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approach would be to think about the various concrete ideas that they
contain, and about the ways in which these ideas might be applied
and developed under different conditions (or, conversely, about the
ways in which certain approaches popular in the West have become
transformed in Russia — the whole panoply of ideas pertaining to
“humanitarization” and “humanization,” to give one example). This,
of course, cannot be done within the scope of a single chapter.
Conversely, one may give further thought not to individual studies,
but to the organization of scientific work as a whole, explicitly or
implicitly comparing it with how matters stand in other countries.
The observation that immediately comes to mind is that increasing
centralization, control, the role of so-called accreditation, and so on,
which many see as the best means of improving quality, in reality cannot
guarantee high quality. Among the studies examined above, along
with interesting and substantive works, we encountered a considerable
number of patently weak works, which nonetheless have successfully
passed through the multistage system of centralized control and
evaluation.
Very weak (just like very strong) dissertations can probably be found
without difficulty in any country. But both the strong and the weak
aspects of dissertations to some extent exhibit distinctive features in
different countries. The arguments demonstrating the effectiveness of
some chosen approach, which were used in a number of the works
discussed above, will not always appear convincing, for example to a
Western reader; the reader might judge the system of argumentation
to be biased and not objective. Reliance on theory, which we would
describe as a positive feature in general, can also be excessive — the
lists of thinkers who have influenced an author in the writing of various
methodological recommendations often include major philosophers or
mathematicians whose work is rather distant from the subject examined
in these recommendations. The tendency to generalize and to engage
in general, abstract reasoning, while commendable in principle, is often
excessive; at times, the writing style begs to be parodied. Instead
of saying that there are, for example, three quantitative attributes,
some authors would invent something grandiose and convoluted,
such as the element of a ternary relation defined over the set of real
numbers.
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Usually, a very large amount of work goes into both Russian
Doctor’s dissertations and Candidate’s dissertations. In response to
the question that students love to ask about how many pages they have
to write, one may say that the number of pages that has to be written
to obtain a Doctor’s (and even a Candidate’s) degree is indeed great.
This refers not only to the dissertation itself but also to published
papers which are required, and to methodological and educational
materials that implement the author’s approach. Here we come to what
we would consider the main merit of Russian scientific works: they are
works that, at least in terms of their subject matter, aim to improve
teaching in schools.
Kilpatrick (2010), talking about a past period, has noted: “Much
Soviet research in mathematics education took place in schools rather
than laboratories, and it dealt with concepts from the school curriculum
rather than artificial constructs — features that were especially attractive
to U.S. researchers” (p. 361). While the situation in the West has some-
what changed in subsequent years, it would not be an exaggeration
to say that in the West work that is specifically aimed at improving
how children are taught — work on textbooks and programs — is
largely (even if with important exceptions) a commercial, rather than
a scientific, concern. As for scientific work, it is often focused on far
narrower problems, which in our view pertain, strictly speaking, to
psychology, not to mathematics education. The loss here is twofold:
commercial textbooks lack deep methodological ideas (or sometimes
any methodological ideas), while scientific works lack a sense of reality
and practical applicability.
It is by no means necessary to agree with all of the methodological
approaches developed by the authors of the works cited above. What
is important, however, is that these authors feel the need for a
connection — even if sometimes a purely nominal one — between
their research and real schools and real colleges (however obscured
this connection might be by complicated terminology). The sharp rise
in the number of doctoral dissertations defended in recent decades
was probably not accompanied by an improvement in their quality:
the inflation in the significance of academic degrees that can be seen
everywhere in the world is fully in force in Russia. Yet the orientation
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toward schools, and toward the teaching of mathematics in schools,
endures. This fact sustains our interest in the development of Russian
research on mathematics education.
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