Commentary on Theories of Mathematics Education

Appreciating Scientificity in Qualitative Research 391
knowledge, a state of dynamic epistemology exists which then suffers the same circular
process of scientific discovery. The philosophy of epistemology is mainly to
attend only to the existence of knowledge, how it originated and its limits. The force
of knowledge; the motivating force; the dynamic that sets it up as ‘new’ knowledge
is epistemology and dynamic epistemology is a subset of epistemology but
is seen a necessary part of the scientific discovery process to establish a circular
link. In assessing the phenomenology of knowledge construction we must reflect on
the dynamic of our science in order to truly understand the nature of our scientific
discovery. The dynamic epistemology adheres to a Kuhnian philosophy of paradigmatic
revolutions, or paradigmatic shifts (Kuhn 1970) rather than static portrayals
of knowledge in terms of episteme (Foucault 1980). Objects of knowledge which
are a function of the self, society and the interaction of two—the psychology and
philosophy of a society—surely lead to a generating force, i.e., one which is motional,
and not static portrayals of a ‘new’ knowledge. Even if knowledge is devised
in schemes of knowledge and they are the microscopic of knowledge’s minutia, each
nut, screw, bolt or device in the ‘giant ontological machine’ has an effect and so is
‘dynamic.’
In attending to the third part of the three-fold doctrine I address the following:
• Is the discovery ‘dynamic’?
• What mechanism have I established to distribute ‘my’ knowledge?
• How is the thesis syn-thesised?
• What mechanism allowed this procedure?
• What is ‘new’ about it?
• Is the ‘new’ knowledge testable/utilizable?
• Does it have purpose, i.e., who is it useful for?
• What is the nature of the knowledge, i.e., again who wants it?
• Do ‘they’ find it useful?
• Who are ‘they’?
• How do I deliver it?
• Are there any holes in my argument?
• How are the ‘holes’ criticized?
• Does the ‘new’ knowledge lead to ‘advanced’ knowledge, i.e., dynamic epistemology?
It is the very sense of the ‘dynamic’ which gives rise to revolution and thus the circular
endeavor of scientific discovery that is established by the three-fold doctrine.
The process is illustrated below with.
One example of this process can be observed in the establishment of a mathematical
knowledge theory in education. Deborah Ball and Heather Hill defined Mathematical
Knowledge for Teaching (MKT) as not only that knowledge common to
practitioners in an educational setting but also the knowledge that allows teachers to
diagnose and remedy students’ errors, and how particular procedures work or help a
learning process. This theory was refined from iterative research to incorporate other
constructs such as Unpacking Pedagogical Content Knowledge (Hill et al. 2008a).
Recent work (Hill et al. 2008b) has pointed out that there is still little understood