Commentary on Theories of Mathematics Education

Appreciating Scientificity in Qualitative Research 389
Epistemology Identity
The assessment of the very nature of the phenomenon we have constructed involves
a contextualized observation of the state of the knowledge and its generic attributes.
From this approach, one might observe how the knowledge has been established. In
describing the continuum, which will have been constructed by the epistemologist,
the limits will be evident in the constructing process. As the qualitative scientist
reflects upon his/her actions in constructing this phenomenon, the very shape, form,
and appearance of the knowledge is constructed by the epistemologist. It is the very
nature of the epistemologist which gives rise to the episteme and so in this metaconstructionist
phenomenology the scientist must assess the very epistemological
identity of the self in order to describe the very nature of the object of knowledge
discovered.
Three types of knowledge are generally agreed upon philosophically:
1. knowledge-how,
2. knowledge-that, and
3. knowledge of.
Whilst (1) and (3) are fairly mundane in assessing (2) one must observe the dualistic
nature of such knowledge. Once again two types of knowledge-that are often
prescribed:
1. empirical and
2. apriori.
The former attains to un-inferred observation-statements by induction, whereas the
later is knowledge derived from its self-evident axiomatic bases. This paper has
alluded to this form of knowledge-discovery, but through self-evident axiomatic
bases the researcher is placed in a selfish environment of self-construction. It is especially
important for vigilance and rigor to be attended to in formulating methodological
constructs. It does appear evident, though, that many qualitative educational
researchers do attend to empirical epistemology, in some vane attempt to assimilate
quantitative rigor.
In summary, one must acknowledge what type of knowledge is being established,
how that is transferred and what is one’s epistemological identity. In acknowledging
one’s identity, the limits of one’s scientific discovery might be more readily
acknowledged.
Reflexivity
As a position of authority is established with respect to the knowledge conceived
and constructed, the very assumptions of the thesis established should be outlined
and assessed. An assessment of the fundamental assumptions and constructs of the
thesis should be assessed in a reflexive manner and this part of the discovery process