation of the world one might
need to associate one’s synthesis as a reflection of a world-reality—an ontological
variation of some sociologically established identity.