Commentary on Theories of Mathematics Education

<strong>Commentary</strong> on Modalities of a Local Integration of Theories in Mathematics Education 557
A theoretical approach is based on a system of basic theoretical principles combined with
a methodology, hence, guiding and directing thinking and action. A theoretical perspective
is a filter for looking at the world based on theoretical principles, thus with consequences
for the construction of the subject and problem field in research (after Wedege 2009b, p.3)
In the paper, as a case I looked at Gellert (2008) who compares and combines two
sociological perspectives on mathematics classroom practice meaning, which he
termed “structuralist” and “interactionist” respectively—just like he is naming the
two integrated theories “semiotic” and “structuralist”—in order to emphasise the
theoretical grounds of the two perspectives. Gellert used the two terms “perspective”
and “approach” alternatively without any terminological clarification. However,
it seemed that his choice of terms was deliberate and that his usage matches
the distinction proposed above (Wedege 2009b). In this book, he does not use the
term “theoretical approach” and I suppose that “theory” is to be understood as “theoretical
perspective”.
Implicitness in Instruction and in Research
Gellert presents and discusses an example of local integration of two theories—
or theoretical perspectives—in the analysis of a piece of empirical data from a
5 th grade mathematics classroom in Germany. The clip comes from the very first
lesson after the summer holidays with a group of students in a new school with
a new teacher. The data is “generated” in a research project with one of the foci
being “the degree of explicitness in mathematics teaching practice and the consequences
of this teaching practice for the students’ learning” (p. 7). The term “generated”
used by Gellert, indicates that he sees the data as a product in the research
process and this epistemological viewpoint matches mine. The data does not fall
down from heaven. It is produced through a process of design and empirical investigations.
In any educational study, the data is a consequence of four interrelated
decisions in the design process: purpose (why), research questions (what), method
(how) and sampling strategy (who, what, where, when). Moreover, this part of the
research process is directed by a theoretical approach in the meaning of Radford
(2008).
In his discussion of the general issue of combining two theoretical perspectives,
Gellert (2008) used a piece of data—a short transcript of sixth-graders’ collaborative
problem solving. He states that “by selecting and focusing on this particular
piece of data I have already taken a structuralist theoretical perspective” because,
from this perspective, the passage is “a key incident of specification of inequality in
the classroom” (p. 223). In the present text, where this issue is integrating locally
two theoretical perspectives, there is silence about the theoretical approach generating
the presented data. But, this passage is a key incident of implicitness in the
teacher’s instructional practice and maybe selected from the structuralist perspective?