Commentary on Theories of Mathematics Education

534 H. Jungwirth
necessary step; not only with the use of a fresh corpus of data but with those in the
given study as well.
Whatever position may be adopted, empirically substantial concepts can be immediately
used for checks while empirically empty ones have to undergo the process
of theoretical elaboration first. For instance, in my case the idea that dealing with
mathematical tasks for the first time does not involve practical activities at a computer
could be checked directly and put aside already after the analysis of the
minimum-maximum problem episode. Thus, an inclusion of theories having empirical
substance is advantageous for synthesizing a grounded theory: The process
is tightened up. “Deductions that lead nowhere” (Glaser 1978, p. 40) that involve
empirically rich concepts can be perceived at a first glance, so to speak.
To summarize the considerations about compatibility: My study has revealed
three aspects of theories that provide certain favouring constellations for combining
theories. They contribute to the business of theory connection on different stages of
the process: Consistent paradigms promise a sound networking, through neighbouring
sites of phenomena a combination of theories will become feasible, and different
empirical loads make the very development of a combined grounded theory particularly
effective. Of course, the findings reflect the strategies and their use in my
research. It is evident, for instance, that the empirical load of theories will not be
relevant if synthesizing does not involve data analysis at all. Whether or not theories
can be considered as compatible is related to the intended kind of networking. In
my study criteria for synthesizing and co-ordinating matter, and provide a grid for
inspecting theories that will be used in connections on these levels. Moreover, not
only the kind of the strategy plays a role but also the actual understanding of the
relationship of theory and empirical work in research.
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