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Russian Mathematics Education: Programs and Practices
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On Algebra Education in Russian Schools
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basic or advanced (“profile”) level. The students must make this choice
in accordance with the life goals they set for themselves at the moment.
The division of education into basic and advanced levels (which exists
in all subjects, not just in mathematics) makes it possible for the
students to concentrate their efforts on the more intensive study of
that specific range of subjects which will, in the future, be connected
with their professional activity or are simply more interesting to them.
Thus, if the main goal of studying mathematics at the basic level is
to facilitate the general cultural development of the students, then at
the advanced level, in addition to this goal, the study of mathematics
must provide the students with the possibility of entering those
departments of institutions of higher learning in which mathematics
is one of the main subjects and of continuing their professional
education there.
Precisely this difference in the aims of high school mathematics
education was at one time one of the main factors that determined
the differences in the content of mathematics education and in the
graduation requirements in mathematics that were set down by
the Standard. Precisely this difference determines the difference in
approaches to presenting material in mathematics textbooks in high
schools at the basic and advanced levels.
As in basic school, different series of textbooks are used for studying
mathematics at each educational level (basic or advanced) in high
school; all of these textbooks meet the Standard’s requirements, but
their methodological approaches vary. It should be noted that prior
to the official introduction of furcation at the high school stage
(established in 1998), mathematics in all schools (except for classes
with an advanced course of study in mathematics, which used their
own original programs) was officially studied on one level (in the
early 1990s, classes oriented toward the humanities also began to
appear). Since approximately 1.5% of students in Russia select an
advanced course in mathematics, and since such classes are usually
taught by authoritative and very highly qualified teachers who use
their own original curricula and unique methodologies, which cannot
be generalized and applied on a mass scale, this layer of Russian
mathematics education will not be addressed in this chapter.
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Russian Mathematics Education: Programs and Practices
The content of the contemporary basic course in mathematics
corresponds to the content of the general course that was previously
in use, with minor changes in the direction of reducing the amount of
educational material and simplifying the requirements for the level of
its assimilation. This makes it possible to employ all existing educational
toolkits in teaching this course.
We should point out that mathematics as presented in the basic
course, which is intended for the majority of Russian schoolchildren, is
conceived of as being just one element of general education. However,
although we have been teaching mathematics to all students at the
high school level for many decades, ever since secondary education
was made mandatory, no traditions of teaching this subject as part of
general education have yet taken root in Russia.
As for the advanced course in mathematics, one of the main objec-
tives that it is meant to address — to teach mathematics in accordance
with the modern conception of school mathematics education and,
at the same time, specifically, to provide students with the possibility
of entering a college — could not have been achieved using existing
textbooks, in our view, and required fundamentally new developments
in the field of educational literature.
To illustrate the contemporary state of mathematics teaching at
the basic and advanced levels, we will look at two educational-
methodological sequences. The first consists of the textbook for grades
10–11 by Kolmogorov et al. (2007), whose original version came out
in the 1970s, at the same time as the already-mentioned textbooks by
Vilenkin et al. and Makarychev et al., and traditionally considered their
continuation. Since that time, these textbooks have been substantially
revised. At present, they are the most widely used textbooks in Russian
schools.
The second series of textbooks, by Dorofeev, Kuznetsova, and
Sedova (2003, 2008), Dorofeev and Sedova (2007), and Dorofeev,
Sedova, and Troitskaya (2010), which was written with the partic-
ipation of some of the authors of this chapter, may be seen as a
development of the ideas contained in the textbooks by Dorofeev,
Sharygin et al. and Dorofeev, Suvorova et al. These are new textbooks
for students who wish to acquire a deeper education in mathematics.
