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4
On Various Forms of Distance Learning
In this section, we will begin to discuss forms of extracurricular work
that take place outside specific schools (although, of course, the role
of the teacher and the school in providing information about them to
the students and in offering subsequent support is very important).
The first activity of this kind that should probably be mentioned is
independent reading.
Above, we referred to many books published specifically for
schoolchildren interested in mathematics. Both in the USSR and,
later on, in Russia, numerous collections of difficult problems have
been published and republished, along with comparatively short and
accessible presentations of various mathematical theories. In particular,
we would single out books from the series “The Little Kvant Library,”
as well as the already-mentioned pamphlets from the series Popular
Lectures in Mathematics. Books with a more explicit and closer
connection with the school course in mathematics, which are intended
for an audience of many thousands or perhaps even many millions, have
been and continue to be published as well. Among them, we would
single out books published under the general title Supplemental Pages
for the Textbook.
Depman and Vilenkin’s book (1989 and other editions), addressed
to fifth and sixth graders, contains, for example, the following sections:
• How people learned to count
• The development of arithmetic and algebra
• From the science of numbers
• Mathematical games
• Mathematics and secret codes
• Stories about geometry
• Mathematics and the peoples of our homeland
• How measurements were made in antiquity, etc.
This book is, to be precise, not a textbook. Students can (and will
want to) read it at home on their own. It is written in a colloquial style
and contains many historical and entertaining facts, but also includes
a considerable number of problems and stories about various areas of
mathematics.
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Russian Mathematics Education: Programs and Practices
Supplemental Pages for the Algebra Textbook (Pichurin, 1999), a
book addressed to students in grades 7–9, is written in a somewhat drier
style, but has the same objective: to give an accessible and entertaining
account of topics which comparatively strong students could have
been told about in class, but which inevitably remain beyond the
bounds of the school course in mathematics. The text includes stories
about the evolution of algebra and several of its sections (for example,
Diophantine equations or continued fractions), and generally attempts
to identify key mathematical ideas and stages in the development
of mathematics (for example, a section entitled “Turning Point in
Mathematics” tells about Descartes’s contribution and the appearance
of the concept of variables).
Other books in the series were meant to accompany other parts of
the mathematics curriculum, such as, Supplemental Pages for the Geom-
etry Textbook (Semenov, 1999) and Supplemental Pages for the Mathe-
matics Textbook for grades 10–11 (Vilenkin et al., 1996). The purpose
of these and other books was to support independent reading and
self-education by students. Thus, Pichurin (1999) concluded his book
with a section entitled “Reading Is the Best Way to Learn,” in which
he listed various books that interested students could use to continue
their mathematical education.
It might be noted, however, that while the aforementioned book
by Pichurin was published in 1990 in an edition of 500,000 copies
(in Russia, the size of the edition is indicated in the book), in
1998 it was reissued in an edition of only 10,000 copies; the whole
system of book publishing had undergone a radical transformation.
Nonetheless, independent reading remains an extremely important way
for many thousands of students to become more closely acquainted
with mathematics. Moreover, the limited availability of printed books
is partly compensated for by the Internet; for example, the website of
the Moscow Center for Continuous Mathematical Education contains
quite a decent mathematics library.
Yet, no matter how significant independent reading may be, a stu-
dent often cannot get by without guidance from a teacher. Sometimes,
teachers can and want to offer such help, and that is all to the good; but
even in the absence of such support in school, students can acquire help
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