Page 426 - Cultural Studies of Science Education

33 “What Is Ours and What Is Not Ours?” 401

I am not generalising that this case represents an attribute of all mathematics
teacher educators who have been oriented according to your narrow foundation-
alism. But this encounter suggests that the non-sceptical posture embedded in
the foundation of mathematics education does not help mathematics teachers and
teacher educators go beyond the narrow structural boundary of mathematical
knowledge (Hersh 1997). Here, the notion of narrow structural boundary means the
unhelpful myth that mathematics is always structured in a singular, objective and
incorrigible way. How can you expect innovation if you educate teachers to be mute
followers? Thus, I argue that healthy scepticism helps mathematics teachers renew
their pedagogical praxis and knowledge about mathematics.
You may raise a question here: Which version of scepticism do I want to promote
in mathematics teacher education programs? In my mind, scepticism (or doubt) and
belief presuppose each other, for there is no scepticism or doubt where there is no
belief. Perhaps a healthy scepticism is an expression generated through dialectical
relationships between believing and being sceptical at the same time (Bell 2005).
7
With the help of dialectical thinking, I prefer to promote a “middle way” that
neither rejects foundationalism totally nor prevents prospective teachers from ques-
tioning the so-called indubitable foundation of mathematics education. How can
your logical and psychological foundations fit within my vision? As far as the logical
aspect (e.g., Kuroda 1958) of the foundation is concerned, prospective teachers
and teacher educators will be able to realise the limitations of conventional logics
(e.g., propositional, deductive and analytical) and the linear hierarchical structure
(of mathematics) embedded in mathematics education. And, there are possibili-
8
ties that your conventional logical structure of mathematics can be modified and
adapted together with emergent structures arising from knowledge systems embed-
ded in local cultural practices.
Dear Dr. Authority, it seems to me that another key element of your foundation
is behaviourism, which promotes a mechanical view of learning as a linear combi-
nation of stimulus and response. An immediate implication of this school of
thought in mathematics education is that learning is possible only through repeti-
tion, practice and drill (Hilgard and Bower 1977). Do you really believe that the
phenomenon of learning can be explained only this way? Here, I am hinting at yet
another possible “foundation” that promotes largely cognitive approaches, which
regard learning as an exclusively mind-centric activity (Shuell 1986). You may
think that I align myself exclusively with cognitivism. On the contrary, I hold the
view that these theoretical labels do not help much in conceiving the contingent,
contextual and emergent nature of the phenomenon of learning. Therefore, a
healthy scepticism helps raise questions about the adequacy of your and others’
foundations in capturing the experiential landscape of learning.

7 In eastern Wisdom Traditions, Middle Way has served as a perspective to articulate ontological
and epistemological spaces that allow us to conceive the relative nature of sometimes opposing
ideas (Nagarjuna et al., 1990).
8 Smitherman (2005) calls these logics ‘narrow analytics,’ which are subservient to reductionist
Newtonian science, which promotes dualism and narratives of stability.